molecules Article
iPPBS-Opt: A Sequence-Based Ensemble Classifier for Identifying Protein-Protein Binding Sites by Optimizing Imbalanced Training Datasets Jianhua Jia 1,2, *, Zi Liu 1 , Xuan Xiao 1,2, *, Bingxiang Liu 1 and Kuo-Chen Chou 2,3 Received: 18 November 2015 ; Accepted: 7 January 2016 ; Published: 19 January 2016 Academic Editor: Derek J. McPhee 1 2 3
*
Computer Department, Jing-De-Zhen Ceramic Institute, Jing-De-Zhen 333403, China;
[email protected] (Z.L.);
[email protected] (B.L.) Gordon Life Science Institute, Boston, MA 02478, USA;
[email protected] Center of Excellence in Genomic Medicine Research (CEGMR), King Abdulaziz University, Jeddah 21589, Saudi Arabia Correspondence:
[email protected] (J.J.);
[email protected] (X.X.); Tel.: +86-1397-9866-529 (J.J.); +86-1387-9809-729 (X.X.)
Abstract: Knowledge of protein-protein interactions and their binding sites is indispensable for in-depth understanding of the networks in living cells. With the avalanche of protein sequences generated in the postgenomic age, it is critical to develop computational methods for identifying in a timely fashion the protein-protein binding sites (PPBSs) based on the sequence information alone because the information obtained by this way can be used for both biomedical research and drug development. To address such a challenge, we have proposed a new predictor, called iPPBS-Opt, in which we have used: (1) the K-Nearest Neighbors Cleaning (KNNC) and Inserting Hypothetical Training Samples (IHTS) treatments to optimize the training dataset; (2) the ensemble voting approach to select the most relevant features; and (3) the stationary wavelet transform to formulate the statistical samples. Cross-validation tests by targeting the experiment-confirmed results have demonstrated that the new predictor is very promising, implying that the aforementioned practices are indeed very effective. Particularly, the approach of using the wavelets to express protein/peptide sequences might be the key in grasping the problem’s essence, fully consistent with the findings that many important biological functions of proteins can be elucidated with their low-frequency internal motions. To maximize the convenience of most experimental scientists, we have provided a step-by-step guide on how to use the predictor’s web server (http://www.jci-bioinfo.cn/iPPBS-Opt) to get the desired results without the need to go through the complicated mathematical equations involved. Keywords: protein-protein binding sites; physicochemical property; stationary wavelet transform; PseAAC; Optimize training dataset; KNNC; IHTS; target cross-validation
1. Introduction Individual proteins rarely function alone. Most proteins whose functions are essential to life are associated with protein-protein interactions [1]. Actually, these kinds of interactions affect the biological processes in a living cell. To really understand protein-protein interactions, however, it is indispensable to acquire the information of protein-protein binding site (PPBS). Despite many studies on the binding site of a protein or DNA with its ligand (small molecule) have been made [2–8], relatively much less studies have been conducted on PPBS, particularly based on the sequence information alone. It is both time-consuming and expensive to determine PPBS purely based on biochemical experiments. Facing the enormous number of protein sequences generated in the postgenomic era, it is highly
Molecules 2016, 21, 95; doi:10.3390/molecules21010095
www.mdpi.com/journal/molecules
Molecules 2016, 21, 95
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desired to develop computational methods to identify PPBSs for uncharacterized proteins so that they can be timely used for both basic research and drug development, such as conducting mutagenesis studies [9] and prioritize drug targets. Given a protein sequence, how can one identify which of its constituent amino acid residues are located in the binding sites? Actually, considerable efforts were made to address this problem [10,11]. Although the aforementioned works each have their own merits and did play a role in stimulating the development of this area, further work is needed due to the following shortcomings: (1) The datasets used by these authors to train their prediction methods were highly imbalanced or with a strong bias; i.e., the number of non-PPBS samples was significantly larger than that of PPBS samples; (2) None of their prediction methods has a publicly accessible web server, and hence their practical application value is quite limited, particularly for the majority of experimental scientists. The present study is initiated in an attempt to develop a new PPBS predictor by addressing the aforementioned shortcomings. According to the Chou’s 5-step rule [12] and the demonstrations in a series of recent publications [13–20], to establish a really useful sequence-based statistical predictor for a biological system, we should make the following five aspects crystal clear: (1) how to construct or select a valid benchmark dataset to train and test the predictor; (2) how to formulate the biological sequence samples with an effective mathematical expression that can truly reflect their intrinsic correlation with the target to be predicted; (3) how to introduce or develop a powerful algorithm (or engine) to operate the prediction; (4) how to properly perform cross-validation tests to objectively evaluate its anticipated accuracy; (5) how to establish a user-friendly web-server that is accessible to the public. Below, we are to address the five procedures one-by-one. 2. Materials and Methods 2.1. Benchmark Dataset Two benchmark datasets were used for the current study. One is the “surface-residue” dataset and the other is “all-residue” dataset, as described below. The protein-protein interfaces are usually formed by those residues, which are exposed to the solvent after the two counterparts are separated from each other [21]. Given a protein sample with L residues as expressed by: P “ R1 R2 R3 R4 R5 R6 R7 ¨ ¨ ¨ R L
(1)
where R1 represents the 1st amino acid residue of the protein P, R2 the 2nd residue, and so forth. The residue Ri pi “ 1, 2, ¨ ¨ ¨ , Lq is deemed as a surface residue if it satisfies the following condition: φ pRi q “
ASApRi |Pq ą 25% ASA pRi q
(2)
where ASA(Ri |P) is the accessible surface area of Ri when it is a part of protein P, ASA(Ri ) is the accessible surface area of the free Ri that is actually its maximal accessible surface area as given in Table 1 [22], and φ pRi q is the ratio of the two. Table 1. Maximum accessible surface area (ASA) of different amino acids a .
a
AA
A
B
C
D
E
F
G
H
I
K
L
M
MaxASA AA MaxASA
106 N 157
160 P 136
135 Q 198
163 R 248
194 S 130
197 T 142
84 V 142
184 W 227
169 X 180
205 Y 222
164 Z 196
188
Amino acids are represented by their one-letter codes. Here, B stands for D or N; Z for E or Q, and X for an undetermined amino acid.
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In for Section small 3, target we present detection. the In experimental Section 3, we results. present Section the experimental 4 is the conclusion results. Section 4 is the easily easily mixed mixed easily up up with mixed with the up the background with background the background clutters clutters in size in clutters size and and in easily size easily overlapped and overlapped easily overlapped by by vegetation, vegetation, by vegetation, roads, roads, rivers, rivers road consisting of optical retina andhave visual which is nonuniform and nonlin Due to[9], theresulting layers structure, the algorithm computational complexity becomes the prime concern. bridgesbridges [9], bridges resulting [9], resulting atwo huge afalse huge a For huge rate false false in rate traditional rate innumerous traditional insystem, traditional algorithm. algorithm. algorithm. 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Although numerous methods have been[9], proposed, of false themrate may certain circumstances ground-sky background [8], which inmany the helicopter view. In in this situation, targets are where e.g., P represents “a member in the theory.isincommon e.g., ground-sky background [8], of” which is set common the helicopter view. In this situation, targets are In order to design an appropriate method, a small target detecti e.g., background [8], which is common theeasily helicopter view. by In this situation, targets are easilyground-sky mixed up with the background clutters in sizeinand overlapped vegetation, roads, rivers easily mixed up with the background cluttersvisual in sizesystem and easily overlapped by vegetation, roads, rivers, beenoverlapped designed inbythis paper. HVS is a rivers kind o easily up with athe background in (HVS) sizealgorithm. andhas easily vegetation, roads, bridgesmixed [9], resulting huge false rateclutters in traditional bridges [9], resulting a huge false rate in traditional algorithm. consisting ofaoptical system, retina andmethod visual pathways, is non bridges [9], resulting huge false rate in traditional algorithm. In order to designaan appropriate method, small target detection inspired bywhich the human In order to design an appropriate method,this a small target detection method inspired by the human paper asisfollows. Section 2, weprocessing describe fra In order to (HVS) designhas an been appropriate method, aorganized smallHVS target method inspired by the the human visual system designed in thisis paper. adetection kind ofInlayered image system visual system (HVS) has been designed in thisfor paper. HVS is a kind of layered image processing system target detection. Section 3, we present the experimental visual system (HVS) system, has beenretina designed in this paper. HVS is In a kind of layered image processing consisting of optical andsmall visual pathways, which is nonuniform and nonlinear. Thesystem rest o consisting of optical system, retina and visualof pathways, which is nonuniform and nonlinear. The rest of this article. consisting of optical system, retina and visual pathways, which is nonuniform and nonlinear. The rest o this paper is organized as follows. In Section 2, we describe the framework of the proposed algorithm this paper is organized as follows. In Section 2, we describe the framework of the proposed algorithm this papertarget is organized as follows. In3,Section 2, wethe describe the framework of the proposed algorithm for small detection. In Section we present experimental results. Section 4 is the conclusion for small target detection. In Section 3, we present the experimental results. Section 4System is the conclusion 2. Algorithm Based on Human Visual for small target detection. In Section 3, we present the experimental results. Section 4 is the conclusion of this article. of this article. of this article. Figure 1. A schematic drawing to show how to Framework use the extended chain of Equation (7) to define the 2.1. of the Proposed Two Stage Algorithm—A Brief Desc 2. Algorithm Based on (6) Human Visual System working segments of Equation for those sites when their sequence positions in the protein are less 2. Algorithm Based on Human Visual System 2. Algorithm on Human Visual System than ξ or greater LBased ´ ξ , where the left dummy segment stands for the mirror image of R1 R2 ¨ ¨ ¨ Rξ at HVS divides the sceneatinto small patches and select important in N-terminus and the right dummy segment for that of R theDescription C-terminus. L´ξ`1 ¨ ¨ ¨ R L´1 R L 2.1. Framework of the Proposed Two Stage Algorithm—A Brief 2.1. Framework of the Proposed Two Stage Algorithm—A Brief Description selection mechanism to make it easy to understand and analyze. O 2.1. Framework of the Proposed Two Stage Algorithm—A Brief Description 2.3. Using Pseudo Amino Acid Composition to Represent Peptide Chains vision processing, it facilitates subsequent pro of low-level artificial HVS divides the scene into small patches and select important information through visual attention HVS divides the scene into small patches cost, and select important information in through visual attention Based on which is a keyand consideration real-time applications. One of the most challenging problems in computational biology today information is effectively HVS divides the scene into small patches and select important through visual attention selection mechanism to make it easy to understand analyze. Onhow thetoother hand, as a componen selection mechanism to make it easy to understand and analyze. On the other hand, as a component formulate the sequence of a biological sample (such as protein/peptide, and DNA/RNA) with a framework consisting of two procedures stages inspired by HVS as follows (S selection mechanism to make it easy to itunderstand and analyze. On the other hand, ascomputationa a componen of low-level artificial vision processing, facilitates subsequent by reducing a discreteartificial model orvision a vectorprocessing, that can considerably keepsubsequent its sequenceprocedures order information or capture its key of low-level it facilitates by reducing computational a saliency map(SM) is obtained and most salient computationa region is pick of low-level vision (1) processing, it facilitates subsequent procedures by reducing cost, which isartificial a key consideration in real-time applications. Based on thethe we propose reasons are as follows: If using the sequential model, i.e., the model inabove whichknowledge, all the cost, features. which isThe a key consideration in real-time applications. Based on the above knowledge, we propose In real-time detection stage, a support vector machines (SVM) classifier isstage use cost, isconsisting a key consideration in applications. Based on the above knowledge, we propose samples are which represented by their original sequences, it is hardly able train a machine that can cover a framework of two stages inspired by HVS astofollows (See Figure 1). In predetection a framework consisting of two stages inspired by HVS as follows (See Figure 1). In predetection stage, all theapossible casesconsisting concerned,of as two elaborated (2)by AllHVS the existing computational stages inspired as follows (See Figure 1). In predetection stage a framework saliency map(SM) is obtained and in the[36]; most salient region is picked up toalgorithms, improve detection speed a saliency is obtained and correlation-angle the most salientapproach region is picked up todiscriminant improve detection such asmap(SM) optimization approach [37], [38], covariance (CD) [39],speed. a saliency is obtained and the most(SVM) salientclassifier region isispicked improve detection speed detectionmap(SM) stage, a support vector machines used toup gettothe target quickly. neuralIn network K-nearest (KNN) [41], OET-KNN [42], SLLE random In detection stage, a [40], support vectorneighbor machines (SVM) classifier is used to getalgorithm the target[43], quickly. detection stage, a neighbor support vector machines (SVM) classifier is used get the target forest In [44], Fuzzy K-nearest [45], and ML-KNN algorithm [46], can only to handle vector butquickly.
