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Genetic Particle Swarm Optimization–Based Feature Selection for Very-High-Resolution Remotely Sensed Imagery Object Change Detection Qiang Chen 1,2 , Yunhao Chen 1,2, * and Weiguo Jiang 2,3, * 1 2 3

*

State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University, Beijing 100875, China; [email protected] College of Resources Science and Technology, Beijing Normal University, Beijing 100875, China Academy of Disaster Reduction and Emergency Management Ministry of Civil and Ministry of Education, Beijing Normal University, Beijing 100875, China Correspondence: [email protected] (Y.C.); [email protected] (W.J.); Tel.: +86-10-5880-6098 (Y.C.); +86-10-5880-2070 (W.J.)

Academic Editor: Jason K. Levy Received: 10 June 2016; Accepted: 25 July 2016; Published: 30 July 2016

Abstract: In the field of multiple features Object-Based Change Detection (OBCD) for very-high-resolution remotely sensed images, image objects have abundant features and feature selection affects the precision and efficiency of OBCD. Through object-based image analysis, this paper proposes a Genetic Particle Swarm Optimization (GPSO)-based feature selection algorithm to solve the optimization problem of feature selection in multiple features OBCD. We select the Ratio of Mean to Variance (RMV) as the fitness function of GPSO, and apply the proposed algorithm to the object-based hybrid multivariate alternative detection model. Two experiment cases on Worldview-2/3 images confirm that GPSO can significantly improve the speed of convergence, and effectively avoid the problem of premature convergence, relative to other feature selection algorithms. According to the accuracy evaluation of OBCD, GPSO is superior at overall accuracy (84.17% and 83.59%) and Kappa coefficient (0.6771 and 0.6314) than other algorithms. Moreover, the sensitivity analysis results show that the proposed algorithm is not easily influenced by the initial parameters, but the number of features to be selected and the size of the particle swarm would affect the algorithm. The comparison experiment results reveal that RMV is more suitable than other functions as the fitness function of GPSO-based feature selection algorithm. Keywords: feature selection; particle swarm optimization; change detection; remote sensing

1. Introduction Object change detection in Very-High-Resolution (VHR) remotely sensed imagery has become a hot topic in the field of remotely sensed imagery analysis, and object-oriented image analysis has been the primary way to solve the “salt and pepper” problem [1], which commonly occurred in pixel-based image analysis. In the field of object-based change detection (OBCD), VHR imagery is usually segmented to several objects and the image objects are regarded as the basic processing units. The main difference between pixel-based change detection and object-based change detection is that image objects have more feature information, so multi-feature image analysis can identify more change information for VHR remotely sensed imagery [2,3]. Feature selection selects a subset of relevant features from the available features to improve change detection performance relative to using single features. Existing feature selection algorithms can be broadly classified into two categories: filter approaches and wrapper approaches [4]. Wrappers achieve better results than filters, because wrappers include a learning algorithm as part of the evaluation Sensors 2016, 16, 1204; doi:10.3390/s16081204

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function. There are two components of a feature selection algorithm: the search algorithm and the evaluation function [5]. Common methods of feature selection are principal component analysis [6], Sequential Forward Selection (SFS) [7], Sequential Float Forward Selection (SFFS) [8] and Backtracking Search Optimization Algorithm (BSO) [9]. It is difficult to implement a global search in the high-dimensional feature space for these algorithms. Further, the search process is separate from the evaluation process, so it is easy to fall into the trap of local convergence. Subsequently, Evolutionary Computation (EC) algorithms have been used for the feature selection problem, such as simulated annealing [10], Genetic Algorithms (GA) [11,12], Differential Evolution algorithm (DE) [13] and swarm intelligent algorithms, in particular Cuckoo Search (CS) [14,15], ant Colony Optimization (CO) [16] and Particle Swarm Optimization (PSO) [17]. These algorithms have the advantages of high efficiency, high speed and low cost, but they also have random components and some results are hard to reproduce in experiments. As a typical example of EC algorithms, PSO has a high search ability and is computationally less expensive than some other EC algorithms, so it has been used as an effective technique in feature selection. Starting with a random solution, PSO searches for the optimum solution in the feature space according to some mechanism, and the search space can be expanded to the whole problem space without incurring more cost. That is, PSO is an adaptive probabilistic search algorithm, and only the objective function rather than gradient information is needed to evaluate the fitness of solutions. Moreover, PSO is an easily implemented algorithm, has less adjustable parameters and is also computationally inexpensive in both speed and memory requirements [18]. The genetic particle swarm optimization (GPSO) algorithm integrates PSO with GA to improve solution speed and global search ability, and has been widely used in optimal selection problems [18–22]. GPSO has some advantages such as optimization ability of fast approaching to the optimal solution, simple parameters setup and high global search ability to avoid the local optimal problem. But the drawbacks of GPSO mainly include that it easily falls into the local optimal solution in late iteration, and the different parameters setup, such as swarm scale, would affect the efficiency and cost of algorithm [18]. Nazir proposed an efficient gender classification technique for real-world facial images based on PSO and GA selecting the most import features set for representing gender [19]. Inbarani proposed a supervised feature selection method based on hybridization of PSO and applied this approach to diseases diagnosis [20]. Yang proposed a novel feature selection and classification method for hyperspectral images by combining PSO with SVM, and the results indicate that this hybrid method has higher classification accuracy and effectively extracts optimal bands [21]. Chuang et al. [22] applied the so-called catfish effect to PSO for feature selection, claiming that the catfish particles help PSO avoid premature convergence and lead to better results than sequential GA, SFS, BSO and other methods. Additionally, GPSO has also been applied in the field of remotely sensed imagery analysis, such as image segmentation [23], image classification [24,25] and hyperspectral band selection [26]. Up to now, several PSO-based feature selection methods have been proposed in the literature [4,18,25,27,28]. However, GPSO-based feature selection has seldom been used in remotely sensed image change detection. Fitness functions are an important part of GPSO-based feature selection algorithms, and they are used to evaluate the selected feature subset during the search process, by comparing the current solution with established evaluation criterion for particle updates and termination of the procedure. Fitness functions are commonly built based on correlation, distance metrics and information gain. Furthermore, the classification error rate of a classifier also has been used to build the fitness function in the wrapper feature selection method. It is worth noting that the fitness function used for GPSO should be related to the aim of the research. Existing studies on OBCD for VHR remotely sensed imagery base feature selection primarily on expert knowledge or experimental data, both of which have a low efficiency rate and a low precision rate [29]. This paper proposes a GPSO feature selection algorithm to be utilized in OBCD by using object-based hybrid multivariate alternative detection (OB-HMAD) model, and analyzes the fitness

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convergence and OBCD accuracy of the algorithms using the ratio of mean to variance (RMV) as the fitness function. Additionally, we discuss the sensitivity of the number of features to be selected and the scale of the particle swarm to the precision and efficiency of the algorithm, and analyze the reliability of RMV by comparing with other fitness functions. Therefore, our paper is organized into five sections. Section 2 presents the theoretical constructions behind our proposed GPSO-based feature selection approach using a RMV fitness function, and illustrates how our technique can be used for multiple features OBCD. Analysis of our results obtained for two experimental cases are reported in the Section 3, sensitivity of GPSO-based feature selection algorithm has been discussed in the Section 4, while Section 5 outlines our conclusions. 2. Methodology 2.1. Genetic Particle Swarm Optimization PSO uses an information-sharing mechanism that allows individuals to learn from each other to promote the development of the entire swarm. It has excellent global search ability even in high-dimensional solution spaces. In PSO, possible solutions are called particles, and each particle i comprises three parts: xi , the current position of the particle; vi , the current velocity of the particle, which also denotes the recursive solution update; and pbesti , the personal best position of the particle which is the best local solution. The solution space is searched by starting from particles randomly distributed as in a swarm. Assume M features are to be selected, and let a particle xi (of size M ˆ 1) denote the selected feature indices, and vi denote the update for selected feature indices. Then the particle swarm is composed of N particles (N is the size of particle swarm), and every particle has a position vector xi to indicate its position and a velocity vector vi to indicate its flying direction and speed. As the particle flies in the solution space, it stores the best local solution pbesti and the best global solution gbesti . Here, possible solutions are called particles, and recursive solution update is called velocity. Initially, the particles are distributed randomly and updated depending on the best local solution pbesti and global solution gbesti . The algorithm then searches for the optimal solution by updating the position and the velocity of each particle according to the following equations: νi pt ` 1q “ ωνi ptq ` c1 r1 ppbesti ptq ´ xi ptqq ` c2 r2 pgbesti ptq ´ xi ptqq

