Paper. Face Recognition Based on Incremental Predictive Linear. Discriminant Analysis. I Gede Pasek Suta Wijaya. â,ââ. Non-member,. Keiichi Uchimura. ââ.
電気学会論文誌 C（電子・情報・システム部門誌）
IEEJ Transactions on Electronics, Information and Systems Vol.133 No.1 pp.74–83 DOI: 10.1541/ieejeiss.133.74
Paper
Face Recognition Based on Incremental Predictive Linear Discriminant Analysis I Gede Pasek Suta Wijaya∗,∗∗ Non-member, Keiichi Uchimura∗∗ Gou Koutaki∗∗ Member
Member
(Manuscript received March 28, 2012, revised July 3, 2012)
This paper present an alternative approach to PDLDA for incremental data which belong to old/known and new classes called as incremental PDLDA (IPDLDA). The IPDLDA not only can overcome the main problem of the conventional LDA in terms of large computational cost for retraining but also can provide almost the same optimum projection matrix (W ) as that original LDA for each incremental data. The proposed method can be realized by redefining new formulation for updating the between class scatter (Sb ) using constant global mean assignment and simplifying the equation for updating the within class scatter (Sw ). These new updating algorithms make the IPDLDA require much less time complexity for retraining the incremental data. In addition, they also make the IPDLDA have almost the same properties as the original one in terms of the power discriminant and scattering matrix. To know the ability of the IPDLDA on features clustering, we implement it for face recognition with the DCT-based holistic features as the dimensional reduction of raw face image. The experimental results show the proposed method provides robust recognition rate and less processing time than that of GSVD-ILDA and SP-ILDA in several challenges databases when the experiments were done by retraining the system using two scenarios: the incremental data belonging to new and old classes. Keywords: incremental data, LDA, holistic features, face recognition
1. Introduction The linear discriminant analysis (LDA) is one of the most popular features clustering method in pattern recognition which is mostly implemented for face recognition. It has received significant attention during past few years even though several reliable methods for features clustering exist, e.g., Principle Component Analysis (PCA) and Support Vector machine (SVM). This evidence is caused by two main reasons: it is simple and easy to be implemented, and it is can be used not only for features clustering but also for dimensional reduction. In addition, the LDA’s optimum projection matrix (W ) is obtained by using eigen analysis of both between class scatter (Sb ) and within class scatter (Sw ). However, the LDA and its variations have to retrain all of data samples to get most favorable projection matrix when new data come continuously into the system (as shown in Fig. 1, where Ti represents i-th incremental data). This problem make the LDA based features classifier require large computational cost for incremental data. Recently, several methods (1)–(5) have been proposed to
Fig. 1. The illustration of incremental data (5) .
address to this problem. The incremental LDA (ILDA (1) ) algorithm redefined the Sw formulation and made simplification of calculating the global mean and determined the W using singular value decomposition (SVD). While Zhao et al. (2) proposed another strategy to this problem called as generalized SVD incremental LDA (GSVD-ILDA) which determined W of incremental data using SVD which has less computation time than that of ILDA. Those approaches avoided to recalculate the eigen analysis of (Sb−1 Sw ) which requires O(n3 ) time complexity, where n is the dimensional input features vector of face image. However, they will work well for incremental data when the data samples have moderate number of classes and the n is much larger than L (L n, where L is the number of classes). In contrast, if the n is much less than L (n L), the ILDA will require large computational cost for recalculating the Sb because all terms on summation depend on global mean and summation should be recalculated from scratch. In other side, the GSVD-ILDA still has to recalculate the global mean for constructing the Hb and requires QR de-
∗
Electrical Engineering Dept., Engineering Faculty, Mataram University Jl. Majapahit 62, Mataram, West Nusa Tenggara, Indonesia ∗∗ Computer Science and Electrical Engineering of GSST, Kumamoto University 2-39-1, Kurokami, Kumamoto 860-8555, Japan c 2013 The Institute of Electrical Engineers of Japan.