not sequence samples. However, a vector defined in a discrete model may completely lose the sequence-order information as elaborated in [47,48]. To cope with such a dilemma, the approach of pseudo amino acid composition [36,49] Figure 1. The proposed framework inspired or Chou’s PseAAC [50,51] was proposed. Ever since it was introduced in 2001 [36], the concept of PseAAC has been penetrating into nearly all the areas of computational biology (see, e.g., [52–56] as Due the two layers algorithm computational comp well as a long list of references cited in [48,57] and a to recent review [58]).structure, Itinspired has alsothe been selected as a Figure 1. The proposed framework by HVS. Figure 1. The proposed framework inspired by HVS. special topic for a special issue onFigure “drug development and biomedicine” [59]. Recently, the concept simplicity and highinspired processing speed, saliency detection me 1.For Thethe proposed framework by HVS. of PseAAC was further extended to represent the feature vectors of DNA and nucleotides [60–64]. Due to the two layers structure, the used, algorithm becomes the prime concern Because itslayers being widely and threecomputational types of open complexity access soft-ware, called Due to the of two structure, theincreasingly algorithm computational complexity becomes the prime concern. Due to the two layers structure, the algorithm computational complexity becomes the concern “PseAAC-Builder” [65], “propy” [50],processing and “PseAAC-General” [57], detection were established: theinformer two prime For the simplicity and high speed, saliency methods the frequency domain are For the simplicity and high processing speed, saliency detection methods in the frequency domain are are forFor generating variousand modes of processing Chou’s special PseAAC; while the 3rd one for those the simplicity high speed, saliency detection methods in of theChou’s frequency domain are general PseAAC. According to [12], PseAAC can be generally formulated as: P “ rΨ1 Ψ2 ¨ ¨ ¨ Ψu ¨ ¨ ¨ ΨΩ sT
(9)
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where T is the transpose operator, while Ω an integer to reflect the vector’s dimension. The value of Ω as well as the components Ψu “ pu “ 1, 2, ¨ ¨ ¨ , Ωq in Equation (9) will depend on how to extract the desired information from a peptide sequence. Below, we are to describe how to extract the useful information from the aforementioned benchmark datasets (cf. Equations (4) and (5)) to define the working protein segments via Equation (9). For the convenience of formulation below, we convert the p2ξ ` 1q-tuple peptide in Equation (6) to: Pξ “ R1 R2 R3 R4 R5 R6 R7 ¨ ¨ ¨ Rp2ξ`1q
(10)
2.3.1. Physicochemical Properties Different types of amino acid in the above equation may have different physicochemical properties. In this study, we considered the following seven physicochemical properties: (1) hydrophobicity [66] or Φp1q ; (2) hydrophicility [67] or Φp2q ; (3) side-chain volume [68] or Φp3q ; (4) polarity [69] or Φp4q ; (5) polarizability [70] or Φp5q ; (6) solvent-accessible surface area (SASA) [71] or Φp6q ; and (7) side-chain net charge index (NCI) [72] or Φp7q . Their numerical values are given in Table 2. Table 2. The original values of the seven physicochemical properties for each amino acid. Physicochemical Property (cf. Equation (11)) a Amino Acid Code
A C D E F G H I K L M N P Q R S T V W Y
Φp1q
Φp2q
Φp3q
Φp4q
Φp5q
Φp6q
Φp7q
H1
H2
V
P1
P2
SASA
NCI
0.62 0.29 ´0.9 ´0.74 1.19 0.48 ´0.4 1.38 ´1.5 1.06 0.64 ´0.78 0.12 ´0.85 ´2.53 ´0.18 ´0.05 1.08 0.81 0.26
´0.5 ´1 3 3 ´2.5 0 ´0.5 ´1.8 3 ´1.8 ´1.3 2 0 0.2 3 0.3 ´0.4 ´1.5 ´3.4 ´2.3
27.5 44.6 40 62 115.5 0 79 93.5 100 93.5 94.1 58.7 41.9 80.7 105 29.3 51.3 71.5 145.5 117.3
8.1 5.5 13 12.3 5.2 9 10.4 5.2 11.3 4.9 5.7 11.6 8 10.5 10.5 9.2 8.6 5.9 5.4 6.2
0.046 0.128 0.105 0.151 0.29 0 0.23 0.186 0.219 0.186 0.221 0.134 0.131 0.18 0.291 0.062 0.108 0.14 0.409 0.298
1.181 1.461 1.587 1.862 2.228 0.881 2.025 1.81 2.258 1.931 2.034 1.655 1.468 1.932 2.56 1.298 1.525 1.645 2.663 2.368
0.007187 ´0.03661 ´0.02382 0.006802 0.037552 0.179052 ´0.01069 0.021631 0.017708 0.051672 0.002683 0.005392 0.239531 0.049211 0.043587 0.004627 0.003352 0.057004 0.037977 0.023599
a
H1, hydrophobicity; H2, hydrophilicity; V, volume of side chains; P1, polarity; P2, polarizability; SASA, solvent accessible surface area; NCI, net charge index of side chains.
Thus, the peptide segment Pξ of Equation (10) can be encoded into seven different numerical series, as formulated by: $ p1q p1q p1q p1q p1q p1q p1q p1q ’ Φ1 Φ2 Φ3 Φ4 Φ5 Φ6 Φ7 ¨ ¨ ¨ Φ2ξ`1 ’ ’ ’ p2q p2q p2q p2q p2q p2q p2q p2q ’ ’ Φ1 Φ2 Φ3 Φ4 Φ5 Φ6 Φ7 ¨ ¨ ¨ Φ2ξ`1 ’ ’ ’ ’ p3q p3q p3q p3q p3q p3q p3q p3q ’ ’ & Φ1 Φ2 Φ3 Φ4 Φ5 Φ6 Φ7 ¨ ¨ ¨ Φ2ξ`1 p4q p4q p4q p4q p4q p4q p4q p4q Pξ “ Φ1 Φ2 Φ3 Φ4 Φ5 Φ6 Φ7 ¨ ¨ ¨ Φ2ξ`1 ’ ’ p5q p5q p5q p5q p5q p5q p5q p5q ’ ’ Φ1 Φ2 Φ3 Φ4 Φ5 Φ6 Φ7 ¨ ¨ ¨ Φ2ξ`1 ’ ’ ’ p6q p6q p6q p6q p6q p6q p6q p 6q ’ ’ Φ1 Φ2 Φ3 Φ4 Φ5 Φ6 Φ7 ¨ ¨ ¨ Φ2ξ`1 ’ ’ ’ % p7q p7q p7q p7q p7q p7q p7q p 7q Φ1 Φ2 Φ3 Φ4 Φ5 Φ6 Φ7 ¨ ¨ ¨ Φ2ξ`1
(11)
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p1q
p2q
where Φ1 is the hydrophobicity value of R1 in Equation (10), Φ2 the hydrophilicity value of R2 , and so forth. Note that before substituting the physicochemical values of Table 2 into Equation (10), they all are subjected to the following standard conversion: pξq Φi
@ ϕD Φϕ i ´ Φi pϕ “ 1, 2, ¨ ¨ ¨ , 7; i “ 1, 2, ¨ ¨ ¨ , 2ξ ` 1q ð SDpΦϕ i q
(12)
where the symbol x y means taking the average for the quantity therein over the 20 amino acid types, and SD means the corresponding standard deviation. The converted values via Equation (12) will have zero mean value over the 20 amino acid types, and will remain unchanged if they go through the same standard conversion procedure again. 2.3.2. Stationary Wavelet Transform Approach The low-frequency internal motion is a very important feature of biomacromolecules (see, e.g., [73–75]. Many marvelous biological functions in proteins and DNA and their profound dynamic mechanisms, such as switch between active and inactive states [76,77], cooperative effects [78], allosteric transition [79–81], intercalation of drugs into DNA [82], and assembly of microtubules [83], can be revealed by studying their low-frequency internal motions as summarized in a comprehensive review [84]. Low frequency Fourier spectrum was also used by Liu et al. [85] to develop a sequence-based method for predicting membrane protein types. In view of this, it would be intriguing to introduce the stationary wavelet transform into the current study. The stationary wavelet transform (SWT) [86] is a wavelet transform algorithm designed to overcome the lack of shift-invariance of the discrete wavelet transform (DWT) [87]. Shift-invariance is achieved by removing the downsamplers and upsamplers in the DWT and upsampling (insert zero) the filter coefficients by a factor of 2 j´1 in the j-th level of the algorithm. The SWT is an inherently redundant scheme as the output of each level of SWT contains the same number of samples as the input-so for a decomposition of N levels there is a redundancy of N in the wavelet coefficients. Shown in Figure 2 is the block diagram depicting the digital implementation of SWT. As we can see from the figure, the input peptide segment is decomposed recursively in the low-frequency part. The concrete procedure of using the SWT to denote the p2ξ ` 1q-tuple peptides is as follows. For each of the p2ξ ` 1q-tuple peptides generated by sliding the scaled windowr´ξ, `ξs along the protein chain concerned, the SWT was used to decompose it based on the amino acid values encoded by the seven physicochemical properties as given in Equation (11). Daubechies of number 1 (Db1) wavelet was selected because its wavelet possesses a lower vanish moment and easily generates non-zero coefficients for the ensemble learning framework that will be introduced later. Preliminary tests indicated that, when ξ “ 7, i.e., the working segments are 15-tuple peptides, the outcomes thus obtained were most promising. Accordingly, we only consider the case of ξ “ 7 hereafter.
Figure 2. A schematic drawing to illustrate the procedure of multi-level SWT (stationary wavelets transform). See Equations (10)–(12) as well as the relevant text for further explanation.
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Using the SWT approach, we have generated five sub-bands (Figure 2), each of which has four coefficients: (1) αi , the maximum of the wavelet coefficients in the sub-band i p1, 2, ¨ ¨ ¨ 5q; (2) βi , the corresponding mean of the wavelet coefficients; (3) γi , the corresponding minimum of the wavelet Algorithms Algorithms 2015, xx 2015, xx Algorithms Algorithms 2015, 2015, xx xx 2 coefficients; (4) δi , the corresponding standard deviation of the wavelet coefficients. Therefore, for Algorithms Algorithms 2015, 2015, xx xx 2 2 each working segment, we can get a feature vector that contains Ω “ 5 ˆ 4 “ 20 components by using each of the seven properties ofsimple Equation (11). In algorithm other we have seven different clutters. clutters. In recent In years, recent ayears, series aof series clutters. simple In of recent and In recent years, fastand algorithm years, afast series a series based of words, simple of on based simple fourier and on fast and fourier transform algorithm fast algorithm was based proposed, was based on2 fourier propose on fot lgorithms 2015, Algorithms xx 2015, Algorithms xxphysicochemical 2015, xxclutters. 2 transform modes of PseAAC as given below: clutters. clutters. In recent In recent years, years, a series a series of simple of simple and fast andalgorithm fast algorithm based based on fourier on fourier transform transform was proposed, was proposed,
lgorithms 2015, Algorithms xx assuch 2015, Algorithms 2015,residual(SR) xx such 2of fourier 2 such spectral asxxspectral residual(SR) [5], as phase such spectral [5],as spectrum phase spectral residual(SR) spectrum ofresidual(SR) fourier of[5], fourier transform(PFT) phase [5],transform(PFT) phase spectrum spectrum [6], of hypercomplex fourier [6], hypercomplex transform(PFT) transform(PF fourier fouri [6 ” [5], phase ıTfourier such as such spectral as spectral residual(SR) residual(SR) [5], phase spectrum spectrum of fourier of transform(PFT) transform(PFT) [6], hypercomplex [6], hypercomplex fourier fourier pWith ktransform(HFT) q pkqregards pksmall q pk[7]. q pkq regards transform(HFT) With [7]. transform(HFT) target small With target With detection, frequency regards small target domain target detection, method detection, method istransform frequency quite isdifferent frequency quite domain differe dom m pk “ 1,to2, ¨frequency ¨ ¨ to ,domain 7q (13) Ppkrecent Ψregards Ψ2simple Ψ ¨ ¨ ¨to Ψ ¨algorithm ¨ ¨detection, Ψ[7]. lutters. In recent clutters. years, Intransform(HFT) arecent series clutters. years, of[7]. simple In aq “ series and years, fast algorithm ato series of fast based on and fast based algorithm transform onsmall fourier based was transform proposed, on fourier was proposed, was propo usimple 3 and 20fourier 1 of transform(HFT) transform(HFT) [7]. With [7]. regards WithItfrom regards to small toairspace target small target detection, detection, frequency domain domain method method isdefines quite isthe different quite different from other from methods. other methods. transforms transforms other the from methods. other the airspace methods. information It information Itfrequency transforms to the the frequency to airspace the the frequency airspace information domain, information domain, to defines significant to frequency the significa frequen dom lutters. In recent clutters. years, recent aclutters. series years, of In simple recent aItseries and years, offast simple aofalgorithm series and of fast simple based algorithm and ontransforms fourier fast based algorithm on fourier based was transform on proposed, fourier was transform proposed, was propose uch as spectral such residual(SR) as In spectral such [5], residual(SR) as phase spectral spectrum residual(SR) [5], phase fourier spectrum [5], transform(PFT) phase of fourier spectrum transform(PFT) [6], oftransform fourier hypercomplex transform(PFT) [6], hypercomplex fourier [6], hypercomplex fourier fou where: from other from methods. other methods. It transforms It transforms the airspace the airspace information information to the to frequency the frequency domain, domain, defines defines significant significant $ target and target tests and in tests the frequency in the target frequency domain. target and tests domain. and While, in tests the While, spectral in frequency the spectral frequency residual domain. residual (SR) domain. While, approach (SR) While, spectral approach does spectral residual not does rely residual not (SR) on rely the approa (SR) on th a uch as spectral such residual(SR) as With spectral such residual(SR) [5], as spectral phase spectrum residual(SR) [5], of fourier spectrum [5],ptarget transform(PFT) of spectrum fourier transform(PFT) of[6], fourier hypercomplex transform(PFT) [6],method hypercomplex fourier hypercomplex fourier kqphase ansform(HFT) transform(HFT) [7]. regards transform(HFT) [7]. to With small regards target [7].phase With todetection, small regards frequency towhen detection, small domain frequency domain is frequency quite different domain is[6], quite method different is quite fouri diffe ’ αµ 1 target ď µresidual ď detection, 5 method ’ target target and tests and in tests the in frequency the frequency domain. domain. While, While, spectral spectral residual (SR) approach (SR) approach does not does rely not on rely the on the ’ parameters. parameters. It calculates calculates the difference parameters. the parameters. difference between calculates between Itthe calculates original the the difference original signal thefrequency difference and signal between smooth and between the adifferent smooth one original the inquite the original one signal log in the amplitude signal and loga amplitud smooth and a sm ’ pkqItto ansform(HFT) transform(HFT) [7]. With transform(HFT) regards [7]. 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It parameters. calculates the Itparameters. difference calculates the between It calculates difference the original the between difference signal the original between and11a ď smooth signal original one andin a smooth the signal log and amplitude oneainsmooth the logone amplitude in the log amplit δµ´15 when µthe ď 20 small small targets targets from the from reconstruction the reconstruction that is that calculated is calculated only by only the by phase the phase spectrum spectrum of the of input the signal. input signal. omitsand It the omits the It computation SR Ittransforming omits in of It the SR omits the in computation the thebetween amplitude computation spectrum, of spectrum, SR which of in SR the saves in which amplitude thelog about amplitude saves spectrum, 1/3 about computational spectrum, 1/3 which computational saves cost. saves about co arameters. Itparameters. calculates the parameters. 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Optimizing Imbalanced Training Datasets HFT approach HFT approach explains explains the intrinsic HFT the approach intrinsic HFT theory approach of theory explains saliency explains of the saliency detector intrinsic the detector intrinsic in theory the frequency in theory of the saliency frequency of domain saliency detector domain and detector use in the and spectral in frequency use the spectr frequ pectrum, andspectrum, then the makes and spectrum, up then a saliency makes up map then aissaliency by makes transforming up map a saliency transforming SR map spatial by transforming domain. SR spatial PFT domain. approach to input spatial PFT detects domain. 