(1)

xi pt ` 1q “ xi ptq ` νi pt ` 1q

(2)

where i = 1,2, . . . ,n, N is the total number of particles in the swarm, r1 and r2 are random numbers chosen uniformly from (0,1), c1 and c2 are learning factors (c1 denotes the preference for the particle’s own experience, and c2 denotes the preference for the experience of the group), t is the number of iteration, and ω is the inertia weight factor that controls the impact of the previous velocity vi which provides improved convergence performance in various applications [30]. Because feature indices are discrete values, rounding off the solutions to adapt the continuous PSO to a discrete form is necessary. Adapted from the GA, a crossover operator is used in PSO to improve the global searching capability and to avoid running into local optimum. After updating the position vector xi and the velocity vector vi of the particle using Equations (1) and (2), the algorithm calculates a crossover with two particles, as follows: child1 pxi q “ ωi ˆ parent1 pxi q ` p1 ´ ωi q ˆ parent2 pxi q

(3)

child2 pxi q “ ωi ˆ parent2 pxi q ` p1 ´ ωi q ˆ parent1 pxi q

(4)

pparent1 pνi q ` parent2 pνi qq ˆ |parent1 pνi q| |parent1 pνi q ` parent2 pνi q|

(5)

child1 pνi q “

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child2 pνi q “

pparent1 pνi q ` parent2 pνi qq ˆ |parent2 pνi q| |parent1 pνi q ` parent2 pνi q|

(6)

Relative to PSO, this GPSO algorithm has a crossover operation that occurs after updating the position and velocity, and uses the gendered descendant particles rather than the parent particles for the next iteration. The crossover operation helps the descendant particles to inherit the advantages of their parent particles and maintains population diversity. The crossover mechanism selects the particle from all particles into the cross-matching pool with a certain degree of crossover probability, which has been determined beforehand and remains unchanged throughout the crossover process; matches any two particles in the pool randomly, determines the crossover point by the crossover weight wi , which has been calculated by the fitness value of particle, generates the descendant particle by the crossover operation. 2.2. Ratio of Mean to Variance Fitness Function According to the purpose of change detection, we choose RMV as the fitness function for evaluating the fitness of particles in the GPSO algorithm, which denotes the availability of the candidate feature in the image object feature dataset. In general, the mean and variance of a data set are related to the important feature information, so some features are used to compare the samples belonging to different classes [31]. This denotes the separability of a multi-class sample by normalizing the mean of the feature dataset according to its variance and comparing it among the different classes. Assume that A and B are feature datasets belong to different classes, where A is the dataset of changed samples that have the feature f, and B is the dataset of unchanged samples that have the feature f. Then, the importance of feature f can be expressed by Equations (7) and (8):

Sf “

ˇ ˇ ˇ ˇ ˇmean f pAq ´ mean f pBqˇ Vf

(7)

d Vf “

Var f pAq Var f pBq ` nA nB

(8)

where Sf is the significance of feature f and represents the potential to classify the two dataset A and B, meanf (A) and meanf (B) are the means datasets A and B, Varf (A) and Varf (B) are the variances of datasets A and B, and nA and nB are the number of samples in A and B, respectively. The optimum features are selected from the feature dataset once the features have been sorted by the feature importance index. Assume that M features are to be selected, then the importance matrix S can be constructed by the obtained importance index of M features for each class, and the mean value of the feature importance SAVG can also be calculated using the feature importance matrix S, which has M feature importance indices: M 1 ÿ S AVG “ Sf (9) M f “1

The objective function J is given as follow: J “ Vs ˆ S2AVG VS “

M ÿ f “1

S f , if S f ą S AVG

(10) (11)

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It It is is apparent and J indicate stronger classification capability of the apparentthat thatlarger largervalues valuesof ofSSAVG AVG and J indicate stronger classification capability of the selected feature subset from the feature dataset, the fitness fitness function functionofofRMV RMVis:is: selected feature subset from the feature dataset, so so the ˛2 ¨ 2  1 M  ÿ M (12)(12)  VS“ ´V ˆ ˝ Fitness S 1 Sf ‚ Fitness  RMVpRMV q  MS f 1 f M   



f “1

2.3. GPSO-Based ChangeDetection Detection 2.3. GPSO-BasedFeature FeatureSelection Selectionfor for Object-Based Object-Based Change When selectionalgorithm algorithmisisused usedininthe the field multiple Whenthe theproposed proposedGPSO-based GPSO-based feature feature selection field of of multiple features objectedbased basedchange changedetection, detection, the essential are selected from thethe features objected essentialstep stepisishow howthe thefeatures features are selected from feature set.After Afterthe thefeatures featureshave have been been extracted extracted from features setset hashas been feature set. fromthe theimage imageobject objectand andthe the features been built in the field of OBCD, we give each feature an index, then these feature indices have been selected built in the field of OBCD, we give each an index, then these feature indices have been selected GPSO-basedfeature featureselection selectionalgorithm. algorithm. Figure indexes update in the byby GPSO-based Figure 11explains explainshow howthe thefeature feature indexes update in the iterationofofGPSO GPSOalgorithm, algorithm,and and itit illustrates illustrates one iteration step when iteration one particle particlebefore beforeand andafter afterone one iteration step when selectingsix sixfeatures features from from the the image setset which hashas L features. At the six selecting imageobject objectfeature feature which L features. Att-th theiteration, t-th iteration, T, and GPSO determines the update v(i) = features are selected by each particle, x(t) = (F1,F2,…,F6) T six features are selected by each particle, x(t) = (F1,F2, . . . ,F6) , and GPSO determines the update (v1,v2,…,v6)T. At the (t + 1)-th iteration, the selected feature indices becomes x(t + 1) = (F1’,F2’,…,F6’)T. v(i) = (v1,v2, . . . ,v6)T . At the (t + 1)-th iteration, the selected feature indices becomes x(t + 1) = (F1’,F2’, According to the Figure 1, one particle xi denote a kind of feature combination, also can be regarded . . . ,F6’)T . According to the Figure 1, one particle xi denote a kind of feature combination, also can as a potential solution for the feature selection problem. At the end of iterations, the feature indices be regarded as a potential solution for the feature selection problem. At the end of iterations, the included in the best global solution gbesti of the particle swarm is the optimal result of feature feature indices included in the best global solution gbesti of the particle swarm is the optimal result of selection. feature selection.

Figure 1. 1. Illustration (GeneticParticle ParticleSwarm SwarmOptimization)-based Optimization)-based Figure Illustrationofofone oneparticle particle update update for for GPSO GPSO (Genetic feature selection. feature selection.