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Face Recognition Based on IPDLDA Analysis（I Gede Pasek Suta Wijaya et al.）
composition, and twice SVD to obtain the W for each incremental data. In addition, three recent methods (3)–(5) have been proposed for solving the incremental problems. Kim et al. (3) proposed an incremental LDA which works using sufficient spanning sets for converting the large eigen problem of classical LDA into a smaller eigen problem. However, it requires less computational complexity when the n is much larger than L. In case of n L, its computational complexity is strongly influenced by several eigen analyses, therefore the computational time become almost the same as that of PDLDA (5) for obtaining the W for each incremental data. It also possible has singularity problem when the incremental data have small sample size. Hisada et al. (2009) (4) also proposed the an incremental LDA for multi task recognition problems. This method is an extended version of ILDA with the knowledge transfer as its extension part. The knowledge transfer is done to find the useful discriminant information from mutually related data. Finally, Wijaya et al. (5) also proposed another strategy to incremental data on conventional LDA called as predictive LDA (PDLDA) which is based on constant global mean assignment on Sb and Sw determination. However, it does not work for incremental data which belong to old (already trained) or known classes. This paper present an alternative approach to PDLDA which can retrain incremental data not only belonging to new class but also belonging to old/known classes (already trained classes). In addition, this method called as incremental PDLDA (IPDLDA) does not only overcome the main problems of the conventional LDA in terms of large computational cost for retraining but also can provide almost the same optimum W as that original LDA for each incremental data belonging to old and new classes. The proposed method can be realized by redefining new formulation for updating the Sb using constant global mean assignment and simplifying the equation for updating Sw . The redefined and simplified Sb and Sw have the same properties as the original one in terms of the power discriminant but having much less time complexity. This paper is organized as follows: section 2 describes the conventional LDA versus the predictive LDA (PDLDA) and incremental PDLDA (IPDLDA) algorithms including their advantages and disadvantages; section 3 explains the implementation of IPDLDA as face recognition including holistic features extraction, retraining; section 4 presents the experimental results and results discussion; and the rest concludes the paper.
each class has Nk samples, Xik represents data matrix of i-th samples of k -th class, xki represents features vector of i-th samples of k -th class, where i=1, ... , Nk , and k =1, ... , L. Let M = L k=1 Nk is total samples. Let define μk as mean features vector of k -th class and Nμka as xki mean features vector of all samples: μk = N1k i=1 L 1 and μa = M k=1 Nk μk , respectively. From the data samples, we can define the Sb and Sw , as follows: Sw =
L Nk 1 (xki − μk )(xki − μk )T , · · · · · · · (1) M i=1 k=1
Sb =
L
P (xk )(μk − μa )(μk − μa )T . · · · · · · · · · (2)
k=1
where, P (xk ) = Nk /M . The optimum W of classical LDA (CLDA), which is determined from both the Sb and the Sw , has to satisfy the following Fisher criterion. JCLDA (W ) = arg max W
| W T Sb W | · · · · · · · · · · (3) | W T Sw W |
The W = [w1 , w2 , w3 , ..., wm ], which satisfy the Eq. (3), can be obtained by solving eigen problem of matrix (Sb−1 Sw ) and then select m orthonormal eigenvectors corresponding to the largest eigenvalues (i.e. m n). Using the W, the optimum projected features called as LDA-based projected features can be determined by yik = W T xki . It has good and stable performance in both small and large sample size data as shown in Refs. (5) (10) , when it was implemented for face recognition. However, it has to retrain all data samples to obtain most favorable W when new data samples enter into the system. To solve this problem, we previously proposed a simplification of the Sw and redefinition the Sb using global means assignment. If the μa is forecasted by calculating it from l sub-samples data which are randomly selected from L data samples (i.e l L), the Sb can be simplified as follows: Sbp =