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In thisvegetation, Insituation, situation, targets targets are are `[8], ´ easily mixed with up the with background easily background easily mixed mixed up with inbeen up size with in and background size the easily background overlapped easily clutters overlapped clutters in inthis and by size vegetation, easily and roads, easily overlapped rivers, roads, overlappe river by v lter to suppress filter repeated to suppress filter patterns.S repeated toup suppress patterns.S repeated patterns.S p2828q p24614q forthem all residues p27442q “xx all methods Although numerous Although methods numerous Although have been numerous proposed, have been many proposed, have of them many may proposed, fail of in xx certain many may of fail circumstances, them inbysize certain may fail circumstances, in certain circumstan allmethods all Algorithms Algorithms 2015, 2015, easily easily mixed mixed up with up the with background the background clutters clutters in size in and size easily and easily overlapped overlapped by vegetation, by vegetation, roads, roads, rivers, rivers, clutters. In recent years, a helicopter series of simple and fast algorithm based on fourier t bridges bridges [9], resulting [9], resulting a is huge afalse bridges huge rate bridges false [9], in traditional resulting rate [9], in resulting traditional aproposed, algorithm. huge afail false huge algorithm. false inof rate traditional traditional algorithm. Although numerous Although methods numerous Although have methods numerous been proposed, have methods been many proposed, have of been them may of them in many certain may fail them circumstances, inthis certain may fail circumstances, inalgorithm. certain circumstance .g., ground-sky e.g., background ground-sky e.g., [8], background ground-sky which common [8], background which in is the [8], common helicopter which inmany is the view. common In this inrate the situation, view. helicopter Inin targets situation, are In targets situation, are targets where theresulting figures in the parentheses denote the sample numbers taken from Section 2.1.view. As we canthis see bridges bridges [9], [9], resulting a huge a false huge rate false in rate traditional in traditional algorithm. algorithm. such as spectral residual(SR) [5], phase spectrum of transform(PFT) [6 In order In[8], to order design toclutters design an appropriate an In appropriate order In method, order to design method, ato design an ahelicopter appropriate target small an appropriate detection target method, detection method method, aview. small method inspired afourier small target inspired by target detection the by human detection the method huma ma .g., background ground-sky e.g., ground-sky background which isbackground [8], common which in is[8], the common which helicopter in issmall common the view. In in this the view. situation, helicopter In this targets situation, are In this targets situation, are targets asilyground-sky mixed e.g., up easily with mixed the background easily up with mixed the background up with in the background and easily insamples size overlapped clutters and easily in size by overlapped vegetation, and easily by roads, overlapped vegetation, rivers, by roads, rivers, roads, riv from Equation (15), the numbers ofsize theclutters negative are nearly nine and four times the sizes ofvegetation, the clutters. 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HVS isHVS a kind isis aof kind layered layered image image processing processing system system this reflect the real world in which the non-binding sites are always the majority other methods. It transforms the airspace information the frequency dom consisting consisting of system, system, retina consisting consisting and retina visual of and optical of pathways, visual optical system, pathways, system, retina which retina and nonuniform visual and isof nonuniform visual pathways, and pathways, nonlinear. and which nonlinear. which isThe nonuniform rest isby The nonunifo of an ridges [9], resulting [9], aAlthough huge bridges resulting false [9], rate amight huge resulting in traditional false afrom rate in algorithm. false traditional rate in algorithm. traditional algorithm. 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Section present the Section experimental 4 the is the experimental 4 conclusion is the results. conclusio resul Sec isual system visual (HVS) system has visual been (HVS) designed system has been (HVS) in this designed has paper. been in HVS designed this is paper. a kind in HVS this of layered paper. is a kind HVS image of layered is processing a kind image of layered system processing image system processing syste non-binding ones [88]. 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Section present 3, the In we Section experimental present 3, the we experimental present results. the Section experimental results. 4 is the Section conclusion results. 4 is Section the conclusion 4 is the conclusi f this article. of this article. of this we usedarticle. the K-Nearest Neighbors Cleaning (KNNC) treatment to remove redundant small targets from the reconstruction small that targets is calculated from theonly reconstruction by thesome phase that spectrum is calculated of theonly inputbys 2. 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Aselect similar HVS divides HVS the scene thetointo scene HVS intopatterns.S patches divides HVS small divides patches the and, remove scene select and scene into important select small into important small patches information patches information and through and important through visual important attention visual information attentio inform e.g., ground-sky background [8], which is common in the helicopter view. In t .1. Framework 2.1. ofHVS Framework the Proposed 2.1. of Framework Two the Proposed Stage of Algorithm—A the Two Proposed Stage Algorithm—A Brief Two Description Stage Algorithm—A Brief Description Brief Description method, called the Neighborhood Cleaning Rule (NCR), was also been used by Laurikkala et al. [89], divides HVS divides the scene the scene into small into small patches patches and select and select important important information information through through visual visual attention attention Although methods have been proposed, numerous many methods oftothem have may been fail proposed, ina certain many of selection selection mechanism mechanism tonumerous makeselection toitmake easy selection itto mechanism easy understand mechanism to Although understand to and make to analyze. make itand easy analyze. itOn toeasy understand the On other understand the hand, and other analyze. as and hand, component analyze. asOn a circumsta compone theOn othe the easily mixed up with the background clutters inpractice. size and easily overlapped by v .1. Framework 2.1. ofFramework the Proposed 2.1. Framework ofmechanism the Two Proposed Stage ofto[91] Algorithm—A the Two Proposed Stage Algorithm—A Two Brief Stage Description Algorithm—A Brief Description Brief Description Xiao et al. [90], and Liu etmake al. although their details are different withOn the current Also, the selection selection mechanism to make it easy it to easy understand to understand and analyze. and analyze. the On other the hand, other hand, as a component as a component e.g., ground-sky background [8], which e.g., ground-sky isimportant common background in the helicopter [8], which view. isIn common this situation, in procedur the targe helic of low-level of low-level artificial artificial vision processing, vision ofscene low-level of processing, low-level it artificial facilitates it artificial facilitates vision subsequent vision processing, subsequent processing, procedures it facilitates procedures itthrough by facilitates reducing subsequent byused reducing subsequent computational procedures computation by HVS divides the HVS scene divides into HVS the small scene divides patches into the small and select patches into important small and select patches information and select through information important visual information attention through attention visual atten current KNNC approach is more flexible because it contains afalse variable Kinand hence can bevisual to bridges [9], resulting a huge rate traditional algorithm. of low-level ofwith low-level artificial artificial vision vision processing, processing, it facilitates facilitates subsequent subsequent procedures procedures by reducing by reducing computational computational easily mixed up with the background easily mixed in up size with and the easily background overlapped clutters by vegetation, inwe size roads, easily cost, cost, is which a easy key is consideration ainto key consideration cost, which into cost, real-time which ineasy aitreal-time key applications. istoclutters consideration ainformation key applications. consideration Based in real-time on Based in the real-time on applications. the knowledge, above applications. Based Based on propose the we on above propo the r deal various different training datasets. HVS divides HVS the scene divides into HVS the scene divides patches the small and select patches into small important and patches select important and select through information important visual information through attention visual through attention visual attenti election mechanism selection towhich mechanism make selection itsmall to mechanism to make understand itscene easy to make and understand analyze. itis and On understand the analyze. other and hand, On analyze. the as other aabove component hand, the as other aknowledge, component hand, asand amethod compo In order to design an appropriate method, aOn small target detection cost, which cost, which is a we key isused consideration a [9], key consideration in instages real-time applications. applications. Based Based on the on above the above knowledge, knowledge, we propose we propose Second, the Inserting Hypothetical Training (IHTS) treatment toby add some resulting a real-time huge false rate bridges in traditional [9], resulting algorithm. ainspired huge false rate in traditional algorithm. a framework amake framework consisting consisting of atoframework of stages two asubsequent framework consisting inspired consisting HVS of bySamples as two HVS follows ofstages two as follows stages (See Figure (See by Figure 1). HVS In as HVS predetection 1). follows In aspredetection follows (See Figure (Seestag Fi1 election mechanism selection to mechanism selection it easy mechanism tovision make to ittwo easy make to and understand itfacilitates analyze. easy toby and understand On analyze. the other and On hand, analyze. the as other ainspired On component hand, the other as aby component hand, as astage, compone f low-level artificial of low-level vision artificial ofbridges processing, low-level artificial itunderstand processing, facilitates vision itinspired processing, procedures subsequent it facilitates by procedures reducing subsequent computational by procedures reducing computational reducing computati visual system (HVS) has been designed in this paper. HVS is a kind of layered im hypothetical positive samples into the positive subset so as to enhance the ability in identifying the a framework a framework consisting consisting of two of stages two stages inspired inspired by HVS by as HVS follows as follows (See Figure (See Figure 1). In 1). predetection In predetection stage, stage, In order to design an appropriate In method, order to a small design target an appropriate detection method method, inspired a small by target the d h a saliency a saliency map(SM) map(SM) is obtained is a saliency obtained and a saliency the map(SM) and most the map(SM) salient most is obtained salient region is obtained region is and picked the and is most picked up the to salient most improve up salient to region improve detection region is picked detection is speed. picked up to spee up im f low-level ofcost, vision ofartificial low-level vision artificial facilitates vision subsequent processing, ittofacilitates procedures itsubsequent facilitates byprocedures subsequent reducing computational by procedures reducing by computational reducing computation ost, which isartificial a low-level key which consideration iscost, aprocessing, key which in consideration real-time isitdetails aprocessing, keyapplications. consideration real-time Based applications. in real-time on the above applications. Based knowledge, on thevisual Based above we on knowledge, propose the we knowledge, propose we pro consisting of optical system, retina and pathways, is nonuniform an interactive pairs. For the ofinhow generate the hypothetical training samples, see above thewhich Monte a saliency a saliency map(SM) map(SM) isastage, obtained is(HVS) obtained and the and most the salient most salient region region is(HVS) picked is picked up to up improve to improve detection detection speed. speed. visual system has been designed visual in system this paper. HVS has is been a kind designed of layered in this image paper. processing HVS is a sy In detection In detection stage, support a support vector In detection In machines vector detection stage, machines (SVM) stage, a support (SVM) classifier a support vector classifier is vector machines used to machines used get (SVM) the to get target (SVM) classifier the quickly. target classifier is quickly. used is to used get to the g ost, which is cost, a key which consideration cost, is a key which consideration in real-time is a key consideration applications. in real-time in applications. Based real-time on the applications. Based above on knowledge, the Based above on we knowledge, the propose above knowledge, we propose we propo Calo samples expanding approach in [92,93], or in [94], orstage, the SMOTE framework consisting a framework of two aconsisting framework stages inspired of consisting two stages by HVS ofinspired two asisfollows stages byseed-propagation HVS inspired (Seeas follows by HVS 1).approach (See as predetection follows Figure 1). (See In Figure predetection 1). the In predetection stage, this paper organized asFigure follows. In Section 2, we describe framework ofst In detection In detection stage, stage, a support a support vectorsystem, vector machines machines (SVM) (SVM) classifier classifier is usedissystem, to used get to the get target the target quickly. quickly. consisting of optical retina consisting and visual of pathways, optical which is retina nonuniform and visual and nonlinear. which Thespr (synthetic over-sampling technique) approach in follows [95]. framework aconsisting ofamap(SM) consisting framework two stages of inspired consisting two stages by HVS inspired two as stages follows by HVS inspired (See as Figure by HVS 1). (See asregion Infollows Figure predetection (See 1). InFigure stage, predetection Inpathways, predetection stage, saliency map(SM) aframework saliency is obtained aminority saliency and is the obtained map(SM) most salient and isof obtained theregion most and salient isdetection. picked the most region up to is improve picked up detection is to picked improve speed. updetection to1).improve speed. detection for small target Insalient Section 3, we present the experimental results. stag Sec After the above two treatments, we can change an original highly skewed training dataset to this paper is organized as follows. this In Section paper is 2, organized we describe as follows. the framework In Section of the 2, we proposed describe algo th aInsaliency is obtained map(SM) a stage, saliency is map(SM) obtained the most and salient obtained theclassifier most region and salient ismachines the most region salient tothe improve region upquickly. is detection topicked improve up speed. to detection improve speed. detection nsaliency detectionmap(SM) stage, detection a support Invector detection aand support machines stage, vector (SVM) ais support machines vector (SVM) is picked used classifier toup (SVM) getis ispicked used target classifier to get isthe used target to get quickly. the target quickly. spee article. a balanced training dataset withofitsthis positive subset and negative subset having exactly the same size. for target In Section forused 3, small weto present target detection. the experimental Section 3,the weSection present 4the is the experim concl n detection stage, In detection a support In stage, detection vector asmall support machines stage, vector adetection. support (SVM) machines classifier vector (SVM) machines is classifier (SVM) getisthe used classifier target to get quickly. is In the used target toresults. get quickly. target quickly. of this article. of this article. 2. Algorithm Based on Human Visual System
2. Algorithm Based on Human Visual 2. Algorithm System Based on Human System Figure 1. The 1. proposed The framework Figure framework Figure inspired 1. The 1. inspired proposed by The HVS. proposed byVisual framework HVS.framework inspired inspired by HVS. by H 2.1.Figure Framework ofproposed the Proposed Two Stage Algorithm—A Brief Description FigureFigure 1. The1.proposed The proposed framework framework inspired inspired by HVS. by HVS.