The procedures of the proposed GPSO-based feature selection algorithm are described as The procedures of the proposed GPSO-based feature selection algorithm are described as follows follows (Figure 2) (Figure [26]. 2) [26]. Step Normalizeand andset setthe theparameters, parameters, including swarm N,N, thethe learning ‚  Step 1: 1: Normalize including the thesize sizeofofthe theparticle particle swarm learning factors c 1 and c2, the inertia weight factor ω and the maximum number of iterations itermax; factors c1 and c2 , the inertia weight factor ω and the maximum number of iterations itermax ;  Step 2: Assume that M features are about to be selected from the feature set, and randomly ‚ Step 2: Assume that M features are about to be selected from the feature set, and randomly initialize N particles xi, and each particle includes M indices of the features to be selected; initialize N particles xi , and each particle includes M indices of the features to be selected;  Step 3: Evaluate the fitness of each particle by Equation (12), and determine pbesti and gbesti; ‚  Step 3: 4: Evaluate fitness ofand each particle by Equation (12), and determine pbest i and gbesti ; Step Update the the position velocity vectors of each particle using Equations (1)–(6); ‚  Step 4: 5: Update the position and velocity vectors of each particle using Equations (1)–(6); Step If the algorithm is converged, then stop; otherwise, go to Step 3 and continue; ‚  Step 5: If the algorithm is converged, then stop; otherwise, go to Step 3 and continue; Step 6: The particle yielding the global optimum solution gbesti is the final solution and includes the6:selected featureyielding subset. the global optimum solution gbesti is the final solution and includes ‚ Step The particle theAdditionally, selected feature subset. to validate the fitness convergence and OBCD accuracy of proposed GPSO-based feature selection to algorithm, we fitness chooseconvergence Backtrackingand Search Optimization and Additionally, validate the OBCD accuracy ofalgorithm proposed (BSO) GPSO-based Cuckoo Search (CS) algorithm to compare with the GPSO algorithm. feature selection algorithm, we choose Backtracking Search Optimization algorithm (BSO) and Cuckoo also a kind of bionicwith algorithm and algorithm. a population-based iterative evolution algorithm Search BSO (CS) is algorithm to compare the GPSO designed to be a global minimizer. The crossover strategy improved the iterative global search ability algorithm of BSO, BSO is also a kind of bionic algorithm and a population-based evolution which is similar with the GPSO. Different with GPSO, BSO has a boundary control mechanism, which designed to be a global minimizer. The crossover strategy improved the global search ability of

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is effective in achieving population diversity, ensuring efficient searches, even in advanced BSO, which is similar with the GPSO. Different with GPSO, BSO has a boundary control mechanism, generations [9], and it may be where more advanced than GPSO. Similar with the GPSO, CS which is effective in achieving population diversity, ensuring efficient searches, even in advanced algorithms also is a swarm intelligent algorithm, and the selection of optimal solution depends on generations [9], and it may be where more advanced than GPSO. Similar with the GPSO, CS algorithms the comparison of fitness value. Different with GPSO, CS updates the location and search path also is a swarm intelligent algorithm, and the selection of optimal solution depends on the comparison according to the random-walk mechanism, which has better global ability than GPSO and can keep of fitness value. Different with GPSO, CS updates the location and search path according to the a good balance between local search strategy and exploration of the entire search space. Nevertheless, random-walk mechanism, which has better global ability than GPSO and can keep a good balance the GPSO has improved its global search ability by importing into the cross operator in the iteration between local search strategy and exploration of the entire search space. Nevertheless, the GPSO has procedure. improved its global search ability by importing into the cross operator in the iteration procedure.

v i (t  1)   v i (t )  c 1 r1 ( pbest i (t ) - x i (t ))  c 2 r2 ( gbest i (t ) - x i (t )) x i (t  1)  x i (t )  v i (t  1)

Figure 2. Flowchart of GPSO-based feature selection algorithm. Figure 2. Flowchart of GPSO-based feature selection algorithm.

3. Results 3. Results To validate the the reliability andand effectiveness selectionalgorithm algorithmfor for To validate reliability effectivenessofofGPSO-based GPSO-based feature feature selection multimulti-feature OBCD, two experiments were carried out on two pairs of Worldview-3 and Worldview-2 feature OBCD, two experiments were carried out on two pairs of Worldview-3 and Worldview-2 VHR VHR remotely sensed images. Moreover, we also analyzed the fitness convergence and theand accuracy of remotely sensed images. Moreover, we also analyzed the fitness convergence the accuracy GPSOofalgorithm by comparison with BSO andBSO CS and algorithms. GPSO algorithm by comparison with CS algorithms. 3.1. Case A: Feature Selection for Multiple Features OBCD in Farmland Area 3.1. Case A: Feature Selection for Multiple Features OBCD in Farmland Area 3.1.1. Materials and Study Area 3.1.1. Materials and Study Area The multi-temporal VHR remotely sensed imagery data used in experiment Case A was taken by The multi-temporal VHR satellites remotely [32]. sensed dataimage used in experiment Case A was the Worldview-3 and Worldview-2 Theimagery WV-3 VHR was taken 17 October 2014,taken by WV-2 the Worldview-3 satellites [32].These The WV-3 VHR image was cropped taken 17into October and the VHR imageand wasWorldview-2 taken 27 September 2010. two images have been 2014, and the WV-2 VHR image was taken 27 September 2010. These two images have been cropped sub-images of size 500 ˆ 500 pixels with four spectral bands: blue, green, red and NIR, with spatial into sub-images of size × 500 pixels with four spectral bands: blue, green, red and NIR, with resolutions of 1.38 m and 1.84500 m, respectively. spatial resolutions of 1.38 m and 1.84 m, respectively.

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Geometric correction and relative radiometric correction of multi-temporal remotely sensed Geometric correction and relative radiometric correction of multi-temporal remotely sensed imagery are important procedures in VHR image change detection [33]. First, 50 ground control imagery are important procedures in VHR image change detection [33]. First, 50 ground control points are distributed across each image, ensuring that the root-mean-square error is less than one points are distributed across each image, ensuring that the root-mean-square error is less than one pixel through geometric calibration; Second, 50 pseudo-invariant feature points are selected, and the pixel through geometric calibration; Second, 50 pseudo-invariant feature points are selected, and the differences of solar radiation or atmospheric condition between the two images are eliminated or differences of solar radiation or atmospheric condition between the two images are eliminated or reduced by relative radiometric correction based on robust regression. reduced by relative radiometric correction based on robust regression. Study area A is located to the north of Beijing (China), which is nearby the Modern Agricultural Study area A is located to the north of Beijing (China), which is nearby the Modern Agricultural Demonstrative Garden of Beijing (Figure 3). It is typical farmland area, which dominates the changed Demonstrative Garden of Beijing (Figure 3). It is typical farmland area, which dominates the changed land use type between 2010 and 2014. The changes in land cover include returning farmland to forest, land use type between 2010 and 2014. The changes in land cover include returning farmland to forest, and alterations to the texture or shape of farmland. To validate the accuracy of the test algorithms, and alterations to the texture or shape of farmland. To validate the accuracy of the test algorithms, 212 samples were collected in the study area, which were used to be the test samples. 212 samples were collected in the study area, which were used to be the test samples.

2014

116°26'20"E

116°26'30"E

116°26'40"E 0

125

116°26'50"E 250

40°10'10"N 40°10'0"N 40°9'50"N

40°9'50"N

40°10'0"N

40°10'10"N

2010

116°26'20"E 500

750

116°26'30"E Meters 1,000

116°26'40"E

116°26'50"E

Figure 3. 3. True True color color synthesis synthesis of of images images of ofstudy studyarea areanearby nearbythe theModern ModernAgricultural AgriculturalDemonstrative Demonstrative Figure Garden of of Beijing Beijing (China) (China) acquired acquired by Worldview-2/3 Worldview-2/3 VHR VHR multispectral multispectral sensor sensor on: on: (a) (a)27 27September September Garden 2010; and and (b) (b) 20 20 October October 2014. 2014. 2010;

3.1.2. 3.1.2. Image Image Object Object Feature Feature Extraction Extraction In In the the field field of of object-based object-based image image analysis, analysis, each each image image should shouldbe besegmented segmentedinto intoimage imageobjects, objects, which which are the basic unit of image analysis or processing. The The image image objects objects were were obtained obtained using using the the Multi-Resolution Segmentation (MRS) model [34,35] in this study. The parameters of the MRS model Multi-Resolution Segmentation model [34,35] in this study. The parameters of the MRS model include include the the scale scale of of segmentation, segmentation, the the weight weight of of the the shape shape criterion criterion and and the the weight weight of ofthe thecompactness compactness criterion, criterion, which which we we set set to tobe be150, 150,0.4 0.4and and0.35, 0.35,respectively, respectively,for foranalyzing analyzingthe theheterogeneity heterogeneityof ofimages. images. These These two two multiple-feature multiple-feature temporal temporal images images were were segmented segmented into into 526 526 objects objectsusing usingthe theMRS MRSmodel, model, available software (Trimble Navigation Ltd., Broomfield, CO,CO, USA). To available in ineCognition eCognitionDeveloper Developer9.2 9.2 software (Trimble Navigation Ltd., Broomfield, USA). guarantee that corresponding objects at different times were segmented exactly the same way, we To guarantee that corresponding objects at different times were segmented exactly the same way, carried out out image segmentation on on eight image layers overlain ononthe we carried image segmentation eight image layers overlain thetwo twoimages imageswith withthe the four four spectral spectral bands. bands. Image Image object object features features consist consist of of spectral, spectral, geometric geometric and and texture texture characteristics. characteristics. Table Table 11 illustrates illustrates the the texture features areare calculated using the the greygrey levellevel cothe feature featureset setselected selectedininthis thisstudy, study,where where the texture features calculated using occurrence matrix (GLCM) [36,37]. There are 20 of image object features in theinfeature set, and co-occurrence matrix (GLCM) [36,37]. There arekinds 20 kinds of image object features the feature set, these feature indices werewere coded in a certain order. and these feature indices coded in a certain order.