L
P (xk )(μk − μp )(μk − μp )T · · · · · · · · · (4)
k=1
Furthermore, because the μp is constant, the Sb can be updated using the following equation when a new class, xnew , comes into the system. Sbu =
L
P (xk )(μk − μp )(μk − μp )T
k=1
2. The Proposed Method
+P (xnew )(μnew − μp )(μnew − μp )T
2.1 Brief Conventional LDA vs PDLDA Like PCA, the aim of the LDA is to find a transformation matrix such that features clusters are most separable after the transformation. The most popular conventional LDA analysis that is implemented for face recognition is presented in Refs. (6)–(9) . 1 Suppose we have (X11 , x11 ), ... , (XN , x1N1 ); ... ; (X1L , 1 L L L x1 ), ... , (XNL , xNL ), are data samples from L classes,
= Sbold + Sbnew · · · · · · · · · · · · · · · · · · · · · · · · · · · (5) Statistically, the forecasted μa = μp has close event equal value to the original μa which make the predicorg tive Sb be Sbp ∼ = Sb . Therefore, it absolutely make the discrimination power of the data projection be almost the same as that of the original one with requiring less computational complexity. 75
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The updating of Sb and Sw require O(n2 ) time complexity for all cases for each incremental data, where n is the dimensional of input features vector x. The optimum W is determined by the same procedure as that of PDLDA. In this case, the eigen analysis does not create a bottleneck for the computational cost of LDA, because the dimensional size of input features vector is much less than total data samples, M, (i.e n = 53 and M > 1000). Another benefit is the IPDLDA just need to save the old Sw and Sbold which are small size matrices (n × n elements) for updating the Sb and Sw for each incremental data, while the GSVD-ILDA has to save the large size matrices: Hb ∈ n×L and Hw ∈ n×M . Therefore, this method needs less memory space for handling retraining process.
Let us compare the Eq. (5) with Eq. (2), it seems to have much less complexity than that of original one (Eq. (2)). The time complexity of recalculating Sb using Eq. (5) requires: n2 multiplication operations, n2 multiplication and n2 addition operations. In addition, to get more less time complexity of LDA for incremental data the Sw calculation can be simplified as follows. Let us call back the Eq. (1): Sw =
L Nk 1 (xki − μk )(xki − μk )T M i=1 k=1
L 1 k Sw M k=1 L−1 1 k L = Sw + Sw · · · · · · · · · · · · · · · · · · · (6) M
=
3. The
Implementation of Incremental PDLDA as Face Recognition
k=1
Nk k k where Sw = i=1 (xi −μk )(xki −μk )T . Suppose the xnew as new class which comes into the system, then the Sw can be updated as follows. old 1 u new Sw + Sw , · · · · · · · · · · · · (7) Sw = M + Nnew L Nnew new old k new where Sw = = − i=1 (xi k=1 Sw and Sw μnew )(xki − μnew )T . The Eq. (7) becomes simple which new just calculates the newest class covariance, Sw , and old then adds it to the Sw for each incremental data. u (Eq. (7)) and Sb Next, by substituting the Sw with Sw u with Sb (Eq. (5)) of classical LDA eigen analysis then we get the optimum W called as Predictive (PD) LDA projection matrix (WP DLDA ). This optimum projection matrix is constructed by selecting small number (m) of eigenvectors which correspond to the largest eigenvalues. By using this optimum projection matrix, the projected features of the both training and querying data set can be performed as done by the classical LDA using:
In order to know the ability of the IPDLDA for features clustering, we apply it for face recognition. The IPDLDA based face recognition consists of three components: features extraction, training, and recognition as shown in Fig. 2. The features extraction consists of the face preprocessing and features extraction process. The preprocessing consists of two main processes: YCbCr color space transformation and histogram equalization which is performed to normalize the non uniform lighting effect on image capture. In this research, the chrominance components (Cb and Cr) are included in order to cover the skin color information because the skin information