2015, s 2015,xxxx
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It is instructive to point out that the hypothetical samples generated via the IHTS treatment can Algorithms Algorithms2015, 2015,xxxx only be expressed by their feature vectors as defined in Equation (13), but not the real peptide segment samples as given by Equations (6) or (10). Nevertheless, it would be perfectly 2 reasonable to do so 2 because the data directly used to train a predictor were actually the samples’ feature vectors but nottransform clutters. clutters.InInrecent recentyears, years,a series a seriesofofsimple simpleand andfast fastalgorithm algorithmbased basedononfourier fourier transformwas wasp their sequence codes. This is the key to optimize an imbalanced benchmark dataset in the current such suchasasspectral spectralresidual(SR) residual(SR)[5], [5],phase phasespectrum spectrumofoffourier fouriertransform(PFT) transform(PFT)[6], [6],hypercomplex hypercompl the rationale ofalgorithm such an interesting approach will be further elucidated later. series and based fourier was proposed, a study, seriesofand ofsimple simple andfast fast algorithm basedonon fouriertransform transform was proposed,
nrecent recentyears, years,a transform(HFT) transform(HFT)[7]. [7].With Withregards regardstotosmall smalltarget targetdetection, detection,frequency frequencydomain domainmethod methodis isquite quit ctral [5], phase spectrum ofoffourier transform(PFT) ectralresidual(SR) residual(SR) phase spectrum fourier transform(PFT)[6], [6],hypercomplex hypercomplexfourier fourier 2.5. [5], Fusing Multiple Physicochemical Properties from fromother othermethods. methods.It Ittransforms transformsthe theairspace airspaceinformation informationtotothe thefrequency frequencydomain, domain,defines definessig HFT) (HFT)[7]. [7].With Withregards regardstotosmall smalltarget targetdetection, detection,frequency frequencydomain domainmethod methodis isquite quitedifferent different The random forest (RF) algorithm isfrequency afrequency powerfuldomain. algorithm, which has been residual used in many areas of target and tests ininthe (SR) approach does target and tests the domain.While, While,spectral spectral residual (SR) approach doesnot notrelr methods. It Ittransforms the information totothe domain, defines significant r methods. transforms the information thefrequency frequency domain, defines significant of RF have been 2 2 computational biology (see, e.g., [44,96,97]). The detailed procedures and formulation Algorithms 2015, xxairspace Algorithms 2015, xxairspace parameters. calculates the difference between the original signal and a smooth one inin the log am parameters.It It calculates the difference between the original signal and a smooth one the log very clearly described inspectral [98], andresidual hence there is no need to repeat here. ests domain. While, (SR) approach does testsininthe thefrequency frequency domain. While, spectral residual (SR) approach doesnot notrely relyononthe the spectrum, and then makes upup a saliency map byby transforming SR toto spatial domain. approac spectrum, and then makes a saliency map transforming SR spatial domain. Algorithms Algorithms 2015, xx 2015, Algorithms xx 2015, Algorithms xx 2015, 2approa As shown in Equations (11)–(13), aand peptide segment concerned inamplitude the current study can be 2PFT Algorithms Algorithms 2015, xx 2015, Algorithms xx 2015, Algorithms xx 2015, 2PFT 2 calculates the difference between the original signal axxsmooth one in the log amplitude s.It It calculates the difference between the original signal and axxsmooth one in the log clutters. a series ofofsimple and fast based on fourier transform was proposed, clutters.In Inrecent recentyears, years, a series simple and fastalgorithm algorithm based on fourier transform was proposed, small targets from the reconstruction is is calculated only bythe phase spectrum formulated with seven different PseAAC modes, each of that which can be used to train random forest small targets from the reconstruction that calculated only bythe the phase spectrumofofthe theinpu inp nd then upup a saliency map byby transforming SR toto spatial domain. approach detects then makes a saliency map transforming SR spatial domain.PFT PFT approach detects 2015, xxmakes 2 sand 2015, xx 2 predictor after the KNNC and IHTS procedures. Accordingly, we have a total of seven individual such [5], phase spectrum of fourier transform(PFT) [6], fourier suchasasspectral spectralresidual(SR) residual(SR) [5], phase spectrum of fourier transform(PFT) [6],hypercomplex hypercomplex fourier It Itomits the computation ofof SR in amplitude which 1/3 omits the computation SR inthe the amplitudespectrum, spectrum, whichsaves savesabout about 1/3computatio computat clutters. clutters. In Inthat years, recent clutters. ayears, series In aclutters. of series simple years, of In simple and recent asimple series and years, algorithm of fast simple a algorithm series based and of fast on based algorithm fourier on and fourier transform fast based algorithm transform on was proposed, based was transform on proposed, fourier was trans pro clutters. clutters. Inrecent recent In years, recent clutters. ayears, series Inrecent recent aclutters. of series simple years, of In and recent a fast series fast and years, algorithm of fast simple a algorithm series based and ofsimple fast simple on based algorithm fourier on and fourier transform fast based algorithm transform onfourier was fourier proposed, based was transform on proposed, fourier was tran pr s from reconstruction is iscalculated only by the phase spectrum of the input signal. ets fromthe the reconstruction that calculated only by the phase spectrum of the input signal. predictors for identifying PPBS, as formulated by: transform(HFT) regards totoexplains small detection, frequency domain method different transform(HFT)[7]. [7].With With regards smalltarget target detection, frequency domain method isquite quite different HFT approach the intrinsic ofofsaliency detector inis frequency domain HFT approach explains the intrinsictheory theory saliency detector inthe the frequency domainand anduse u such such asin spectral residual(SR) such residual(SR) asresidual(SR) [5], such phase residual(SR) [5], as[5], spectral spectrum phase spectrum residual(SR) [5], of fourier phase of1/3 spectrum fourier transform(PFT) [5], phase transform(PFT) of spectrum [6], transform(PFT) hypercomplex of [6], hypercomplex transform(PFT) [6], fourier hypercomplex fourier [6], suchas such spectral as spectral residual(SR) such asspectral spectral [5], such phase residual(SR) as spectral spectrum phase spectrum residual(SR) [5], of fourier phase of spectrum fourier transform(PFT) [5], phase transform(PFT) offourier fourier spectrum [6], transform(PFT) hypercomplex offourier [6], fourier hypercomplex transform(PFT) [6], fourier hypercomplex fourier [6],hyfh ofas SR the amplitude spectrum, which saves about computational cost. hecomputation computation ofspectral SRin the amplitude spectrum, which saves about 1/3 computational cost. ecent years, a series of simple and fast algorithm based on fourier transform was proposed, recent from years, aother series of simple and algorithm based on fourier transform was methods. Itfilter the information topkq domain, fromother methods. Ittransforms transforms theairspace airspace information tothe thefrequency domain,defines definessignificant significant tofast repeated patterns.R filter tosuppress suppress repeated patterns.F pk “frequency 1, 2, ¨ ¨ ¨proposed, , 7q (16) PPBS individual predictor “ transform(HFT) transform(HFT) [7]. transform(HFT) With [7]. regards With transform(HFT) regards toregards [7]. With to target regards [7]. detection, target With toWith detection, regards frequency target to frequency detection, small domain target domain method frequency detection, method ismethod domain frequency is different method different domain is isquite meth did transform(HFT) transform(HFT) [7]. transform(HFT) With [7]. regards With transform(HFT) tosmall [7]. small With tosmall target small regards [7]. detection, target tosmall small detection, regards frequency target to frequency detection, small domain target domain method frequency detection, isquite quite domain frequency isquite different quite method different domain quite me ch explains the theory of detector in the frequency domain and use oach explains theintrinsic intrinsic theory ofsaliency saliency detector in the frequency domain and usespectral spectral tral residual(SR) [5], phase spectrum ofof fourier transform(PFT) [6], hypercomplex fourier ectral residual(SR) [5], phase spectrum fourier transform(PFT) [6], hypercomplex fourier target tests in frequency domain. While, spectral residual (SR) does not rely onfail targetand and tests inthe the frequency domain. While, spectral residual (SR)approach approach does not rely onthe Although numerous methods have been proposed, many of them may fail inthe Although numerous methods have been proposed, many of them may incertain certaincircum circu from from methods. other methods. from It other It Itmethods. transforms from the other airspace Itthe methods. airspace information It the information transforms airspace totothe frequency information to the the airspace frequency domain, toinformation domain, frequency defines to defines significant the domain, frequency significant defines domain sign fromother other from methods. other methods. from Ittransforms transforms other methods. transforms from the other airspace Ittransforms the transforms methods. airspace information It the information transforms airspace the frequency information to the the airspace frequency domain, tothe information the domain, frequency defines to defines significant the domain, frequency significant defines doma sig press patterns.R ppressrepeated repeated patterns.F where pkq represents the random forest predictor based on the k-th physicochemical property FT) [7]. With tocalculates small target detection, frequency domain method isand quite different HFT) [7]. Withregards regards to small target detection, frequency domain method is quite different parameters. It calculates the difference between the original signal and a smooth one in the log amplitude parameters. It the difference between the original signal a smooth one in the log amplitude e.g., ground-sky background [8], which is common in the helicopter view. In this situation, ta e.g., ground-sky background [8], which is common in the helicopter view. In this situation, (cf. Equation (13)). target and target tests and inin tests the target frequency in and the tests target domain. in and domain. frequency While, tests While, spectral the domain. frequency spectral While, domain. residual (SR) spectral approach (SR) While, residual approach spectral does (SR) not does residual approach rely not on rely (SR) the does onapproach the not d target and target tests and tests the target frequency in and thefrequency frequency tests target domain. inthe the and domain. frequency While, testsin in While, spectral the domain. frequency spectral While, domain. residual (SR) spectral approach (SR) While, residual approach spectral does (SR) not does residual approach rely not on rely (SR) the does onapproach the notrely rely hghnumerous methods have been proposed, many of them may fail inresidual certain circumstances, numerous methods have been proposed, many of them may fail inresidual certain circumstances, methods. Itspectrum, the towith frequency domain, defines significant methods. Ittransforms transforms theairspace airspace tothe the frequency domain, defines significant spectrum, and then makes upinformation ainformation map by transforming SR toseven spatial domain. PFT approach detects and then makes up a how saliency map by transforming SR to spatial domain. PFT approach detects easily mixed up with the background clutters inin size and overlapped by easily mixed the background clutters size andeasily easily overlapped byvegetation, vegetation,road roa Now, the problem issaliency toup combine the results from the individual predictors to maximize parameters. parameters. Itwhich calculates parameters. 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As indicated by series of previous studies, using the ensemble classifier formed sts ininthe frequency domain. While, spectral residual (SR) approach does not ononthe tests the frequency domain. While, spectral residual (SR) approach does notrely rely theofof small targets from the reconstruction that isaaiscalculated only by the spectrum the signal. small targets from the reconstruction that only by thephase phase spectrum theinput input signal. bridges [9], resulting huge false rate traditional algorithm. bridges [9], resulting acalculated huge false ratein in traditional algorithm. spectrum, spectrum, and then and makes spectrum, then up makes aand saliency spectrum, up then aeasily saliency map and by up map then transforming athen saliency makes transforming map up SR aSR saliency by transforming spatial SR to map domain. spatial by transforming SR domain. PFT to spatial approach PFT domain. 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It calculates the difference between the original signal a spectrum, smooth one inin the amplitude calculates the difference between the signal and a smooth one the log amplitude It Itomits the ofIn SR inoriginal amplitude spectrum, which saves about 1/3 cost. omits thecomputation computation of SR in amplitude which saves about 1/3computational computational cost. In order tothe design anand method, alog target detection inspired order tothe design anappropriate appropriate method, asmall small target detectionmethod method inspiredbybythe t small targets small targets from the small from reconstruction targets the small from that the targets reconstruction is that from isquaternary the calculated reconstruction only that by isby only the byphase that the spectrum is only phase calculated byspectrum the ofthe phase only input ofinput by spectrum the the signal. input phase of signal. the spectrum input subcellular [99,100] and protein structural attribute [101]. Encouraged by targets small targets from the small from reconstruction targets thereconstruction reconstruction small from that the targets reconstruction iscalculated calculated that from is the calculated reconstruction only that iscalculated only calculated thephase by that the spectrum is only phase calculated byspectrum ofthe the phase only of by spectrum the the signal. input phase of signal. the spectrum inpu asmall huge false rate algorithm. ],resulting resulting a huge false rateinlocalization intraditional traditional algorithm. d then makes up a saliency map bythe transforming SR toof spatial domain. PFT approach detects and then makes up a previous saliency map by transforming SR to spatial domain. PFT approach detects HFT explains the intrinsic theory of saliency detector inin frequency domain and spectral HFTapproach approach explains intrinsic theory saliency detector inthe the frequency domain and use spectral visual system (HVS) has been designed in this paper. HVS is ofuse image visual system (HVS) has been designed this paper. 