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Table 1. Spectral, texture and geometric features of image objects. Case Case A

Spectral

Geometric

Texture (GLCM-Based)

Mean NDVI

Shape Index Density

GLCM-Correlation GLCM-Contrast GLCM-Entropy GLCM-Mean

In OBCD, change information is usually reflected in the variance image, which is obtained by directly comparison or image transformation methods [38]. The changed objects then can be extracted from the variance image by threshold segmentation. Considering the purpose of this study, we choose the multivariate alternative detection algorithm [39] to build the variance image, as it is well suited to multi-feature OBCD, and choose the histogram curvature analysis algorithm to extract the changed objects. The resulting OBCD model is the OB-HMAD (Objected-Based Hybrid Multivariate Alternative Detection) algorithm [40], which has the advantages of multi-tunnel processing and maximum retention of original change information, and it can protect the diversity between multi features in OBCD and obtain variation image with the enhance change information by nonlinear transformation, so it is suitable for the OBCD method in this study. 3.1.3. Convergence Analysis of GPSO The convergence analysis of GPSO-based feature selection algorithms is related to the global search ability and efficiency of the algorithm, and compares the average fitness and the optimum fitness. The average fitness (fitnessavg ) represents the efficiency of the algorithm, and can represent the global search ability in combination with the optimum fitness (fitnessopt ). The initial parameters in the GPSO-based feature selection algorithm are set as follows: the initial size of the particle swarm is N = 60, the learning factors are c1 = 2.8 and c2 = 1.3, the inertia weight factor is ω = 0.9, the maximum number of iterations is itermax = 80, and the number of features to be selected is M = 6, so each particle includes six types of feature. To analyze the fitness convergence of the GPSO-based feature selection algorithm, we compare the performance with the BSO and CS algorithms. Additionally, our GPSO, BSO and CS algorithms have been developed and implemented in Matlab 2010b software. In Table 2, Iterationcon is the number of iterations required for the algorithm to converge, and Dcon is the difference between the final values of fitnessavg and fitnessopt . As indicated in Table 2 and Figure 4, BSO has the fastest convergence speed, but Dcon for BSO is much larger than in the other cases, which means that BSO tends to convergence locally. Conversely, CS escapes local optima but has a slower convergence speed than GPSO. The optimum final value of fitnessavg is obtained by GPSO and the convergence curve are more stable than in the others. Additionally, the parameters of Dcon for GPSO in different cases are close to each other. The result reveals that GPSO is superior at finding optima avoiding premature convergence compared with CS and BSO. Table 2. Analysis results of fitness convergence in Case A. Case

Feature Selection Algorithms

BSO

CS

GPSO

Case A

Iterationcon Final fitnessavg Dcon

29 ´296 64

46 ´335 27

40 ´345 17

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0 Fitnessopt

Fitness

-50

Fitnessavg of GPSO

-100

Fitnessavg of CS

-150

Fitnessavg of BSO

-200 -250 -300 -350 -400 0

10

20

30

40

50

60

70

80

Number of Iterations Figure Figure 4. 4. Comparison Comparison analysis analysis of of fitness fitness convergence convergence with with GPSO, GPSO, CS and BSO in Case A.

3.1.4. 3.1.4. Accuracy Accuracy Evaluation Evaluation of of Change Change Detection Detection based Based on on OB-HMAD OB-HMAD To To validate validate the the applicability applicability of of the the proposed proposed GPSO-based GPSO-based feature feature selection selection algorithm algorithm in in OBCD OBCD for VHR remotely sensed imagery, the image object features to be selected by the algorithm for VHR remotely sensed imagery, the image object features to be selected by the algorithm are are processed processed by by the the OB-HMAD OB-HMAD model model [41]. [41]. The The error error confusion confusion matrix matrix for for OBCA OBCA is is then then constructed constructed from from the the test test samples samples by by comparison comparison of of the the result result image image and and ground ground truth truth data, data, which which has has the the change change trajectory defined by the field investigation and visual judgment from Google Earth and actual terrain trajectory defined by the field investigation and visual judgment from Google Earth and actual terrain classification classification image. image. This This ground ground truth truth data data can can be be recognized recognized as as the the reference reference data data to to compare compare the the results of change detection with different feature selection algorithm in OBCD. The OBCD accuracy results of change detection with different feature selection algorithm in OBCD. The OBCD accuracy can can be be evaluated evaluated using using the the false false negative negative rate rate (probability (probability of of missing missing detection), detection), the the false false positive positive rate rate (probability (probability of of false false detection), detection), the the overall overall accuracy accuracy (probability (probability of of correct correct detection), detection), and and the the Kappa Kappa coefficient confusion matrix matrix [40]. [40]. coefficient calculated calculated from from the the error error confusion Table 3 shows the results of feature selection based Table 3 shows the results of feature selection based on on BSO, BSO, CS CS and and GPSO, GPSO, with with feature feature selection selection results results displayed displayed as as 20-bit 20-bit binary binary code, code, all all GLCM-based GLCM-based features features have have four four directional directional values values (0°, (0˝ , 45°, 45˝ , 90° 90˝ and and 135°). 135˝ ). Table A. Table 3. 3. Results Results of of feature feature selection selection with with different different algorithms algorithms in in Case Case A. Case

Case

Case Case A A

Algorithms

Algorithms

Selected Features Selected Features

BSO BSO

Mean, GLCM-Mean(0(0°) ˝ ), GLCM-Mean ˝) Mean,NDVI, NDVI,GLCM-Correlation GLCM-Correlation (0°, (0˝ , 90°), 90˝ ), GLCM-Contrast GLCM-Contrast (0(0°),

CSCS

˝ , 90 ˝ ),GLCM-Entropy (0(0°) ˝) Mean, 90°),GLCM-Entropy Mean,NDVI, NDVI,GLCM-Correlation GLCM-Correlation (0°), (0˝ ), GLCM-Contrast GLCM-Contrast (0(0°,

GPSO GPSO

˝ , 90 ˝ ), GLCM-Entropy ˝) Mean, NDVI,GLCM-Correlation GLCM-Correlation (0°), (0˝ ), GLCM-Contrast GLCM-Contrast (0(0°, (0(0°) Mean, NDVI, 90°), GLCM-Entropy