yik = WpT xki , · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (8) where Wp is WP DLDA . Henceforth, the implementation Predictive Sb into the LDA algorithm called as PDLDA. However, this approach just work for the incremental data which belong to to new class. 2.2 Incremental PDLDA In order to overcome the PDLDA problem for incremental data which belong to known class (already registered class), the modification of PDLDA is proposed called as incremental PDLDA (IPDLDA). By assuming the global means is constant which obtained from sub sample data, if the incremental data belong to the i-th known classes, the Sw and Sb can be updated as follows: u old old new Sw = Sw − Sw + Sw ,· · · · · · · · · · · · · · · · · · · · (9) i i Ni old i i T new = = where Sw j=1 (xj − μi )(xj − μi ) , Swi Ni +1 i i 1 i T j=1 (xj − μnew )(xj − μnew ) , and μnew = Ni +1 (xnew + Ni μi ). Because the μa = μp is constant for all data, therefore
Sbu = Sbold − Ni (μi − μp )(μi − μp )T + Ni+1 (μnew − μp )(μnew − μp )T . · · · · · (10)
Fig. 2. The block diagram of IPDLDA based face recognition. 76
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is mostly placed in these components. It means the recognition is done by three kinds of features vectors from the intensity component (Y) and from the Cb and Cr components for color face image. However, if the face image is grayscale, the recognition is just done by the features from intensity component (Y). Therefore, for color face images, the score fusion mechanism (Eq. 11) is implemented for face verification to represent a balance contribution of each features on the face matching.
based face recognition, several experiments were carried out using data from several challenging face databases: ITS-Lab. Kumamoto University database (ITS) (5) (10) , the ORL database (ORL) (12) (13) , and INDIA database (IND) (14) representing small size databases, and FERET database (FER) (15) representing large size database. Each database has special characteristics: the ITS-Lab. database has 97 face classes and most of them have 11 face variations. The face images were taken by konica minolta camera series vivid 900 under varying lighting condition. The ORL database is a grayscale face database that has 40 face classes, mainly male, each class consists of 10 different expressions which were taken against a dark homogeneous background. The INDIA database has 61 face classes (22 women and 39 men), each class has 11 face variations: looking front, looking left, looking right, looking up, looking up towards left, looking up towards right, and looking down. The INDIA database also included the emotions: neutral, smile, laughter, sad/disgust. From FERET database, we selected about 508 face classes and each class has 4 images (fa, fb, ql, qr ). From each class, half of class member were selected as training samples and the remaining as querying samples. The example of face pose variations of each database is shown in Fig. 3. The first experiment was carried out to prove whether the IPDLDA has the same ability as that of CLDA, PCALDA, and their variations for face recognition (5) . In this case, we also investigated the ability of IPDLDAbased features clustering on with and without HF as dimensional reduction. In this case, the face image is resized into 32 × 32 pixels from 128 × 128 pixels to solve the out memory problem of the LDA and IPDLDA on features clustering without dimensional reduction of the input image. This size was chosen because it is reasonable size which can give high enough recognition rate and it has been used by many researches for features clustering without dimensional reduction (3) . The results show that our proposed method can works well for both with and without HF (baseline) which are indicated by high enough recognition rate by about more than 95% and 80% for all tested databases, respectively, as shown in Fig. 4. In addition, the results also show that the recognition rate of the