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HVS isapproach of layered image processing system em(HVS) (HVS) hasbeen been designed in this paper. HVS isa kind athe kind of layered image processing system ofofSR the spectrum, which about 1/3 computational cost. ecomputation computation SRin in theamplitude amplitude spectrum, which saves about computational cost. Although numerous methods have been proposed, many of1/3 may fail in certain circumstances, Although numerous methods have proposed, many ofthem them may fail in certain circumstances, this paper is organized assaves InIn Section 2, wewe describe the ofofthe this paper is organized asfollows. follows. Section 2, describe theframework framework theproposed proposeda E been 7 filter tofilter toto suppress repeated filter repeated topathways, patterns.R filter patterns.R repeated to patterns.R patterns.R filter tosuppress filter suppress suppress repeated filter repeated tosuppress patterns.F suppress filter patterns.F repeated to suppress patterns.F patterns.F “suppress p1q @repeated ¨ ¨repeated ¨@ p7q “nonlinear. @nonlinear. pkqThe (17) fofoptical system, retina and visual which is isnonuniform and optical system, retina and visual pathways, which nonuniform and Therest restofof k“1 ch the intrinsic of saliency detector incommon frequency domain and use spectral achexplains explains the intrinsictheory theory of saliency detector inthe the frequency domain and use spectral e.g., ground-sky background [8], which is iscommon inSection view. Inexperimental targets are e.g., ground-sky background [8], which inthe thehelicopter helicopter view. Inthis thissituation, situation, targets are 4 4is isthe for small target detection. In Section 3, wewepresent the results. Section for small target detection. In 3, present the experimental results. Section thecoc Although Although numerous numerous Although methods methods numerous have Although been have methods proposed, been numerous proposed, have many methods been ofthe many proposed, them have ofmay been many fail proposed, may inof fail inmany may circumstances, of fail circumstances, them in may circumst inincer Although numerous numerous Although methods methods numerous have Although been have methods proposed, been numerous proposed, have many methods been of many proposed, them have ofthem may them been many fail proposed, may incertain ofthem certain fail them incertain many certain may circumstances, of fail circumstances, them incertain certain mayfail fail circum c s isorganized asAlthough InIn 2,2,wewe describe the framework of the proposed algorithm organized asfollows. follows. Section describe the framework of proposed algorithm ESection ress repeated patterns.R ppress repeated patterns.F whereupup stands for the ensemble classifier, and the symbol @ overlapped for the fusing operator. For roads, the detailed easily with the background clutters ininsize easily byby vegetation, rivers, easilymixed mixed with background clutters sizeand and easilyoverlapped vegetation, roads, rivers, ofthe article. ofthis this article. e.g., e.g., ground-sky background e.g., background ground-sky [8], e.g., which background [8], ground-sky is which common isresults. [8], background common in which the helicopter in ishelicopter [8], common the helicopter view. in is the common In view. helicopter this situation, inthis view. situation, helicopter targets InInthis targets are view. situation, are Inare targ e.g.,ground-sky ground-sky e.g., ground-sky background e.g., background ground-sky [8], e.g., which background [8], ground-sky is which common is [8], background common in which the in is [8], common the which view. in is the common In view. helicopter thisIn In situation, inthe this the view. situation, helicopter targets this targets are view. situation, Inthis this tars get detection. In 3, we the experimental Section 4predictors ishelicopter conclusion arget detection. InSection Section 3, wepresent present the experimental results. Section 4which isthe the conclusion procedures of to fuse the results from the seven individual to reach a final outcome via methods have many them may fail inincertain circumstances, ghnumerous numerous methods havebeen been proposed, many of them may fail certain circumstances, bridges [9], ahow huge false rate ininof traditional algorithm. bridges [9],resulting resulting aproposed, huge false rate traditional algorithm. easily easily up mixed with easily up the with background mixed the background upeasily clutters mixed the clutters up in size with in and the size clutters easily background and overlapped easily in clutters overlapped and by easily in vegetation, size by overlapped and vegetation, easily roads, bywas overlapped rivers, roads, vegetation, rivers, byroads, easilymixed mixed easily up mixed with easily up the with background mixed theeasily background upwith with clutters mixed thebackground background clutters up in size with in and the size clutters easily background overlapped easily insize size clutters overlapped and by easily in vegetation, size by overlapped and vegetation, easily roads, by overlapped rivers, roads, vegetation, rivers, byveget roads veg e. cle. the voting system, see Equations (30)–(35) in [27], where aand crystal clear and elegant derivation -sky [8], which is2. ininthe helicopter view. Intarget situation, targets are d-skybackground background [8], which iscommon common the helicopter view. Inthis this situation, targets are Algorithm Based on Human Visual System InInorder to design an appropriate method, a small target detection method inspired by the human 2. Algorithm Based on Human Visual System order to design an appropriate method, a small detection method inspired by the human elaborated and there is no need to here. To provide anin intuitive picture, a flowchart is bridges bridges [9], [9], bridges resulting ahence huge [9], afalse huge resulting bridges rate false in [9], atraditional rate huge resulting inrepeat false traditional algorithm. rate arate huge in algorithm. false algorithm. traditional algorithm. bridges bridges [9],resulting resulting [9], bridges resulting a huge [9], afalse huge resulting bridges rate false in [9], atraditional rate huge resulting in false traditional algorithm. a huge intraditional algorithm. traditional falserate rate in algorithm. traditional algorithm. the clutters inbeen and overlapped by vegetation, roads, rivers, edupupwith with thebackground background clutters insize size andeasily easily overlapped byis vegetation, roads,into rivers, visual system has designed inin this paper. a kind image processing system visual system designed this paper.HVS HVS is a kindofare oflayered layered image processing system given (HVS) in(HVS) Figure 3has tobeen illustrate how the seven individual RF predictors fused the ensemble classifier. Algorithms 2015, xx Algorithms 2015, xx m Visual InHuman order InIn to order design toSystem design In andesign order appropriate anan toappropriate In method, order ananto appropriate method, adesign aan target method, appropriate detection target a asmall detection method, method target method ainspired detection target by method the detection by human inspired the method bybythe insp hmBased Basedonon Visual InHuman order to order design toSystem In an order appropriate todesign appropriate design In method, order to appropriate method, asmall design small asmall an target small method, appropriate detection target small detection method, method target method asmall inspired detection smallinspired inspired target by method the detection by human inspired thehuman human method the inh 2.1. Framework of the Proposed Two Stage Algorithm—A Brief Description 2.1. Framework of the Proposed Two Stage Algorithm—A Brief Description resulting a huge false rate in traditional algorithm. , resulting a huge false rate in traditional algorithm. consisting of optical system, retina and visual pathways, which is nonuniform and nonlinear. The rest of consisting of optical system, retina and visual pathways, which is nonuniform and nonlinear. The rest of 15, xxxx visual 2is 2015, 2kind visual (HVS) visual (HVS) has system has designed been visual (HVS) designed system in has this been (HVS) paper. in(HVS) designed HVS has paper. been is in HVS athis designed kind paper. ispaper. of a of kind in HVS this ofthis is image paper. apaper. processing image HVS of is processing kind image ofoflayered system processing image visualsystem system visualsystem system (HVS) visual (HVS) hasbeen been system has designed been visual (HVS) designed system in has this been paper. inthis this designed HVS has paper. been is in HVS athis designed kind is alayered kind layered in HVS oflayered layered image a kind processing image HVS oflayered layered isaprocessing asystem kind system image layered system processing imas to anpaper method, afollows. target detection method inspired bybythe r todesign design anappropriate appropriate method, asmall smallIn target detection method inspired thehuman this is isorganized asasfollows. Section 2,2,wewe describe the ofhuman this paper organized In Section describe theframework framework ofthe theproposed proposedalgorithm algorithm work Proposed Stage Algorithm—A Brief Description eworkofofthe the Proposed Two Algorithm—A Brief Description consisting consisting ofTwo ofStage consisting system, system, retina of consisting optical and retina visual system, and of optical pathways, visual retina pathways, system, which visual retina iswhich pathways, nonuniform and isselect visual which and pathways, nonlinear. isnonlinear. and which nonlinear. The ison and rest The nonlinear. of of and The noaw consisting consisting ofoptical optical ofoptical consisting optical system, system, retina of consisting optical and retina visual system, and of optical pathways, visual retina pathways, system, and which visual retina is which pathways, nonuniform and isnonuniform visual nonuniform which and pathways, isnonuniform nonuniform and which nonlinear. The isnonuniform and rest nonuniform The nonlinear. ofrest rest of and Th clutters. In recent years, asmall series of and fast algorithm based on fourier transform clutters. In recent years, aand series ofsimple simple and fast algorithm based fourier transform HVS divides the scene into patches and important information through visual HVS divides the scene into small patches and select important information through visua m has been designed ininthis paper. HVS iswe kind of layered image processing system em(HVS) (HVS) has been designed this paper. HVS isawe apresent kind of layered image processing system for small target detection. In Section 3, the experimental results. Section 4 is the conclusion for small target detection. In Section 3, present the experimental results. Section 4 is the conclusion cent a series of simple and fast algorithm based on transform proposed, ecentyears, years, apaper series of simple and fast algorithm based on fourier transform was proposed, this this is paper organized isthis as paper follows. isas this follows. Inpaper In as isresidual(SR) Section organized follows. 2,Section we 2, In as we Section follows. describe the framework 2,was In we the Section describe framework of 2, the the we proposed of framework describe the proposed algorithm the offramework algorithm proposed algo this paper this is paper organized isorganized this organized as paper follows. isorganized as organized this follows. InSection paper Section In as is organized follows. 2,fourier we describe 2, In as we Section follows. describe the framework 2, In we the Section describe framework of 2, the the we proposed of framework describe the proposed algorithm the ofthe framework the algorithm proposed th alc such spectral [5], phase spectrum ofanalyze. fourier transform(PFT) [6], such as spectral residual(SR) [5], phase spectrum of fourier transform(PFT) [6],hyperco hyperc selection mechanism make itdescribe to understand and On the other hand, asof athe selection mechanism to make iteasy easy to understand and analyze. On the other hand, asof acom fivides system, retina and visual pathways, which istoisnonuniform and nonlinear. The rest ofoptical optical system, retina and visual pathways, which nonuniform and nonlinear. The restof of of this article. of this article. ides the scene into small patches and select important information through visual attention the scene into small patches and select important information through visual attention al residual(SR) [5], phase spectrum of fourier transform(PFT) [6], hypercomplex fourier ctral residual(SR) [5], phase spectrum of fourier transform(PFT) [6], hypercomplex fourier forforsmall for target small detection. target for detection. In target Section for In detection. small Section 3, target present 3, In detection. Section present the experimental 3, the In we Section present results. 3, the wewe experimental results. present Section Section the 4Section experimental results. the 4conclusion Section the conclusion results. 4 method Section conc small for target small detection. target for small detection. In target Section for In detection. small Section 3,we we target present 3,we In we detection. Section present the experimental 3, the In we Section present results. 3, the experimental results. present Section the 4is is experimental results. the 4isconclusion is Section the conclusion results. 4ismethod isthe the Sectio con transform(HFT) [7]. With regards to small target detection, frequency domain is i transform(HFT) [7]. With regards to small target detection, frequency domain ofsmall artificial vision processing, itexperimental facilitates subsequent procedures by reducing compu oflow-level low-level artificial vision processing, itexperimental facilitates subsequent procedures by reducing com as InInSection 2, the framework of proposed algorithm isorganized organized asfollows. follows. Section 2,wewedescribe describe the framework ofthe the proposed algorithm echanism to make it easy to understand and analyze. On the other hand, as a component mechanism to make it easy to understand and analyze. On the other hand, as a component T) [7]. With regards to small target detection, frequency domain method is quite different FT) [7]. of With regards toarticle. small target detection, frequency domain method isairspace quite different article. ofarticle. ofof this ofisother this article. ofthis this ofthis thisarticle. thisarticle. article. ofis this article. from other It It transforms the information toon frequency domain, from methods. transforms theairspace information tothe frequency domain,defin de cost, which aexperimental key consideration real-time applications. Based above we cost, which amethods. key consideration in real-time applications. Based onthethe aboveknowledge, knowledge, w 2.2.vision Algorithm Based on Human Visual System get detection. InIn Section 3,3,we present the experimental results. Section 4 4is is the conclusion Algorithm Based on Human Visual System arget detection. Section we present the results.in Section the conclusion artificial processing, it facilitates subsequent procedures by reducing computational el artificial vision processing, it facilitates subsequent procedures by reducing computational ethods. It Ittransforms information to the frequency domain, defines significant methods. transformsthe theairspace airspace information to the frequency domain, defines significant target tests the frequency domain. While, spectral residual (SR) approach does targetand and testsinin the frequency domain. While, spectral residual (SR) approach doesn a framework consisting of two stages byby HVS follows (See 1). InInpredetectio a framework consisting of two stagesinspired inspired HVSas as follows (SeeFigure Figure 1). predetec e. cle. a in key consideration in real-time applications. Based on the above knowledge, we propose his is athe key consideration in real-time applications. Based on the above knowledge, we propose ts in frequency domain. spectral residual (SR) approach does not rely on the ests the frequency domain. While, spectral residual (SR) approach does not rely on the 2. Algorithm 2.2.Algorithm Based 2.While, on Based Algorithm Human on Human 2. Visual Based Algorithm Visual on System Human Based System Visual on Human System Visual System 2. Algorithm Algorithm Based 2. on Based Algorithm Human on Human 2. Visual Based Algorithm Visual on System Human Based System Visual on Human System Visual System parameters. It It calculates the difference between the original signal and a to smooth one inin the parameters. calculates the difference between the original signal aimprove smooth one th aProposed map(SM) is and the most salient region is ispicked upand detectio asaliency saliency map(SM) isobtained obtained and the most salient region picked upto improve detect 2.1. ofof the Two Algorithm—A Brief 2.1.Framework Framework the Proposed Two Stage Algorithm—A Brief Description kIt consisting of two inspired by HVS asStage follows (See Figure 1). InDescription predetection stage, ork consisting of twostages stages inspired by HVS as follows (See Figure 1).in In predetection stage, calculates the difference between the original signal and a smooth one the log amplitude calculates the difference between the original signal and a smooth one in the log amplitude spectrum, and makes upup amachines saliency map byby transforming SR tototo spatial domain. PFT apa spectrum, and makes amachines saliency map transforming SR spatial domain. PFT In stage, athen support vector (SVM) classifier target Indetection detection stage, athen support vector (SVM) classifieris isused used toget getthe the targetquickly. quickly m Based Human System hm Basedon on HumanVisual Visual System map(SM) is obtained and the most salient region is picked up to improve detection speed. map(SM) is obtained and the most salient region is picked up to improve detection speed. 