Figure illustrates the theOB-HMAD OB-HMADresults resultsofofCase CaseAA single and multiple features selected by Figure 5 5 illustrates forfor single and multiple features selected by the the BSO, CS and GPSO algorithms, 5a,b shows the original 5c is the BSO, CS and GPSO algorithms, wherewhere FigureFigure 5a,b shows the original images, images, Figure 5cFigure is the reference reference map obtained by the ground truth data, Figure 5d shows the OBCD result with single map obtained by the ground truth data, Figure 5d shows the OBCD result with a single spectrala feature spectral feature (average of bands), and Figure 5e–g shows the OBCD results with multiple features. (average of bands), and Figure 5e–g shows the OBCD results with multiple features. Figure 5d is Figure 5d is significantly different from Figure 5c as wellsubfigures, as the other subfigures, containing several significantly different from Figure 5c as well as the other containing several false negative false negative errors and false positive errors. To analyze the problems of missing detection and errors and false positive errors. To analyze the problems of missing detection and false detection,false four detection, examples are shown in Figureto5.the According todata, the reference areas 1toand examples four are shown in Figure 5. According reference changeddata, areaschanged 1 and 2 relate the 2missing relate to the missing detection problem, and unchanged areas 3 and 4 relate to the false detection detection problem, and unchanged areas 3 and 4 relate to the false detection problem. problem. Area 1, which has been marked as changed area in Figure 5c, was covered by wheat in 2010, and it has many obvious ridges, but the land cover type has changed by 2014 and the ridges have

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Area 1, which Sensors 2016, 16, 1204has been marked as changed area in Figure 5c, was covered by wheat 10 ofin 20 2010, and it has many obvious ridges, but the land cover type has changed by 2014 and the ridges have disappeared. texture imageobjects objects covering covering this changed so itsohas beenbeen marked disappeared. TheThe texture of of thethe image thisarea areahave have changed it has marked changed in Figure 5e–g, but this area is not distinguished in Figure 5d. Similar to area 1, the direction changed in Figure 5e–g, but this area is not distinguished in Figure 5d. Similar to area 1, the direction the texture in the image objectscovering coveringarea area 22 has it still fails to be in of theoftexture in the image objects has changed, changed,but but it still fails todistinguished be distinguished in Figure 5d,e. This is possibly related to a lack of GLCM-contrast (90°) ˝in the feature set selected by the Figure 5d,e. This is possibly related to a lack of GLCM-contrast (90 ) in the feature set selected by the BSO algorithm. In area 3, which has been marked as unchanged area in Figure 5c, the spectral feature BSO algorithm. In area 3, which has been marked as unchanged area in Figure 5c, the spectral feature has changed so it is marked as changed in Figure 5d, but area 3 is actually an unchanged area. has changed is marked as the changed in Figure 5d, but area 3give is actually unchanged Referring Referringsotoitother features, multi feature OBCD methods accuratean results as shownarea. in Figure to other features, the multi feature OBCD methods give accurate results as shown in Figure 5e–g. In particular, area 4 is mistakenly identified as changed area in Figure 5e but is correctly 5e–g. In particular, 4 is mistakenly identified as changed area inofFigure 5e features but is correctly identified identifiedarea in Figure 5d, suggesting that the mutual interference multiple may affect the accuracy of OBCD. Therefore, multi feature OBCD algorithms can avoid and in Figure 5d, suggesting that the while mutual interference of multiple features maymany affectmissing the accuracy of false detection while problems, thisfeature methodOBCD may bealgorithms a reliable reference butmany shouldmissing not be used the detection only OBCD. Therefore, multi can avoid and as false criterion. problems, this method may be a reliable reference but should not be used as the only criterion.

Figure 5. Change detection Based-Hybrid Multivariate Figure 5. Change detectionresults results based based on on OB-HMAD(Objected OB-HMAD(Objected Based-Hybrid Multivariate Alternative Detection) with with different feature selection algorithms in Case (a)A: Worldview-2 VHR(Very Alternative Detection) different feature selection algorithms in A: Case (a) Worldview-2 High Resolution) remotely image(b) from 2010; (b) Worldview-3 VHR sensed remotely HighVHR(Very Resolution) remotely sensed imagesensed from 2010; Worldview-3 VHR remotely image image 2014; map (c) theobtained referenceby map obtained by data; ground truth data; (d) OBCD(Objected fromsensed 2014; (c) the from reference ground truth (d) OBCD(Objected Based Change Based Change Detection) resultspectral with a single spectral featureof(average bands); (e) OBCD Detection) result with a single feature (average bands);of(e) OBCD resultresult with with multiple multiple features selected by BSO(Backtracking Search Optimization ); (f) OBCD result with multiple features selected by BSO(Backtracking Search Optimization ); (f) OBCD result with multiple features features selected by CS(Cuckoo Search); and (g) OBCD result with multiple features selected by selected by CS(Cuckoo Search); and (g) OBCD result with multiple features selected by GPSO. GPSO.

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Table 4 shows the accuracy evaluation results for these algorithms in these two experiment cases, and the data in Table 4 are computed by the confusion matrix, which is obtained by comparing test Table 4 shows the accuracy evaluation results for these algorithms in these two experiment cases, sample points in change detection result image and the ground truth image respectively. In Case A, and the data in Table 4 are computed by the confusion matrix, which is obtained by comparing test it is obvious that the precision of multi feature OBCD methods is better than that of single-feature sample points in change detection result image and the ground truth image respectively. In Case A, methods. The CS algorithm has more problems with false detection (FPRCS = 36.49%) and BSO has it is obvious that the precision of multi feature OBCD methods is better than that of single-feature more problems with missing detection (FNRBSO = 54.35%), but GPSO has the highest value of the methods. The CS algorithm has more problems with false detection (FPRCS = 36.49%) and BSO has accuracy evaluation indices (OAGPSO = 84.17%). more problems with missing detection (FNRBSO = 54.35%), but GPSO has the highest value of the accuracy evaluation indices (OAGPSO = 84.17%). Table 4. Accuracy evaluation of OBCD with different feature selection algorithms in Case A.

evaluation ofFNR OBCD algorithms in CaseKappa A. CaseTable 4. Accuracy Methods (%)with different FPRfeature (%) selectionOA (%)

Case A

Single-Feature Methods 69.56FNR (%) Case BSOSingle-Feature54.35 69.56

32.43(%) FPR 14.87 32.43

53.33 OA (%) 53.3370.06

Kappa

0.0648 BSO 54.35 14.87 70.06 0.3267 6.52 36.49 75.00 Case A CS CS 6.52 36.49 75.00 0.5187 GPSO GPSO 10.87 10.87 18.92 18.92 84.1784.17 0.6771 FNR,FNR, falsefalse negative rate; FPR, rate;OA, OA,overall overall accuracy. negative rate; FPR,false falsepositive positive rate; accuracy.

0.0648 0.3267 0.5187 0.6771

3.2. Case B: Feature Selection for Multiple Features OBCD in Urban Area 3.2. Case B: Feature Selection for Multiple Features OBCD in Urban Area 3.2.1. Materials and Study Area 3.2.1. Materials and Study Area The Case B data are made up of a pair of WV-2 VHR images taken on 12 September 2012 and 20 The Case datathey arehave madealso up been of a pair of WV-2 VHR images on 12 September 2012four and September 2013,Band cropped into sub-images oftaken size 1000 × 1000 pixels with 20 September 2013, and they have also been cropped into sub-images of size 1000 ˆ 1000 pixels with bands. During data preprocessing, the similar relative radiometric and geometric corrections with four A bands. preprocessing, similar radiometric and geometric corrections with Case were During carried data out to make the twothe images asrelative comparable as possible. CaseThe A were carried out to make the two images as comparable as possible. study area B is located to the heart of Beijing, which is around the Beijing Olympic Park. As The important study area park B is located to the heart of Beijing, which is around Beijingchange Olympic the most with multiple eco-system service function, thethe dynamic of Park. the As the most important park with multiple eco-system service function, the dynamic change of around buildings have some significantly effect on the park. The dominating changed land coverthe is around buildings have some significantly effect onof thehigh park.buildings The dominating land cover is the the change of construction, where the shadow caused changed the mistake of change change ofbased construction, where the of shadow ofTo high buildings caused the mistake of228 change detection detection on spectral feature images. validate the proposed algorithms, samples were based on spectral feature of images. To validate the proposed algorithms, 228 samples were used for used for accuracy assessment. Figure 6 shows the pairs of VHR remotely sensed images. accuracy assessment. Figure 6 shows the pairs of VHR remotely sensed images. 40°0'10"N 40°0'20"N 40°0'30"N 40°0'40"N 40°0'50"N

40°0'10"N 40°0'20"N 40°0'30"N 40°0'40"N 40°0'50"N

2013

116°22'50"E

116°23'10"E 0

116°23'30"E 260

520

116°23'50"E 1,040

40°0'0"N

40°0'0"N

2012

116°22'50"E 1,560

116°23'10"E Meters 2,080

116°23'30"E

116°23'50"E

Figure6.6.True Truecolor colorcomposition compositionofofimages imagesofofstudy studyarea areanearby nearbythe theOlympic OlympicPark ParkofofBeijing Beijing(China) (China) Figure acquired by Worldview-2 VHR fusion image on: (a) 12 September 2012; and (b) 20 September 2013. acquired by Worldview-2 VHR fusion image on: (a) 12 September 2012; and (b) 20 September 2013.