IPDLDA is almost the same as that of the CLDA for both in case of using HF and without HF. It means, the proposed method has the same ability as the CLDA in terms of features clustering. The HF can provide better recognition rate than that of without HF because it has ability to extract the most significant and remove the noise information of face image. The HF also provides higher discriminatory power than that of without no-dimensional reduction, as reported in Ref. (10) which means the HF already contains much useful discriminant information. Furthermore, the PDLDA and IPDLDA with HF as dimension reduction can provide robust recognition rate than that of some established LDA methods for all tested databases. It means that these combinations can provide more separable feature cluster as that of some established LDA methods. In other words, the PDLDA and IPDLDA also satisfy
Sf = αS1 + βS2 + γS3 · · · · · · · · · · · · · · · · · · · · · (11) where, Sf is the final score, S1 , S2 , and S3 are the matching score between the three kinds of features vectors (Y, Cb, and Cr components) of the querying and training face images. Based on our trial and error, we get the optimum weight coefficients, α = 0.75, β = 0.125, and γ = 0.125. It means the features from intensity component of images provides 75% contribution on the final score because the most discriminant information is placed on this component. Next, the features extraction process is performed to get the specifics information of face image, which performed using DCT (10) and Moment analysis (11) . From these analyses, small numbers of coefficients (less than 100 of 16384 coefficients) that correspond to large magnitude values are selected as holistic features (HF) of the face image (5) (10) . The HF extraction starts from DCT frequency analysis that is employed to get the dominant frequency content of the face image. From the DCT decomposition output, the dominant frequency content is created by three steps: firstly, convert the DCT coefficients to a vector using row ordering technique; secondly, sort the vector descending using quick sort algorithm, finally truncate p first vector elements (i.e., p is less than 100 elements). In addition, the moment information that provides invariant measure of face images shape is included to get more strength global holistic features against any face pose variations. It can be achieved because the invariant moment set is invariant to translation, scale change, and rotation. The HF has applied successfully as dimensional reduction of face image because it has good energy compactness which keep more than 97% of face image energy and it has high discrimination power. On the training process, the system defines the optimum W using the IPDLDA based algorithm as described in sub section 2 with the HF as the raw input. Then, the extracted HF and the obtained optimum W are saved into database for the recognition process. In the recognition process, the Euclidean distance based on nearest neighbor rule is implemented for face classification and the negative samples (non-training faces and non-face images) are used to define a threshold for face verification. If the minimum score is less then the defined threshold the input data is verified as known face and positive face and other wise is concluded as negative face or unknown face. 4. Experiments and Results In order to know the effectiveness of the IPDLDA77
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(a) ITS-Lab. database
(b) ORL database
(c) INDIA database
(d) FERET database
Fig. 3. Example of face pose variation of single subject of the tested databases.
(a) ITS-Lab. database
(b) ORL database
(c) INDIA database
(d) FERET database
Fig. 4. The recognition Rate of IPDLDA with and without HF compared to some established LDA methods.
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Face Recognition Based on IPDLDA Analysis（I Gede Pasek Suta Wijaya et al.） Table 1. The Recognition rate and retraining time of IPDLDA on incremental data belonging to new class.
Table 2. The Recognition rate and retraining time of IPDLDA on incremental data belonging to known class.