2.1. Framework Framework of the 2.1. Proposed of Framework the Proposed 2.1. Two ofpatches Framework Stage the Two Proposed Algorithm—A Stage of Algorithm—A the Two Proposed Stage Brief Algorithm—A Description Brief Two Description Algorithm—A Brief Description Brief Description 2.1. Framework Framework of the 2.1. Proposed of Framework the Proposed 2.1. Two of Framework Stage the Two Proposed Algorithm—A Stage of Algorithm—A the Two Proposed Stage Brief Algorithm—A Description Brief Two Description Algorithm—A Brief Description Brief Description then makes up a2.1. saliency map by transforming SR to spatial domain. PFT approach detects nd then makes up a2.1. saliency map by transforming SR to spatial domain. PFT approach detects HVS divides the scene into small and select important information through visual attention HVS divides the scene into small patches and select important information through visual attention small targets from the reconstruction that isStage calculated only by the phase spectrum small targets from the reconstruction that isStage calculated only by the phase spectrumofofthe t stage, a support vector machines (SVM) classifier is used to get the target quickly. on stage, a support vector machines (SVM) classifier is used to get the target quickly. from reconstruction that is calculated only by the phase spectrum of the input signal. s fromthe the reconstruction that is calculated only by the phase spectrum of the input signal. selection mechanism toto make itomits toBrief understand and analyze. On hand, a acomponent selection mechanism make iteasy easy to understand analyze. Onthe theother other hand,aswhich aswhich component It Itomits the computation ofand ininthe spectrum, saves the computation ofSR SR theamplitude amplitude spectrum, savesabout about1/3 1/3comp com ork Proposed Two Stage Algorithm—A Brief Description workofofthe the Proposed Two Stage Algorithm—A Description HVS divides HVS divides the scene HVS the into scene divides small into HVS the patches small scene divides patches and into the select small and scene important patches select into important small and information select patches information important and through select information through visual important attention visual through information attention visual throu atta HVS divides HVS divides the scene HVS the into scene divides small into HVS the patches small scene divides patches and into the select small and scene important patches select into important small and information select patches information important and through select information through visual important attention visual through information attention visual thr omputation of SR in the amplitude spectrum, which saves about 1/3 computational cost. computation of SR in the amplitude spectrum, which saves about 1/3 computational cost. ofoflow-level vision processing, itthe subsequent procedures by computational low-levelartificial artificial vision processing, itfacilitates facilitates subsequent procedures byreducing reducing computational HFT approach explains intrinsic theory ofofsaliency detector in HFT approach explainsthe the intrinsic theory saliency detector inthe thefrequency frequencydomain domainan Figure 3. A flowchart to illustrate ensemble classifier of Equation (17) that exploits all the different selection selection mechanism mechanism selection to mechanism tomechanism itmake selection ittoitto easy to understand mechanism make to it and to analyze. tomake understand itanalyze. easy On to the and understand On other analyze. the hand, other and On as hand, analyze. the a analyze. other asother On hand, the asother a acomp han selection selection mechanism mechanism selection tomake make to iteasy make selection easy easy to understand mechanism make tounderstand understand iteasy easy and tomake analyze. toand and understand it analyze. easy On to the and understand On other analyze. the hand, other and On as hand, the acomponent component asa acomponent component On hand, the asother com h hch explains the intrinsic of detector in the frequency domain and use spectral explains the intrinsic ofsaliency saliency detector the frequency domain use spectral des the scene into patches and select important information through visual attention vides the scene intosmall patches and select important information through visual attention cost, which issmall key consideration real-time applications. Based onand the above knowledge, wewe propose cost, which isatheory atheory key consideration in real-time applications. Based on the above knowledge, propose filter toin repeated patterns.R filter tosuppress suppress repeated patterns.F groups of features, where D(1) meansinthe decision made by (1) , D(2) means the decision made by ofoflow-level ofoflow-level artificial of artificial vision low-level processing, vision artificial of processing, itvision artificial it processing, facilitates subsequent vision itsubsequent processing, procedures procedures subsequent itprocedures by by procedures subsequent reducing computational by computational procedures reducing by low-level low-level artificial of artificial vision low-level processing, vision artificial oflow-level low-level processing, itfacilitates vision facilitates artificial it processing, facilitates subsequent vision itfacilitates subsequent processing, facilitates procedures subsequent itfacilitates facilitates byreducing reducing by procedures subsequent reducing computational by computational procedures reducingcomputa compu byredu red ess repeated press repeated patterns.F (2),toand so See the text as well as Equations (11) and (16) for further explanation. echanism make easy and analyze. On the other hand, as mechanism topatterns.R makeit itconsisting easy tounderstand understand and analyze. On the hand, asaFigure acomponent component a framework offorth. stages inspired by HVS asother follows (See 1).1).In predetection stage, atoframework consisting oftwo two stages inspired by HVS as follows (See Figure In predetection stage, Although numerous methods have been proposed, many ofofthem fail Although numerous methods have been proposed, many themmay may failinincertain certainc cost, which cost, is which a key is cost, consideration aconsideration key which consideration ismany cost, in key which consideration inthem isreal-time applications. amay key consideration in applications. real-time Based applications. on in Based real-time the onabove applications. Based knowledge, above on knowledge, the we Based above propose on knowledge, weon the propose above we know pr cost, which cost, is which a key is cost, aproposed, key which consideration isamany cost, ainreal-time key real-time which consideration inreal-time is applications. amay key consideration in applications. real-time Based applications. on in Based real-time theabove onthe the applications. Based knowledge, above on knowledge, the we Based above propose knowledge, we the propose above we kn numerous methods have been of them fail in certain circumstances, numerous methods have been of fail in certain vision processing, itisproposed, subsequent procedures by reducing computational elartificial artificial vision processing, itfacilitates facilitates subsequent procedures by reducing computational a asaliency map(SM) and most salient region is picked up detection speed. saliency map(SM) isobtained obtained andthe the most salient is picked uptotoimprove improve detection speed. e.g., background [8], which iscircumstances, ininthe helicopter view. e.g.,ground-sky ground-sky background [8], which iscommon common the helicopter view.InInthis thissituati situa Figure 1.region The proposed framework inspired bybyHVS. Figure 1. The proposed framework inspired HVS. a framework a[8], framework consisting ais consisting framework ofoftwo of aconsisting framework inspired stages ofinspired consisting two by HVS stages byas of HVS inspired two asstages by (See HVS inspired Figure (See as Figure 1). by In HVS predetection (See 1). asIn follows 1). stage, (See InIn Figure predetection stage, 1).1).In a framework a[8], framework consisting aconsisting framework two stages oftwo aconsisting two framework inspired stages of inspired consisting two by HVS stages by asfollows of HVS inspired follows two asfollows stages follows by (See HVS inspired Figure (See asfollows follows Figure 1). by In HVS predetection (See 1). asFigure Inpredetection Figure follows predetection 1). stage, (See Figure predetectio stage, ky which instages the helicopter view. In this situation, are which common in the helicopter view. In this targets are s isa background key consideration ininreal-time applications. Based on the above knowledge, we propose h-sky a background key consideration real-time applications. Based on the above knowledge, we propose In detection stage, aissupport vector machines (SVM) classifier issituation, totargets get the target quickly. In detection stage, acommon support vector machines (SVM) classifier isused used to get the target quickly. easily mixed up the background clutters in size and overlapped easily mixed upwith with the background clutters in size andeasily easily overlappedbybyvegetation, vegetatio athe a asaliency map(SM) map(SM) aproposed issaliency obtained isframework map(SM) obtained aand and the and is most obtained map(SM) the salient most and isHVS. salient region obtained the region ismost and salient isroads, the up region most to up salient issalient to detection region upupdetection is todetection picked speed. improve speed. upspeed. detection to asaliency saliency saliency map(SM) map(SM) asaliency isin obtained isand map(SM) obtained asaliency and saliency the and is most obtained map(SM) the salient most and issalient region obtained themost region ispicked picked and salient ispicked the picked up region most toimprove improve up ispicked toimprove picked improve detection region is to picked speed. improve up detection toimpro imp Figure 1. inspired by Figure 1.The The proposed framework inspired byHVS. background clutters size easily overlapped by vegetation, roads, rivers, dup upwith withthe clutters in size easily overlapped by vegetation, rivers, ofbackground inspired by HVS as follows (See 1). In stage, rkconsisting consisting oftwo twostages stages inspired by as follows (See Figure 1). Inpredetection predetection stage, Due toHVS two layers structure, the algorithm computational complexity bridges [9], resulting a huge false rate in algorithm. Due tothe the two layers structure, the algorithm computational complexitybecomes becomesthe theprime prim bridges [9], resulting aFigure huge false rate intraditional traditional algorithm. detection Infalse stage, aIn stage, support detection a support stage, Instage, machines vector a support machines stage, (SVM) vector a (SVM) support machines classifier vector is (SVM) used machines is tois used classifier get to (SVM) get target isthe classifier quickly. target totoget quickly. is the used target totoget quickly. the detection Indetection detection stage, aIn stage, support detection avector support vector Indetection detection machines vector a support machines stage, (SVM) vector aclassifier (SVM) support classifier machines classifier vector is (SVM) used machines to used classifier getthe the to (SVM) get target isused the used classifier quickly. target get quickly. isthe used target get quickly. thetarg ta sulting aIn huge false rate inthe algorithm. resulting aIn huge rate intraditional traditional algorithm. map(SM) is obtained and most salient region isand up totoimprove detection speed. map(SM) is obtained and the most salient region ispicked picked upappropriate improve detection speed. For simplicity high processing speed, saliency detection methods ininmethod the dom Insimplicity toand design an appropriate method, a asmall target detection inspired Forthe the high processing speed, saliency detection methods thefrequency frequency d Inorder order to design an method, small target detection method inspired
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The final predictor thus obtained is called “iPPBS-Opt”, where “i” stands for “identify”, “PPBS” for “protein-protein binding site”, and “Opt” for “optimizing” training datasets. Note that the iPPBS-Opt predictor contains a parameter K, reflecting how many nearest neighbors should be considered in removing the redundant negative samples from the training dataset during the KNNC treatment (cf. Section 2.4). Its final value is determined by maximizing the overall success rate via cross-validation, as will be described later. 3. Result and Discussion As pointed out in the Introduction section, one of the important procedures in developing a predictor is how to properly and objectively evaluate its anticipated success rates [12]. Towards this, we need to consider the following two aspects: one is what kind of metrics should be used to quantitatively measure the prediction accuracy; the other is what kind of test method should be adopted to derive the metrics values, as elaborated below. 3.1. Metrics for Measuring Success Rates For measuring the success rates in identifying PPBS, a set of four metrics are usually used in literature. They are: (1) overall accuracy or Acc; (2) Mathew’s correlation coefficient or MCC; (3) sensitivity or Sn; and (4) specificity or Sp (see, e.g., [102]). Unfortunately, the conventional formulations for the four metrics are not quite intuitive for most experimental scientists, particularly the one for MCC. Interestingly, by using the symbols and derivation as used in [103] for studying signal peptides, the aforementioned four metrics can be formulated by a set of equations given below [14,30,60,61,104]: $ N` ’ ’ ’ Sn “ 1 ´ ´ ’ ’ N` ’ ´ ’ ’ N` ’ ’ Sp “ 1 ´ ’ ’ ’ N´ ’ ´ ’ ’ N ` ` N` & Acc “ Λ “ 1 ´ ´ N` ` N´ ` ´ ’ ’ N´ ` N` ’ ’ q 1 ´ p ’ ’ ’ N` ` N´ ’ g Mcc “ ’ ¸˜ ¸ ’ f˜ ’ ` ´ ´ ` ’ f N ´ N N ´ N ’ ´ ` ` ´ ’ e 1` ’ 1` ’ % N` N´
0 ď Sn ď 1 0 ď Sp ď 1 0 ď Acc ď 1
(18)
´1 ď Mcc ď 1
` where N ` represents the total number of PPBSs investigated whereas N´ the number of true PPBSs ´ incorrectly predicted to be of non-PPBS; N the total number of the non-PPBSs investigated whereas ´ N` the number of non-PPBSs incorrectly predicted to be of PPBS. ` According to Equation (18), it is crystal clear to see the following. When N´ “ 0 meaning none of the true PPBSs are incorrectly predicted to be of non-PPBS, we have the sensitivity Sn “ 1. ` When N´ “ N ` meaning that all the PPBSs are incorrectly predicted to be of non-PPBS, we have the ´ sensitivity Sn “ 0. Likewise, when N` = 0 meaning none of the non-PPBSs are incorrectly predicted ´ to be of PPBS, we have the specificity Sp “ 1; whereas N` = N ´ meaning that all the non-PPBSs are ` ´ incorrectly predicted to be of PPBS, we have the specificity Sp “ 0. When N´ “ N` “ 0 meaning that none of PPBSs in the positive dataset and none of the non-PPBSs in the negative dataset are ` incorrectly predicted, we have the overall accuracy Acc “ 1 and MCC “ 1; when N´ “ N ` and ´ N` = N ´ meaning that all the PPBSs in the positive dataset and all the non-PPBSs in the negative dataset are incorrectly predicted, we have the overall accuracy Acc “ 0 and MCC “ ´1; whereas when ` ´ N´ “ N ` {2 and N` = N ´ {2 we have Acc “ 0.5 and MCC “ 0 meaning no better than random guess. As we can see from the above discussion, it would make the meanings of sensitivity, specificity, overall accuracy, and Mathew’s correlation coefficient much more intuitive and easier-to-understand by using Equation (18), particularly for the meaning of MCC.