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3.2.2. Image Object Feature Extraction Sensors 2016, 16, 1204

Based on the MRS model, the image was segmented into 837 objects in eCognition Developer12 of 20 9.2 software. First, the two images were overlaid to one image with eight image layers; then the image layer weights in Multi-Resolution Segmentation model are all set to “1” for each image layer. This 3.2.2. Image Object Feature Extraction procedure of image overlay can guarantee that the two images have the same edge of corresponding objects. In this studymodel, case, 20the kinds of image object features were build the feature set, 9.2 Based on the MRS image was segmented into 837extracted objects intoeCognition Developer such as average of bands, NDVI, shape index, density, GLCM-correlation, GLCM-contrast, GLCMsoftware. First, the two images were overlaid to one image with eight image layers; then the image layer ang.2nd moment and GLCM-Homogeneity, and these a certain weights in Multi-Resolution Segmentation model are allfeature set to indices “1” forwere eachcoded imageinlayer. Thisorder. procedure

of image overlay can guarantee that the two images have the same edge of corresponding objects. 3.2.3. Convergence Analysis of GPSO In this study case, 20 kinds of image object features were extracted to build the feature set, such as The initial parameters in the GPSO-based selection algorithm are set as follows: the initial average of bands, NDVI, shape index, density,feature GLCM-correlation, GLCM-contrast, GLCM-ang.2nd size of the particle swarm N = 80, the learning factors c1 = 2.6 and c2 = 1.5, the inertia weight factor moment and GLCM-Homogeneity, and these feature indices were coded in a certain order. ω = 0.9, the maximum number of iterations itermax = 100, and the number of features to be selected M = 7, so each particle includes seven types of feature. Similar with Case A, we also chose the CS and 3.2.3. Convergence Analysis of GPSO BSO algorithms to analyze the fitness convergence of algorithms, relative to the GPSO-based feature selection algorithm. The initial parameters in the GPSO-based feature selection algorithm are set as follows: the initial Asparticle indicated in Table 7, the two groups results are inertia similar: weight BSO hasfactor size of the swarm N5=and 80, Figure the learning factors c1 of = experiment 2.6 and c2 = 1.5, the the fastest convergence speed and the largest D con, indicating that BSO tends to convergence locally. ω = 0.9, the maximum number of iterations itermax = 100, and the number of features to be selected has the best global search ability but has aSimilar slower with convergence thanchose GPSO. The M = Moreover, 7, so each CS particle includes seven types of feature. Case A,speed we also the CS and optimum final value of fitnessavg is obtained by GPSO and the convergence curve are more stable than BSO algorithms to analyze the fitness convergence of algorithms, relative to the GPSO-based feature in the others. Additionally, the parameters of Dcon for GPSO in different cases are close to each other. selection algorithm. It proved again that GPSO has better ability to avoid the avoiding premature convergence compared As indicated in Table 5 and Figure 7, the two groups of experiment results are similar: BSO with CS and BSO.

has the fastest convergence speed and the largest Dcon , indicating that BSO tends to convergence Table 5. Analysis results of fitnessbut convergence in Caseconvergence B. locally. Moreover, CS has the best global search ability has a slower speed than GPSO. The optimum final valueCase of fitness is obtained by GPSO and the convergence curve are more stable avg Selection Algorithms BSO Feature CS GPSO than in the others. Additionally, the parameters GPSO55in different cases are close to each Iterationcon of Dcon for 35 44 Case B fitness avg −327 the −369 −388 premature convergence other. It proved again that GPSO hasFinal better ability to avoid avoiding 88 46 27 Dcon compared with CS and BSO. 0 Fitnessopt

-50

Fitnessavg of GPSO

-100

Fitnessavg of CS

Fitness

-150

Fitnessavg of BSO

-200 -250 -300 -350 -400 -450 0

10

20

30

40

50

60

70

80

90

100

Number of Iterations Figure 7. Comparison convergencewith with BSO, GPSO in Case Figure 7. Comparisonanalysis analysisof of fitness fitness convergence BSO, CS CS andand GPSO in Case B. B. Table 5. Analysis results of fitness convergence in Case B. Case

Feature Selection Algorithms

BSO

CS

GPSO

Case B

Iterationcon Final fitnessavg Dcon

35 ´327 88

55 ´369 46

44 ´388 27

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3.2.4. Accuracy Evaluation of Change Detection Based on OB-HMAD Based on the OB-HMAD algorithm, the change results have been obtained with the features selected by GPSO-based feature selection algorithm. The reference data were defined by the field investigation and visual judgment from Google Earth image. Then, we also use FNR, FPR, OA and Kappa coefficient, calculated by the error confusion matrix, to evaluate the accuracy of change detection results based on these feature selection algorithms in OBCD. Table 6 shows the results of feature selection based on GPSO, CS and BSO, and these algorithms have selected seven features. According to this table, the selected features are similar with each other among these algorithms, and there are four kinds of features all selected by these algorithms. Table 6. Results of feature selection with different algorithms in Case B. Case

Algorithms

Selected Features

BSO

Mean, NDVI, GLCM-Correlation (90˝ ), GLCM-Contrast (0˝ , 90˝ ), GLCM-2nd Angust moment (0˝ ), GLCM-Homogeneity (0˝ )

CS

Mean, GLCM-Correlation (0˝ , 90˝ ), GLCM-Contrast (0˝ , 90˝ ), GLCM-2nd Angust momen t (0˝ , 45˝ )

GPSO

Mean, GLCM-Correlation (0˝ , 90˝ ), GLCM-Contrast (0˝ ), GLCM-2nd Angust moment (0˝ , 45˝ ), GLCM-Homogeneity (0˝ )

Case B

Similar with the results analysis of Case A, the results of Case B have also been divided into several subfigures, as shown t in Figure 8. By analyzing the four example area in Figure 8, we can obtain similar results with Case A: OBCD with single spectral feature has poorer performance than ones with multi features, and Figure 8g is close to the Figure 8c, which means the OB-HMAD result with multiple features selected by GPSO is the closet to the real situation. Besides, Figure 8d,e has some missing detection problems in terms of area 1, while Figure 8e–f has some false detection problems in terms of area 3, these mistakes, caused by different illumination angle, can be corrected with the assistance of GLCM-Homogeneity. The false detection caused by the shadow of a high building can also be avoided with the assistance of texture features, as can be seen in area 2. In particular, area 4 is a pseudo-changed area and this pseudo change is caused by the difference of shooting angle of sensor. This area has been mistakenly identified as changed area by these algorithms but has not changed. Table 7 shows the accuracy evaluation results for these algorithms in this experiment case; it is validated that single-feature OBCD could not detect enough kinds of change and had poor accuracy of OBCD. The BSO algorithm has more problems with false detection (FPRCS = 16.72%) and missing detection (FNRBSO = 27.23%), and CS and GPSO have a similar result, but GPSO is superior at the accuracy evaluation indices (OAGPSO = 83.59%). It is worth noting that there are some pseudo or slightly changed objects in the context of a complex urban environment, but these algorithms mistakenly regarded these pseudo changed objects as changed objects. Table 7. Accuracy evaluation of OBCD with different feature selection algorithms in Case B. Case

Methods

FNR (%)

FPR (%)

OA (%)

Kappa

Case B

Single-Feature BSO CS GPSO

32.35 16.47 11.76 8.82

57.45 27.23 22.47 19.16

49.22 72.63 79.91 83.59

0.0726 0.4517 0.5712 0.6314

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Figure 8. Change detection onOB-HMAD OB-HMAD with different feature selection algorithms Figure 8. Change detectionresults resultsbased based on with different feature selection algorithms in in Case B: (a) Worldview-2 VHR remotely sensed image from 2012; (b) Worldview-2 VHR remotely Case B: (a) Worldview-2 VHR remotely sensed image from 2012; (b) Worldview-2 VHR remotely sensed image from 2013; referencemap map obtained obtained by truth data; (d) (d) OBCD result with with sensed image from 2013; (c)(c) thethe reference byground ground truth data; OBCD result a single spectral feature (average of bands); (e) OBCD result with multiple features selected by BSO; a single spectral feature (average of bands); (e) OBCD result with multiple features selected by BSO; (f) OBCD result with multiple featuresselected selected by by CS; result with multiple features (f) OBCD result with multiple features CS; and and(g) (g)OBCD OBCD result with multiple features selected by GPSO. selected by GPSO.