second retraining time for all tested databases, respectively (see Table 2). It means the IPDLDA can solve the problem of PDLDA (5) for incremental data belonging to old class and support the previous experimental results that the IPDLDA provides the same separable data features after the transformation as that of the PDLDA for incremental data belonging to both known and new classes. In order to show and support the previous achievements that the IPDLDA has better recognition rate and requires less retraining time than that of recent sub-space methods for incremental data (GSVD-ILDA (2) and SP-ILDA (3) methods), the next experiments were performed. In detail, the experiment was done in FERET face database, which representing large size database, using the first scenario. In this case, the face features size was set up 53 elements and the training was performed gradually: firstly, it was trained 208 face classes and then added gradually 20 new face classes to the system until 508 face classes. In term of recognition rate, the IPDLDA have almost the same recognition rate stability as that of PDLDA. It can be achieved because the IPDLDA has the same structure as that of PDLDA except on the updating data for incremental data which belong to the known class. In addition, the IPDLDA also provide higher and more stable recognition rate than that of the recent subspace methods for incremental data, as shown in Fig. 5 (a). This result supports and reproves that our proposed method provides better separable data features after the transformation as that of recent subspace methods for incremental data belonging to new class. It means that the IPDLDA is an alternative algorithm for
the same optimum criterion as that of the CLDA and reprove that the HF, which need small memory space, contains much useful discriminant information. The second experiment was done on ITS, ORL, and INDIA databases to investigate the performance of IPDLDA based face recognition on incremental data which belong to new and old class (known class). For incremental data belonging to new class, the test was performed by selecting half of total class members of each databases as the initial data training and then we incrementally inserted new 5 classes data training into the system until reaching all of class members. For each class, 5 face images were randomly selected for training data and the remaining for testing. From the this scenario, the experimental results show that the IPDLDA can provide high enough recognition rate (more than 90%) for all tested databases, as shown in Table 1. It means the IPDLDA have the same characteristics as that of PDLDA in term of discrimination power and can satisfy optimum criterion of the conventional LDA (Eq. 3). These results also means that the |W T Sbu W | has much the same value as the |W T Sborg W | which make the data clustering of the IPDLDA be the same separable as that of the original one but requiring short computational time. Next, for incremental data belonging to known class, the test was performed by selecting 3 face images per class as initial data training for each databases, then we incrementally inserted 1 face images per class which belong to known class until reaching 7 face images per class. In this scenario, the experimental results show that the IPDLDA also can work well as shown by providing more than 90% recognition rate and less than 2 79
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Face Recognition Based on IPDLDA Analysis（I Gede Pasek Suta Wijaya et al.）
(a) The recognition rate stability (a) The recognition rate
(b) Retraining time
Fig. 5. The recognition rate stability achievements and retraining time consumption of IPDLDA compared to the established ILDA methods.
(b) Retraining time
Fig. 6. The recognition rate achievements and retraining time consumption of IPDLDA compared to GSVD-ILDA methods for retraining the incremental data belonging to old class.
features clustering of large sample size databases, which requires much retraining process such as for incremental data. In addition, the recent establish methods have less recognition rate than our proposed method because the optimum W of GSVD-ILDA is provided by computing the best rank k -th approximation of the matrix X = [A, B] for each incremental data (B ) and the W of SP-ILDA is also defined from the total scatter and between class scatter. The total scatter matrix represents the global covariance matrix of the training set which provides the same information as that of the PCA and the between class scatter provides the null space information. In term of retraining process, our proposed methods provide almost the same retraining time as PDLDA and less than GSVD-ILDA and SP-ILDA for this scenario, as shown in Fig. 5 (b). It can be achieved because the IPDLDA requires the same time complexity as that of PDLDA and requires less time complexity than the GSVD-ILDA and SP-ILDA for the incremental data belonging to new class. In detail, the GSVD-ILDA needs O(nqk + n(L + M )t + q 2 n + k 3 ), where t and k are number of selected leading principle sub matrix of SVD decomposition (2) while the SP-ILDA requires O(d3T,1 t + d3B,1 + ndT,3 db,3 ), where the dT,1 , dT,3 , and dB,1 are equal to n and the dB,3 < n, and our proposed method requires O(n3 ). Even though our proposed method time complexity is greatly affected by the eigen analysis time complexity O(n3 ) but the dimensional size of data input (n) is much less than total data samples (M ). In other words, the eigen analysis does not create a bottleneck for the computational time of
our proposed methods, because the size of HF vector is much less then total data samples. In this test, the size of n is 53 elements, the L is 508 and the M is 1750 images. Regarding to memory space requirement, the GSVDILDA requires to save two pre-definition Sb and Sw matrices called as the Hb ∈ n×L and Hw ∈ n×M . From the data in previous paragraph, the dimensional size of Hb is 53 × 508 (Hb ∈ 53×508 ) and Hw is 53 × 1750 (Hw ∈ 53×1750 ), while the IPDLDA just needs to save old Sbold ∈ 53×53 and Sw ∈ 53×53 and the SP-ILDA also requires almost the same memory space as that of IPDLDA for saving the previous inter and intra class components for retraining process. It means that, the total memory space that is required by IPDLDA and SP-ILDA for saving the supporting matrix for retraining process is 4.69% of that is required by GSVD-ILDA. In addition, the size of Hb and Hw increase in line with the increment of number of classes (L) and number of old data samples (M ). However, the size of Sbold and Sw are fixed for all data. Even though, the IPDLDA needs the same memory space as SP-ILDA but the SP-ILDA provide less recognition rate than IPDLDA (see Fig. 5 (a)). The next experiment was done to deeply investigate the recognition rate stability of the IPDLDA compared with GSVD-ILDA on incremental data which belong to the old class (already trained class) on large size databases. In this test, initial training data set con80
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Face Recognition Based on IPDLDA Analysis（I Gede Pasek Suta Wijaya et al.）
(a) ITS-Lab. database
(b) ORL database
(c) INDIA database
(d) FERET database
Fig. 7. The ROC of IPDLDA compared to some established incremental LDA methods on tested databases.