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It should be pointed out, however, the set of metrics as defined in Equation (18) is valid only for the single-label systems. For the multi-label systems whose emergence has become more frequent in system biology [46,105,106] and system medicine [107], a completely different set of metrics as defined in [108] is needed. 3.2. Cross-Validation and Target Cross-Validation
Once established the evaluation metrics, the next issue is the selection of the most appropriate validation method should be used to derive the values of these metrics. Three cross-validation methods are often used to derive metrics values in statistical prediction: the independent dataset test, subsampling (or K-fold cross-validation) test, and jackknife test [109]. Of the three the jackknife test is deemed the least arbitrary as it can always yield a unique outcome for a given benchmark dataset, as elucidated in [12] and demonstrated by Equations (28)–(32) therein. Accordingly, the jackknife test has been widely recognized and increasingly used by investigators to examine the quality of various predictors (see, e.g., [46,53,54,110–115]. However, to reduce the computational time, in this study we Algorithms 2015, xx 2 adopted the 10-fold cross-validation, as done by most investigators with SVM and random forests algorithms as the prediction engine. Algorithms Algorithms 2015, Algorithms 2015, xx conducting xx2015, Algorithms xxthe 10-fold 2015, Algorithms xx 2015, xx 2 2 2 When for on thefourier currenttransform predictor iPPBS-Opt, however, clutters. In recent years, a series of simple and fastcross-validation algorithm based was proposed, some special consideration is needed. This is because a dataset, after optimized by the KNNC and such as spectral residual(SR) [5], phase spectrum of fourier transform(PFT) [6], hypercomplex fourier ITHTS treatments, may miss many experimental negative samples and contain some hypothetical clutters. clutters. In recent clutters. 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With [7]. regards With transform(HFT) [7]. regards to With small to regards small target [7]. to With target detection, small regards detection, [7]. frequency to With detection, small frequency regards domain target frequency domain to detection, method small method domain target isrely frequency quite detection, is method different quite domain different isproposed, frequency quite method different domain is quit clutters. clutters. Infrequency recent years, recent clutters. ahypothetical series years, of In atransform(HFT) series simple recent ofyears, and simple fast atarget series algorithm and fast of algorithm simple based and on based fourier fast algorithm on transform fourier based transform was on fourier was proposed, transform argettransform(HFT) and transform(HFT) tests inbuttransform(HFT) thenot domain. While, spectral residual (SR) approach does not on the a special cross-validation, the so-called target cross-validation, has been introduced here. 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target and tests in the the frequency domain. spectral residual (SR) approach does not rely on the HFT approach HFT approach HFT explains approach explains the intrinsic HFT explains the approach intrinsic theory the intrinsic theory HFT explains of saliency approach oftheory saliency the detector intrinsic explains detector inonly theory the the detector in frequency intrinsic of the saliency frequency in theory domain the detector frequency of domain and saliency in use and domain spectral detector frequency use spectral and in use domain the spectral frequency and small targets small from targets from reconstruction small the targets reconstruction that from isWhile, the calculated that reconstruction issaliency by that the only isphase calculated by the spectrum phase only spectrum ofthe by the the input phase of the signal. spectrum input signal. of ut Although numerous methods have been proposed, ofof them may fail in certain circumstances, 10 ď many ď ďcalculated ď Itsuppress calculates the difference between the original andwhich a psmooth one inwhich the log amplitude to filter suppress tobackground suppress filter repeated tocomputation repeated patterns.S filter repeated patterns.S suppress patterns.S filter to patterns.S ¨ spectrum, ¨of ¨repeated “ “ In (19) all all p1repeated qSR all p2qpatterns.S p10 qsignal iqabout Itparameters. omits It the omits the computation Itto ofomits in the ofthe computation amplitude the amplitude SRallin spectrum, the which amplitude spectrum, saves 1/3 about computational 1/3 saves computational about cost. 1/3cost. com e.g., filter ground-sky [8], which isSR common ininsuppress the helicopter view. this situation, targets are i“saves 1 all spectrum, and then makes up a saliency map by transforming SR to spatial domain. PFT approach detects Although Although numerous Although numerous methods numerous methods Although have methods been have numerous proposed, been Although have proposed, methods been many numerous proposed, many of have them methods been of many may them proposed, fail of may have them in fail been certain many may in proposed, certain fail of circumstances, them in circumstances, certain many may fail circumstances, of them in certain may circu fail a approach HFT approach explains explains the HFT intrinsic approach the intrinsic theory explains saliency theoverlapped of intrinsic saliency detector theory detector in offrequency saliency in the frequency detector domain in and domain theuse frequency spectral and use domain spectral easily mixedHFT up with the background clutters in size andoftheory easily bythe vegetation, roads, rivers, and: small targets from the reconstruction that isincalculated by the phase spectrum input e.g.,[9], ground-sky e.g., ground-sky ground-sky background e.g., [8], background ground-sky which [8], ise.g., common [8], background isground-sky which common is thecommon [8], in helicopter background which helicopter the view. common [8], helicopter view. 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Ininview. this the situation, helicopter Inalgorithm. this targets view. are Intargets this situat are visual system (HVS) has been designed in this paper. HVS istraditional ais kind of layered processing system filter to suppress repeated patterns.S Step 2. One of the 10 sets, say , was singled out as the testing dataset and the remaining nine In order In order to design In to order design an appropriate to an design In appropriate order an method, appropriate to design method, In a order small an method, a appropriate to small target design a target detection small an method, detection appropriate target method a detection small method method, inspired target method inspired a by detection small the inspired by human target the method human by detection the inspired human metho by allup p1q with easilyupmixed with the up easily with background the mixed background clutters in the clutters size background and in size easily and clutters overlapped easily in overlapped size byand vegetation, easily by overlapped roads, by vegetatio rivers, consisting ofeasily opticalmixed system, retina and visual pathways, which is nonuniform and nonlinear. The restvegetation, ofroads, rivers, sets as the training dataset. Although numerous methods have been proposed, ofthis may inpaper. certain circumstances, visualvisual system (HVS) visual system has been has visual (HVS) been system has designed in (HVS) visual this designed in paper. this system has paper. been HVS (HVS) this designed is HVS paper. a many kind has israte abeen HVS in of kind layered designed is of paper. athe layered kind image HVS of infail image this layered processing is aalgorithm kind processing image HVS of system layered processing issystem a kind image of system layered process bridges [9], bridges resulting [9], resulting adesigned huge bridges false a been huge [9], rate resulting false in traditional rate aininhuge traditional algorithm. false algorithm. inthem traditional algorithm. his paper issystem organized as(HVS) follows. In Section 2, we describe the framework of proposed Step 3. The training set was optimized using the KNNC and IHTS treatments as described in e.g., ground-sky background which is common inwhich helicopter view. In this targets are consisting consisting of optical consisting of optical system, of system, optical consisting retina retina system, and of visual and optical consisting retina visual pathways, system, and pathways, of visual which retina pathways, system, and is nonuniform visual isdetection which retina nonuniform pathways, is and and visual nonlinear. which nonlinear. pathways, issituation, and The nonuniform nonlinear. rest The which of rest is and The of nonuniform nonlinear. rest of a In order In to order design to andesign In [8], order an appropriate to method, design method, an aoptical small appropriate target athe small method, target detection anonuniform method small target inspired method detection inspired by the method human by the inspired human for small target detection. In Section 3, we present the experimental results. Section 4would isand the conclusion Section 2.4. After such aappropriate process, the original imbalanced training dataset become a balanced easily mixed with background clutters in size and easily overlapped by vegetation, roads, rivers, thisarticle. paper this paper isone; organized this is paper organized asis follows. organized this asthe paper follows. Inand as Section is follows. organized In this Section 2, paper Inthis as2, Section describe ishas follows. we organized describe 2,HVS the we In framework as Section describe follows. framework 2, the we of In framework the Section describe of proposed 2,the proposed of we framework algorithm describe proposed algorithm the of algorithm the framework proposed o i.e., itsup positive subset negative subset would contain same number samples. Note that visual system visual (HVS) system has (HVS) visual been has designed system been (HVS) designed inwe paper. in been this designed paper. isthe aaHVS kind in this is of alayered paper. kind ofthe HVS image layered is processing athe image kind of processing layered system image system pro of this although the starting value forwe Kfor in the KNNC treatment could be arbitrary, the following empirical bridges [9], aoptical huge false rate in traditional algorithm. for small forconsisting small target for target detection. small detection. target Inof for Section detection. small In Section 3, target In 3, Section present detection. we small present the 3, target we In experimental Section the present detection. experimental 3, theand we results. In experimental present Section results. Section the 3, we Section results. experimental 4present is the 4Section is conclusion the the experimental conclusion 4 is the Section conclusion results. 4rest is the consisting ofresulting optical system, consisting retina system, of and retina optical visual and system, pathways, visual retina pathways, which is visual which nonuniform pathways, is nonuniform and which nonlinear. and isresults. nonuniform nonlinear. The rest The ofand nonlin ofSe approach might be of help to reduce the time for finally finding its optimal value. Suppose the starting Inpaper order to design an appropriate method, aaswe small detection inspired by the human of thisofarticle. this article. of this article. this article. article. 2. Algorithm Based on Visual System this isHuman paper organized isof organized asthis follows. asof follows. is Inthis organized Section In Section follows. describe 2,target weIndescribe the Section framework the 2,method we framework of describe the proposed of thethe framework proposed algorithm of algorithm the prop valuethis for K is K p0q, then wepaper have according to 2, our experience visual system (HVS) has been designed in this paper. HVS is a kind of layered image processing system for smallfor target small detection. target detection. forInsmall Section target In 3, Section we detection. present 3, weIn the present experimental the3,experimental we present results.the Section results. experimental 4Section is the conclusion results. 4 is the Section conclusion 4 is „ Section ´ N 2. Algorithm 2. Algorithm 2. Based Algorithm Based on Human on 2. Based Human Algorithm Visual on Human Visual System Based 2. Algorithm System Visual on Human System Based Visual on Human System Visual System consisting of optical system, retina and visual pathways, which is nonuniform and nonlinear. The rest of 2.1. Framework of the Two of Stage Brief of this article. ofProposed this article. this Algorithm—A article. K p0q “ IntDescription (21) N` this paper is organized as follows. In Section 2, we describe the framework of the proposed algorithm HVS the scene into patches and important information through visual 2.1. divides Framework 2.1. 2.1. of Framework the of Proposed thesmall 2.1. Proposed of Framework Two theAlgorithm Stage Two 2.1. Stage Algorithm—A ofselect the Two Algorithm—A Proposed Stage Algorithm—A Brief ofthe Two the Description Brief Proposed Stage Description Algorithm—A Brief Two Description Stage Algorithm—A Briefattention Description Description forFramework small detection. InProposed Section 3,Framework we present experimental results. Section 4 is theBrief conclusion 2. Algorithm 2.target Algorithm Based on Based Human 2. on Human Visual Based System Visual on Human System Visual System selection mechanism to make it easy to understand and analyze. On the other hand, as a component of this article. HVS divides HVS divides the HVS scene the divides scene into the HVS small into scene small patches into patches the HVS small andscene select divides and patches into select important the small and important scene select patches information into important information and small select through patches information important through and visual select through visual attention information important attention visualthrough attention information visua of low-level 2.1. artificial vision processing, itdivides facilitates subsequent procedures by reducing computational Framework 2.1. Framework of the Proposed 2.1. of the Framework Proposed Two Stage of Two the Algorithm—A Stage Proposed Algorithm—A Two BriefStage Description Brief Algorithm—A Description Brief Description mechanism toBased mechanism make to selection make itreal-time easy toitmechanism to make easy understand selection toit understand easy to mechanism make to and understand analyze. itand easy tothe to make and On understand the analyze. On it other easy the to and other hand, Onunderstand the analyze. hand, as apropose component asOn hand, and a component the analyze. asother a component hand, On theasoth ac cost,selection whichselection is2.mechanism a Algorithm keyselection consideration in applications. Based onanalyze. above knowledge, weother on Human Visual System of low-level of low-level artificial of divides low-level artificial vision artificial vision of processing, low-level processing, vision it artificial of facilitates processing, low-level it small facilitates vision subsequent itartificial processing, facilitates subsequent vision procedures subsequent it patches facilitates procedures processing, by procedures reducing subsequent by itinformation facilitates reducing computational byprocedures reducing computational subsequent computational by procedures reducing com by HVS HVS the divides scene the into HVS scene small divides into patches the and patches select into and small important select important information and select through important visual through information attention visual attention through a framework consisting of two stages inspired by HVS asscene follows (See Figure 1). In predetection stage, cost, which cost, which is cost, a key iswhich aconsideration key consideration iscost, a keywhich in consideration real-time is in acost, real-time keyapplications. which consideration in real-time applications. is a key Based applications. in consideration real-time Based on theon above Based applications. the in real-time above knowledge, on theknowledge, above Based applications. weknowledge, on propose the we above propose Based we knowledge, on propose the abovw
hms 2015, xx
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where N ` and N ´ are the numbers of the total positive and negative samples in the benchmark dataset, respectively, and Int is the “integer truncation operator” meaning to take the integer part for the number in the brackets right after it [116]. Substituting the data of Equation (15) into Equation (21), we obtained K p0q “ 3 or 8 for the surface-residue case or of all-residue case, respectively. Step 4. Use the aforementioned balanced dataset to train the operation engine, followed by applying the iPPBS-Opt predictor to calculate the prediction scores for the testing dataset, which had been singled out in Step 2 before the optimized treatment and hence contained the experiment-confirmed samples only. Step 5. Repeat Steps 2–4 until all the 10 divided sets had been singled out one-by-one for testing validation. Step 6. Substituting the scores obtained from the above 10-round tests into Equation (18) to calculate Sn, Sp, Acc, and MCC. The metrics values thus obtained should be a function of K; for instance, the overall accuracy Acc can be expressed as Acc(K). Step 7. Repeat Steps 2–6 by increasing K with a gap of 1, we consecutively obtained Acc(3), Acc(4), . . . ., Acc(12) for the surface-residue case or Acc(8), Acc(9), . . . ., Acc(17) for the all-residue case, respectively (Figure 4). The value of K that maximized Acc would be taken for iPPBS-Opt in the current study, as given in the footnote c of Table 3. It is instructive to emphasize again that it is absolutely fair to use the above 10-fold cross-validation steps to compare the current predictor with the existing ones. This is because all the predictors concerned were tested using exactly the same experiment-confirmed samples and that all the added hypothetical samples had been completely excluded from the testing datasets.