4. Discussion

4. Discussion

Some parameters affect the accuracy and efficiency of the GPSO-based feature selection

Some parameters affect for theVHR accuracy and sensed efficiency of thesoGPSO-based featurethe selection algorithm algorithm used in OBCD remotely imagery, we should analyze sensitivity of used the in OBCD for VHR remotely sensed imagery, we should sensitivity of thetothree three algorithms. In this study, we choose theso images of Caseanalyze A as thethe experiment subject analyze In thethis sensitivity of the algorithms, and the sensitivity of the GPSO-based feature the algorithms. study, we choose the images of Case A as analysis the experiment subject to analyze selection algorithm focuses on the influence of the number of features to be selected and the of sensitivity of the algorithms, and the sensitivity analysis of the GPSO-based feature selectionsize algorithm the particle swarm. The RMV fitness function is also analyzed to compare with other fitness functions. focuses on the influence of the number of features to be selected and the size of the particle swarm. The RMV fitness function is also analyzed to compare with other fitness functions. 4.1. Number of Features to Be Selected

4.1. Number Features to Be Selected As of one of the initial parameters of the GPSO-based feature selection algorithm, the number of features to be selected, M, affects the efficiency and reliability of the algorithm. A larger value of M

As one of the initial parameters of the GPSO-based feature selection algorithm, the number of creates more data redundancy and increases the running time of the algorithm, while a smaller value features to be selected, M, affects the efficiency and reliability of the algorithm. A larger value of M creates more data redundancy and increases the running time of the algorithm, while a smaller value of M decreases the accuracy and loses more critical change information. Thus, it is necessary to analyze the sensitivity of the accuracy of OBCD to M to find the optimum value of M.

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of M decreases the accuracy and loses more critical change information. Thus, it is necessary to analyze the sensitivity of the accuracy of OBCD to M to find the optimum value of M. Figure 9 illustrates the sensitivity analysis results for the influence of M on the overall accuracy and running time of our algorithm for OBCD. The overall accuracy is calculated from the error confusion matrix matrixconstructed constructedfrom from samples, the running time the GPSO and OBthethe testtest samples, andand the running time for thefor GPSO and OB-HMAD HMAD algorithms on a personal withCore an Intel Core i7 2.93-GHZ 4 GB of is memory algorithms on a personal computercomputer with an Intel i7 2.93-GHZ CPU andCPU 4 GBand of memory shown is on the secondary The other parameters ofas GPSO are as the initial number onshown the secondary Y-axis. TheY-axis. other parameters of GPSO are follows: thefollows: initial number of particles of particles is N = 60, the learning c1 c=2 2.8 andthe c2 =inertia 1.3, the inertiafactor weight factor is and ω = 0.9, is N = 60, the learning factors are factors c1 = 2.8are and = 1.3, weight is ω = 0.9, the and the maximum of iterations max = 100. maximum number number of iterations is itermaxis= iter 100. In Figure 9 and Table 8, 8, the the overall overall accuracy accuracy of the algorithm increases steadily as M increases from 1 to 9; however, however, when when M Mě ≥ 10, the accuracy decreases. Increasing Increasing M M drives drives an increase in the running time, particularly when M ě ≥ 10. 10. Taking Taking into into consideration consideration the the accuracy accuracy and efficiency of the algorithm, the theoptimum optimumnumber numberofof features to select is to sixeight. to eight. Compared with CSBSO, andGPSO BSO, features to select is six Compared with CS and GPSO best performance of accuracy, as the maximum mean for higher GPSO has thehas bestthe performance in termsinofterms accuracy, as the maximum and meanand values for values GPSO are are the other cases, and thedeviation standardand deviation and average rate are both thanhigher in thethan otherincases, and the standard average change ratechange are both lower than lower in the than in the other cases. This means that GPSO is less sensitive to the number of features to be selected other cases. This means that GPSO is less sensitive to the number of features to be selected and is less and is less susceptible to theofinfluence the initial value. susceptible to the influence the initialofvalue. 0.90 0.85

BSO

0.90

700

0.85 0.80

500

0.70

400

0.65 0.60

300

0.55

200

0.50

0.40 0

5

10

15

700

CS

600

0.75 500

0.70

400

0.65 0.60

300

0.55

200

0.50

100 Overall Accuracy Time

0.45

800

100 Overall Accuracy Time

0.45

0

Time (S)

Overall Accuracy

600

0.75

Time (S)

Overall Accuracy

0.80

800

0

0.40 0

20

5

10

15

20

Number of Selected Features M

Number of Selected Features M

(a)

(b)

(c) Figure 9. Impact OBCD with with different different Figure 9. Impact of of the the number number of of features features on on precision precision and and running running time time of of OBCD feature selection algorithms: algorithms: (a) algorithm; (b) (b) CS CS algorithm; algorithm; and and (c) (c) GPSO GPSO algorithm. algorithm. feature selection (a) BSO BSO algorithm; Table 8. Accuracy statistics of sensitive analysis of M in OBCD.

Algorithms BSO CS

Maximum 81.7% 83.1%

Mean 67.0% 69.4%

Standard Deviation 10.7% 10.2%

Average Change Rate 8.1% 7.8%

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Table 8. Accuracy statistics of sensitive analysis of M in OBCD. Algorithms

Maximum

Mean

Standard Deviation

Average Change Rate

BSO CS GPSO

81.7% 83.1% 86.9%

67.0% 69.4% 73.1%

10.7% 10.2% 9.1%

8.1% 7.8% 5.3%

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4.2. Size of the Particle Swarm 4.2. Size of the Particle Swarm It is essential to discuss the effect of the size of the particle swarm on the fitness convergence is running essentialtime to discuss the effectasofathe sizeparticle of the particle on the fitness convergenceand anda and It the of algorithm, small swarmswarm may lead to local convergence the running time of algorithm, as a small particle swarm may lead to local convergence and a large large particle swarm increases the running time of the algorithm. Trelea found that a suitable size particle swarm increases running of the algorithm. Trelea found a suitable size for the particle swarm is the between 20 time and 100 [42]. In our experiment, wethat choose N = 20, 40,for 60,the 80 particle swarm is between 20 and 100 [42]. In our experiment, we choose N = 20, 40, 60, 80 and 100 as and 100 as the initial numbers of particles, denoted by 20GPSO, 40GPSO, 60GPSO, 80GPSO and the initial respectively. numbers of The particles, denoted by 20GPSO, 40GPSO, 80GPSO and are 100GPSO, 100GPSO, number of features to be selected is M =60GPSO, 6, the learning factors c1 = 2.8 respectively. of features be selected is M = 6, the learning factors 1 = 2.8 and and emphc2 =The 1.3,number the inertia weight to factor is ω = 0.9, and the maximum numberare of citerations is citer 2 = 1.3, the inertia weight factor is ω = 0.9, and the maximum number of iterations is itermax = 100. = 100. max In In Figure Figure 10 10 and and Table Table 9, 9, the the convergence convergence speed speed and and running running time time of of the the algorithms algorithms increase increase as as N increases, but the final converged fitness values, which represents the error rate of the N increases, but the final converged fitness values, which represents the error rate of the algorithm, algorithm, are 20GPSO algorithm. While the the algorithm converges faster in this are similar, similar, except exceptininthe thecase caseofofthe the 20GPSO algorithm. While algorithm converges faster in instance, the final converged fitness value is higher, meaning that 20GPSO has a problem with this instance, the final converged fitness value is higher, meaning that 20GPSO has a problem with premature premature convergence. convergence. Overall, Overall, 60GPSO 60GPSO has has the the minimum minimum converged converged fitness fitness value, value, so so we we consider consider that GPSO with N = 60 has the best performance in terms of precision and running time. that GPSO with N = 60 has the best performance in terms of precision and running time. 0 20GPSO 40GPSO 60GPSO 80GPSO 100GPSO