sisted of 508 classes and each classes consist of 2 images taken from FERET database. In the retraining process, we added 40 images which belong to old class. From each step of the retraining, we also did the recognition and determined the retraining time consumption. In this experiment, we did not compare the result with the SP-ILDA and PDLDA, because the SP-ILDA has been known to provide much less recognition rate than that of GSVD-ILDA and IPDLDA (see Fig. 5 (a)), while the PDLDA does not support the retraining data belonging to old class. The experimental result supports and reproves the previous achievements (see Table 2) that the IPDLDA can solve the problem of PDLDA in term of retraining data which belong to old class. The IPDLDA also provides higher recognition rate and shorter retraining time than those of GSVD-ILDA, respectively (see Fig. 6) which reconfirm the experimental results in Fig. 5. It can be achieved because the time complexity for updating Sb and Sw of IPDLDA require about O(n2 ) operations and the scatter of Sb and Sw is exactly the same as that of PDLDA which has been proved to provide almost the same performance as that of DLDA (5) . In other case, GSVD-ILDA does not provide as good recognition rate as IPDLDA because the optimum projection matrix of GSVD-ILDA is an approximation of the original one. The GSVD-ILDA also need longer retraining time for incremental data belonging to old class because the GSVD-ILDA require QR and SVD decomposition for determining the optimum pro-
jection matrix. It seems the QR and SVD decomposition is much affected the retraining time of the GSVD-ILDA for incremental data belonging to old class. The last experiment was performed to know the accuracy of the proposed method. In this test, we investigated two important parameters, namely the false rejection rate (FRR) and the false acceptance rate (FAR). FAR is the success probability of unauthorized user to be falsely as recognized as legally user. FRR is the success probability FRR legally registered user to be falsely rejected by the system. If the value of FAR and FRR is equal than this point is called as equal error rate (EER). The system, which performs perfectly classification, is denoted by 0% FRR rate and 0% FAR or the value of EER is very small or close to zero. The tests were performed in the four mentioned databases. The training data are subjected as predicted positive (known face) and the other frontal face images are subjected as predicted negative (unknown face). The experimental result is plotted in Fig. 7 for all tested databases. From the Fig. 7, the proposed method provides much better accuracy, which is shown by much smaller EER (less than 0.05), than that of SP-ILDA for all tested databases. Even though the IPDLDA have bit smaller accuracy than that of GSVD-ILDA, but the IPDLDA need much less retraining time (see Fig. 6 (b) and 5 (b)). These results also reproves that the IPDLDA has much more optimum W such that feature clusters are most separable after the transformation than that of SP81
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Face Recognition Based on IPDLDA Analysis（I Gede Pasek Suta Wijaya et al.）
ILDA. However, for the ORL database, the IPDLDA and GSVD-ILDA provide closely the same accuracy because the original data do not much overlap to each others. It can be known by higher discriminatory power score of the original data (4.899) than that of other databases (3.109, 1.565, and 0.169 for the ITS. Lab, INDIA, and FERET respectively). Overall, it can be concluded that our proposed method provides robust and better recognition rate than those of the recent ILDA methods for all tested databases. It also provides less and almost the same retraining time parameters than that of GSVD-ILDA and SP-ILDA, and as that of PDLDA, respectively for incremental data belonging to old and new classes.