Figure 4. A plot of Acc vs. K for (a) the surface-residue benchmark dataset (cf. Equation (4)); and (b) the Algorithms 2015, xx 2 all-residue benchmark dataset (cf. Equation (5)). It can be seen from panel (a) that the overall accuracy reaches its peak at K “ 9, and from panel (b) that the overall accuracy reaches its peak at K “ 15 .
s. In recent years, a series of simple and fast algorithm clutters. In based recent on years, fourieratransform series of simple was proposed, and fast algorithm based on fourier Table 3. Comparison of the iPPBS-Opt with the other existing methods via the 10-fold cross-validation s spectral residual(SR) phase spectrum ofsuch fourier as spectral transform(PFT) residual(SR) hypercomplex [5], phase spectrum fourierofdataset fourier transform(PFT) [6 on [5], the surface-residue benchmark dataset (Equation (4)) [6], and the all-residue benchmark (Equation rm(HFT) [7]. With regards to(5)). small target detection, transform(HFT) frequency[7]. domain Withmethod regards istoquite smalldifferent target detection, frequency domain ther methods. It transforms the airspace information from other to the methods. frequency It transforms domain, defines the airspace significant information to the frequency do Benchmark Dataset Method Acc (%) MCC Sn (%) Sp (%) AUC and tests in the frequency domain. While, spectral target residual and tests(SR) in the approach frequency does domain. not relyWhile, on thespectral residual (SR) appro a Deng N/A 0.3456 76.77 63.16 0.7976 b eters. It calculates the difference between theChen original parameters. signal75.09 Itand calculates a smooth theone difference in43.81 the log between amplitude 0.4248 92.12 the original 0.8004 signal and a smooth Surface-residue iPPBS-PseAAC c 84.04 0.5821 58.26 94.14 0.8934 m, and then makes up a saliency map by transforming spectrum, SRand to spatial then makes domain. up aPFT saliency approach map detects by transforming SR to spatial doma Deng a N/A 0.3763 76.33 78.61 0.8465 argets from the reconstruction that is calculated small only targets by the from phase the0.3286 spectrum reconstruction of the that input96.52 issignal. calculated only by the phase spec 73.77 24.95 0.8001 Chen b All-residue c iPPBS-PseAAC 0.4662of1/3 39.14 96.66cost.spectrum, 0.8820 s the computation of SR in the amplitude spectrum, It omitswhich the 85.45 computation saves about SRcomputational in the amplitude which saves about a Results reported by Deng et al. [10]; b Results reported by Chen et al. [11]; c Results obtained on the same pproach explains the intrinsic theory of saliencyHFT detector approach in theexplains frequency thedomain intrinsicand theory use spectral of saliency detector in the frequency testing dataset by the current predictor iPPBS-Opt with its parameter K “ 9 for the surface-residue benchmark suppress repeated patterns.S filter to for suppress repeated patterns.S dataset surf (cf. Equation (4)) and K “ 15 the all-residue benchmark dataset all (cf. Equation (5)). Also see Figure 4 for the details. hough numerous methods have been proposed, many Although of them numerous may failmethods in certain have circumstances, been proposed, many of them may fail i ound-sky background [8], which is common in e.g., theground-sky helicopter view. background In this[8], situation, which targets is common are in the helicopter view. In mixed up with the background clutters in size easily and easily mixed overlapped up with the bybackground vegetation, roads, cluttersrivers, in size and easily overlapped by s [9], resulting a huge false rate in traditional algorithm. bridges [9], resulting a huge false rate in traditional algorithm. rder to design an appropriate method, a small target In order detection to design method an appropriate inspired bymethod, the human a small target detection method
7]. With regards to small target detection, transform(HFT) frequency domain [7]. With method regards is quite to small different target detection, frequency domain method i s. It transforms the airspace information fromtoother the frequency methods. domain, It transforms defines thesignificant airspace information to the frequency domain, de the frequency domain. While, spectral target residual and tests (SR)inapproach the frequency does not domain. rely onWhile, the spectral residual (SR) approach does ulates the difference between the original parameters. signal and It calculates a smooth one the in difference the log amplitude between the original signal12and a smooth one in th Molecules 2016, 21, 95 of 19 makes up a saliency map by transforming spectrum, SR to and spatial thendomain. makes up PFT a saliency approachmap detects by transforming SR to spatial domain. PFT a the reconstruction that is calculated small only by targets the phase from spectrum the reconstruction of the input thatsignal. is calculated only by the phase spectrum of t 3.3. Comparison with the Existing Methods utation of SR in the amplitude spectrum, It omits which thesaves computation about 1/3 of computational SR in the amplitude cost. spectrum, which saves about 1/3 com Listed in Table 3 are the values of the four metrics (cf. Equation (18)) obtained by the current lains the intrinsiciPPBS-Opt theory of predictor saliency using detector HFTthe approach in the10-fold frequency explains the domain intrinsic and use of saliency benchmark detector indataset the frequency domain target cross-validation ontheory the spectral surface-residue epeated patterns.Ssurf (Equation (4)) and filter suppressbenchmark repeated patterns.S the to all-residue dataset all (Equation (5)), respectively. See S1 Dataset for the details of the two benchmark datasets. For facilitating the corresponding rous methods have been proposed, many Although of them numerous may fail inmethods certain have circumstances, beencomparison, proposed, many of them may fail in certain results obtained by the existing methods [10,11] are also given there. ackground [8], which is common in the e.g.,helicopter ground-sky view. background In this situation, [8], which targets is common are in the helicopter view. In this situa As we can see from the table, the new predictor iPPBS-Opt proposed in this paper remarkably ith the background clutters inits size andeasily easilymixed overlapped up with the vegetation, background roads, clutters rivers, in size easily accuracy, overlapped by vegetatio outperformed counterparts, particularly inby Acc and MCC; the former stands for and the overall and in thetraditional latter for the stability. the resulting first glance, although value of Sn by Deng et al.’s method [10] ng a huge false rate algorithm. bridgesAt[9], a huge falsetherate in traditional algorithm. is higher thanathat of the current predictor whenantested by the benchmark its method inspired ign an appropriate method, small target In order detection to design method inspired appropriate bysurface-residue the method, humana small target dataset, detection corresponding Sp value is more than 30% lower than that of the latter, indicating the method [10] is S) has been designed in this paper. HVS visual is asystem kind of(HVS) layeredhas image beenprocessing designed insystem this paper. HVS is a kind of layered image pr very unstable with extremely high noise. al system, retina and Because visual pathways, consisting which is nonuniform of optical and nonlinear. retina and The visual rest(see, of pathways, which ishere nonuniform and nonlin graphic approaches can providesystem, useful intuitive insights e.g., [117–122]), we also provide a graphic comparison of the current predictor with their counterparts via the Receiver ized as follows. In Section 2, we describe this paper the framework is organizedofasthefollows. proposed In algorithm Section 2, we describe the framework of the prop Operating Characteristic (ROC) plot [123], as shown in (Figure 5). According to ROC [123], the larger tection. In Section 3, we present the experimental for small target results. detection. Section In 4Section is the conclusion 3, we present the experimental results. Section 4 i the area under the curve (AUC), the better the corresponding predictor is. As we can see from the of this figure, the area under the ROCarticle. curve of the new predictor is remarkably greater than those of their
ed on Human
counterparts fully consistent with the AUC values listed on Table 3, once again indicating a clear improvement in comparison with the Visual existing System ones. Visual Systemof the new 2. predictor Algorithm Based on Human
the Proposed Two Stage Algorithm—A 2.1. Brief Framework Description of the Proposed Two Stage Algorithm—A Brief Description
e scene into small patches and select important HVS divides information the scene through into small visualpatches attention and select important information through sm to make it easy to understand andselection analyze.mechanism On the other to make hand,itaseasy a component to understand and analyze. On the other hand, ial vision processing, it facilitates subsequent of low-level procedures artificialby vision reducing processing, computational it facilitates subsequent procedures by reducing y consideration in real-time applications. cost,Based whichon is the a key above consideration knowledge, in we real-time propose applications. Based on the above knowled sting of two stages inspired by HVS as a framework follows (See consisting Figure 1). of In two predetection stages inspired stage, by HVS as follows (See Figure 1). In pre M) is obtained and the most salient region a saliency is picked map(SM) up toisimprove obtaineddetection and the speed. most salient region is picked up to improve d a support vector machines (SVM) classifier In detection is used stage, to get a support the target vector quickly. machines (SVM) classifier is used to get the target q Figure 5. The ROC (Receiver Operating Characteristic) curves to show the 10-fold cross validation by iPPBS-Opt, Deng et al.’s method [10], and Chen et al.’s method [11] on (a) surface-residue benchmark dataset; and (b) the all-residue benchmark dataset. As shown on the figure, the area under the ROC curve for iPPBS-Opt is obviously larger than those of their counterparts, indicating a clear improvement of the new predictor in comparison with the existing ones.
Figure 1. TheAll proposed framework inspired byiPPBS-Opt HVS. Figure by HVS. the above facts have shown that is really1.a The very proposed promising framework predictor for inspired identifying
protein-protein binding sites. Or at the very least, it can play a complementary role to the existing methods in this area. Particularly, none ofthe theprime existing predictors has provided a web layers structure, prediction the algorithm computational Due to complexity the two layers becomes structure, the algorithm concern. computational complexity becomes the server. In contrast to this, a user-friendly and publically accessible web server has been established and high processing speed, saliency For detection the simplicity methods and in the high frequency processing domain speed, aresaliency detection methods in the freque for iPPBS-Opt at http://www.jci-bioinfo.cn/iPPBS-Opt, which is no doubt very useful for the majority of experimental scientist in this or related areas without the need to follow the complicated mathematical equations. Why could the proposed method be so powerful? The reasons are as follows: First, the KNNC and IHTS treatments have been introduced to optimize the training datasets, so as to avoid many misprediction events caused by the highly imbalanced training datasets used in previous studies. Second, the ensemble technique has been utilized in this study to select the most relevant one from seven classes of different physicochemical properties. Third, the wavelets transform technique has
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been applied to extract some important key features, which are deeply hidden in complicated protein sequences. This is just like the studies in dealing with the extremely complicated internal motions of proteins, it is the key to grasp the low-frequency collective motion [74,75] for in-depth understanding or revealing the dynamic mechanisms of their various important biological functions [84], such as cooperative effects [78], allosteric transition [80,81], assembly of microtubules [83], and switch between active and inactive states [76]. Fourth, the PseAAC approach has been introduced to formulate the statistical samples, which has been proved very useful not only in dealing with protein/peptide sequences, but also in dealing with DNA/RNA sequences, as elaborated in a recent review paper [124]. 3.4. Web Server and User Guide To enhance the value of its practical applications, a web-server for iPPBS-Opt has been established at http://www.jci-bioinfo.cn/iPPBS-Opt. Furthermore, to maximize the convenience for the majority of experimental scientists, a step-to-step guide is provided below: Step 1. Opening the web-server at http://www.jci-bioinfo.cn/iPPBS-Opt, you will see the top page of iPPBS-Opt on your computer screen, as shown in Figure 6. Click on the Read Me button to see a brief introduction about the iPPBS-Opt predictor.
Figure 6. A semi-screenshot of the top page for the web server iPPBS-Opt at http://www.jci-bioinfo.cn/iPPBS-Opt.
Step 2. Either type or copy/paste the query protein sequences into the input box at the center of Figure 6. The input sequence should be in the FASTA format. For the examples of sequences in FASTA format, click the Example button right above the input box. Step 3. Click on the Submit button to see the predicted result. For example, if you use the two query protein sequences in the Example window as the input, after 20 s or so, you will see the following on the screen of your computer: (1) Sequence-1 contains 109 amino acid residues, of which 11 are highlighted with red, meaning belonging to binding site; (2) Sequence-2 contains 275 residues, of which 25 are highlighted with red, belonging binding site. All these predicted results are fully consistent with experimental observations except for residues 53 in sequence-1 and residues 62 and 249 in sequence-2 that are overpredicted.
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Step 4. As shown on the lower panel of Figure 6, batch prediction can also be selected by entering an e-mail address and the desired batch input file (in FASTA format naturally) via the Browse button. To see the sample of batch input file, click on the button Batch-example. Step 5. Click on the Citation button to find the relevant papers that document the detailed development and algorithm of iPPBS-Opt. Step 6. Click the Supporting Information button to download the benchmark dataset used in this study. 4. Conclusions It is a very effective approach to optimize the training dataset via the KNNC treatment and IHTS treatment to enhance the prediction quality in identifying the protein-protein binding sites. This is because the training datasets constructed in this area without undergoing such an optimization procedure are usually extremely skewed and unbalanced, with the negative subset being overwhelmingly larger than the positive one. It is anticipated that the iPPBS-Opt web server presented in this paper will become a very useful high throughput tool for identifying protein-protein binding sites, or at the very least, a complementary tool to the existing prediction methods in this area. Supplementary Materials: Supplementary materials can be accessed at: http://www.mdpi.com/1420-3049/21/1/95/s1. Acknowledgments: The authors wish to thank the two anonymous reviewers, whose constructive comments are very helpful for strengthening the presentation of this paper. This work was partially supported by the National Nature Science Foundation of China (No. 61261027, 61262038, 31260273, 61202313), the Natural Science Foundation of Jiangxi Province, China (No. 20122BAB211033, 20122BAB201044, 20132BAB201053), the Scientific Research plan of the Department of Education of JiangXi Province (GJJ14640), The Young Teacher Development Plan of Visiting Scholars Program in the University of Jiangxi Province. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Author Contributions: Jianhua Jia: conducted the computation and wrote the preliminary version for the paper; Zi Liu: helped to establish the web-server; Xuan Xiao: provided the facilities and participated in the analysis and discussion; Bingxiang Liu: provided the facilities and participated in the analysis and discussion; Kuo-Chen Chou: guided the entire research, analyzed the computed results, and finalizing the paper. Conflicts of Interest: The authors declare no conflict of interest.
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Sample Availability: All the samples used in this study for training and testing the predictor are available by downloading them from the web-server at http://www.jci-bioinfo.cn/iPPBS-Opt. © 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).