-60

Fitness

-120

-180

-240

-300

-360 0

5

10

15

20

25

30

35

40

45

50

Number of Iterations

Figure 10. 10. Fitness Fitnessconvergence convergence curves curves of of GPSO-RMV GPSO-RMV based based on on different different scales scales of of particle particle swarm. swarm. Figure Table 9. 9. Sensitivity Sensitivity analysis analysis results results of of size size of of particle particle swarm. swarm. Table

Algorithm Algorithm

TimeTime (s) (s) con Final Fitness avg avgRunning Iteration Iterationcon Final Fitness Running

20GPSO 20GPSO 40GPSO 40GPSO 60GPSO 60GPSO 80GPSO 100GPSO

25 25

−314´314

30

36 36 40 40 44 44

´330 −330 ´345 −345´340 ´332

45

−340

125

100GPSO

44

−332

150

80GPSO

44

70

30 45 70 125 150

4.3. Comparison of Different Fitness Functions Because the fitness function determines the applicability of the algorithm, selection of the fitness function for the GPSO-based feature selection algorithm should be in accordance with the purposes

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4.3. Comparison of Different Fitness Functions Because the fitness function determines the applicability of the algorithm, selection of the fitness function for the GPSO-based feature selection algorithm should be in accordance with the purposes of our research. SensorsTo 2016, 16, 1204 17 of 20 analyze the applicability of RMV, we choose Jeffreys–Matusita Distance (JMD) [43] and Nearest Neighbor Classifier (NNC) to compare with RMV for the fitness convergence of the algorithms. Based algorithms. Based on these functions, theselection GPSO-based feature algorithms are on these fitness functions, thefitness GPSO-based feature algorithms areselection denoted by GPSO-RMV, denoted by GPSO-RMV, GPSO-NNC and GPSO-JMD, respectively. GPSO-NNC and GPSO-JMD, respectively. Figure 11shows showsthe the fitness convergence curve forthree the fitness three fitness functions, all of which Figure 11 fitness convergence curve for the functions, all of which converge converge within 60 Note iterations. Note that the fitnessavg curves are also close to the corresponding within 60 iterations. that the fitness avg curves are also close to the corresponding fitnessopt curve. fitness opt curve. During the first 20 iterations, convergence is fast and there is only a small gap between During the first 20 iterations, convergence is fast and there is only a small gap between fitnessavg and fitness avg and fitnessopt. The convergence of GPSO-JMD is faster than the other two algorithms, with fitnessopt . The convergence of GPSO-JMD is faster than the other two algorithms, with convergence of convergence fitnessavg and fitnessopt occurring after 35 and 38 iterations, respectively, but there is a fitnessavg and of fitness opt occurring after 35 and 38 iterations, respectively, but there is a big gap between big gap between the final of fitness avg and fitnessopt, meaning that GPSO-JMD may have some the final values of fitnessavgvalues and fitness opt , meaning that GPSO-JMD may have some problems with problems premature Foralgorithm, the GPSO-NNC the fitnessavg and fitnessopt premature with convergence. Forconvergence. the GPSO-NNC the fitnessalgorithm, avg and fitnessopt curves are very close curves are very close so it has the lowest error rate, but the fitness avg and fitnessopt values do not so it has the lowest error rate, but the fitnessavg and fitnessopt values do not converge until after around converge until after 50 iterations. For GPSO-RMV algorithm, theand variance between 50 iterations. For the around GPSO-RMV algorithm, thethe variance between the average optimum fitnessthe is average and optimum fitness is small and they converge after the same number of iterations. Overall, small and they converge after the same number of iterations. Overall, the values for GPSO-RMV show the values for GPSO-RMV show close to global convergence, which means that it has powerful global close to global convergence, which means that it has powerful global search ability. search ability. 1.0 0 -50 -100

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(c) Figure 11. Comparison of fitness convergence with different fitness functions: (a) RMV (Ratio of Mean to Figure 11. Comparison of fitness convergence with different fitness functions: (a) RMV (Ratio of Mean Variance); (b) NNC (Nearest Neighbor Cassifier); and (c) JMD (Jeffreys–Matusita Distance). to Variance); (b) NNC (Nearest Neighbor Cassifier); and (c) JMD (Jeffreys–Matusita Distance).

5. Conclusions This study applied GPSO to select the optimum image object features for OBCD of VHR remotely sensed images and chose RMV as the fitness function. We analyzed the fitness convergence and accuracy of OBCD in the GPSO-based feature selection algorithm, and discussed the influence of the number of features to be selected and the size of the particle swarm on the precision and

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5. Conclusions This study applied GPSO to select the optimum image object features for OBCD of VHR remotely sensed images and chose RMV as the fitness function. We analyzed the fitness convergence and accuracy of OBCD in the GPSO-based feature selection algorithm, and discussed the influence of the number of features to be selected and the size of the particle swarm on the precision and efficiency of the algorithm. Additionally, we analyzed the adaptability of the RMV fitness function and compared it with two other fitness functions, JMD and NNC. GPSO has the advantages of strong global search ability, high efficiency and stability, and can effectively avoid premature convergence. The experiments prove that the GPSO-based feature selection algorithm performs better than other algorithms in OBCD of VHR remotely sensed images. In the sensitivity analysis of the GPSO-based feature selection algorithm, a larger the number of features to be selected increases the precision and the computational cost of the algorithm when the number of features to be selected is less than 10. The experiments show that the algorithm has high precision and is fast if the number of features is between six and eight. Additionally, the experiments also found that GPSO is not affected as much by the number of features to be selected as the other two algorithms with which it was compared. Similarly, the size of the particle swarm also affects the convergence speed of the algorithms, with the optimum number of initial particle determined to be 60. As the discriminatory criterion for the GPSO-based feature selection algorithm, the RMV fitness function was analyzed and compared with the JMD and NNC functions. The experiments show that the fitness convergence speed of three fitness functions are similar, and that their final converged fitness values are all close to the optimum fitness value. Relatively speaking, RMV is more suitable to be the fitness function of GPSO-based feature selection algorithm because of the convergence speed and precision of the algorithm. Meanwhile, the OBCD experiment based on OB-HMAD also showed that multi-feature change detection has higher precision than single-feature change detection, and that multi-feature change detection can distinguish some areas where texture or shape has changed, which is not possible with single-feature change detection. Additionally, the experiment also exposed some problems caused by mutual interference between the features. This means that the GPSO-based feature selection algorithm requires artificial visual interpretation to assist in OBCD. Acknowledgments: This work is supported by the fundamental research funds for the central universities (2014KJJCA16) and by the Natural Science Foundation of China (41471348,41171318). The authors gratefully acknowledge the Digital Globe Corporation for providing Worldview-2/3 remotely sensed images. Appreciation is also extended to Jing Li and Hong Tang from the State Key Laboratory of Earth Surface Processes and Resource Ecology of Beijing Normal University. Author Contributions: Qiang Chen wrote the manuscript and was responsible for the entire research. Yunhao Chen put forward initial research ideas and made suggestions for writing this article. Weiguo Jiang gave constructive comments. Conflicts of Interest: The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.

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