(2)
(3)
(4)
(5)
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5. Conclusion and Future Works (7)
From all of the experimental results and their discussions, we conclude the paper as follows. Firstly, IPDLDA has been proved to solve of the PDLDA methods problem for retraining incremental data belonging to old class. Secondly, the IPDLDA-based face recognitions have been proved that it provide stable/robust recognition rate, require less retraining time, and need less memory space for retraining the incremental data. The rest, our proposed methods outperforms over the recent sub-space methods (GSVD-ILDA, SP-ILDA methods) when the holistic features as the raw input. It means the proposed methods is an alternative solution to avoid recalculating the Sb and global mean (μa ) from the scratch, which has to be done by CLDA when new class data is registered into the system. In addition, our proposed method is potentially to be be implemented as security system because it requires short processing time and gives high accuracy. However, this method just implemented for face recognition and still performed the eigen analysis to obtain the optimum projection matrix. In future, we will implement the IPDLDA for other recognition problem such as palm recognition for proving whether our proposed method can be implemented for other pattern recognition problems. In addition, the strategy of LS-ILDA methods to avoid eigen analysis can be adopted for decrease the retraining time. Acknowledgment I would like to send my great appreciation to image media laboratory which giving many supports for this research and my great thank to all people who participate in building ITS-Lab face database as well as to the owner of ORL, INDIA, and FERET face database. Furthermore, the gratefully acknowledge to the FCV 2012 reviewers who have given some helpful comments and suggestions for improving the presentation of this paper.
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I Gede Pasek Suta Wijaya received the B.Eng. degrees in Electrical Engineering from Gadjah Mada University in 1997, M.Eng. degrees in Computer Informatics System from Gadjah Mada university in 2001, and D.Eng. degrees in Computer Science from Kumamoto university, Japan in 2010. During 1998-1999 he worked in Toyota Astra Motor Company in Indonesia as Planning Production Control, and from 19992000, next, he worked as lecturer assistance in Yogyakarta National Technology College in Indonesia, and since 2000 up today, he has been full time lecturer and stays in Informatics Systems Laboratory in Electrical Engineering Department, Mataram University, Indonesia. His research interests are pattern recognition, artificial intelligence, and image processing application on computer vision.
References (1)
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Face Recognition Based on IPDLDA Analysis（I Gede Pasek Suta Wijaya et al.） Keiichi Uchimura (Member) received the B.Eng. and M.Eng. degrees from Kumamoto University, Kumamoto, Japan, in 1975 and 1977, respectively, and the Ph.D. degree from Tohoku University, Miyagi, Japan, in 1987. He is currently a Professor with the Graduate School of Science and Technology, Kumamoto University. He is engaged in research on intelligent transportation systems, and computer vision. From 1992 to 1993, he was a Visiting Researcher at McMaster University, Hamilton, ON, Canada. His research interests are computer vision and optimization problems in the Intelligence Transport System.
Gou Koutaki (Member) received the B.Eng., M.Eng., and Ph.D.degree from Kumamoto University, Kumamoto, Japan, in 2002, 2004, and 2007, respectively. From 2007 to 2010, he was with Production Engineering Research Laboratory, Hitachi Ltd. He is currently an Assistant Professor with the Graduate School of Science and Technology, Kumamoto University. He is engaged in research on image processing and pattern recognition of the Intelligence Transport System.
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