GENDER CLASSIFICATION USING SUPPORT VECTOR MACHINES

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1 GENDER CLASSIFICATION USING SUPPORT VECTOR MACHINES Ashwin Swaminathan ENEE633: Statistical and Neural Pattern Recognition Instructor : Prof. Rama Chellappa Project 2, Part (a) 1. INTRODUCTION Gender classification has been known as one of the most important tasks for humans [13]. Recently, the field of gender classification has caught considerable attention due to its emerging applications in the area of human computer interactions systems [14] and other applications. The problem of gender classification has been widely studied in psychology where they try to model the human recognition system to classify gender. Over the past few years, there have been a few learning based algorithms proposed for gender classification. Most of these methods use neural networks for gender classification [16, 17]. In these works, the authors perform tests over 30 images and show that the neural network can help determine gender from 8x8 images with an average accuracy of 92%. RBF type networks have been widely used for this purpose. The use of Support vector machines for gender classification was proposed by Moghaddam et al. in [14]. It is well known that SVM can provide superior performace and hence it has been widely used in many classification problems. Specifically, it has been very helpful in cases where it is difficult to estimate the density model such as in classification of images e.g. face recognition, etc. The support vector machines employing kernel functions have been useful in cases where the data are not linearly separable. These kernel functions help in transforming the data to a higher dimensional space where they can be distinguished easily. In this paper, the authors use SVM for classification. They use hair-less images from around 1800 faces each in a 21 x 12 format and show that they can achieve an average

2 performance accuracy of around 96% using a support vector machine employing radial basis functions as its kernel. In this project, we explore further on the use of support vector machines for the problem of gender classification. In particular, we study the performance of the SVM under different types of kernel functions such as linear, polynomial, radial basis functions and sigmoid. We then consider the effect of feature generation techniques such as principal component analysis and fisher linear discriminant and compare the results with those obtained using the image pixel intensity values as features. 2. SUPPORT VECTOR MACHINES FOR CLASSIFICATION The SVM is a learning algorithm for classification. It tries to find the optimal separating hyperplane such that the expected classification error for unseen patterns is minimized [18]. Thus, the SVM has very good generalization performance. More precisely, given a set of training samples x i and the corresponding decision values y i { 1, 1}, the SVM aims at finding the best separating hyperplane given by the equation w T x + b that maximizes the distance between the two classes. The set of points for which w T x + b 1 are set to belong to one class and those points for which w T x + b 1 are classified into another. The goal of the optimizing function is to maximize the distance between the two hyper-planes given by 1. This problem can be equivalently formulated of the form w T w minimize w T w subject to the constraint that y i (x T i w + b) 1 i The solution to this optimization problem can be easily obtained when the data are linearly separable. However, complications arise when the data are non-separable. In this case, the SVM handles non-separable data by introducing slack variables ξ i. In this case, the optimization problem can be reformulated of the form minimize w C( ξ i ) k

3 subject to the constraint that x T i w + b 1 ξ i y i = 1 x T i w + b 1 + ξ i y i = 1 ξ i 0 (1) The primal problem as stated above can be converted to its equivalent dual form maximize α i 1 α i α j y i y j x T i x j 2 subject to 0 α i C and i α iy i = 0. In general, the term x T i x j can be rewritten in terms of the kernel functions as K(x i, x j ). In this case, the problem can be equivalently understood in terms of projecting the input data into a higher dimensional space where they are separated using to parallel hyperplanes. There exist many popular kernel functions that have been widely used for classification. The polynomial kernel function is of the form K(x i, x j ) = (1 + x T i x j ) p i j and the radial basis function is given by K(x i, x j ) = exp( γ x j x i 2 ) (2) By using different kernel functions, SVM can implement a wide variety of learning algorithms. It is well known that the SVM has a great potential to perform well. However, the performance of the SVM is very closely tied to the choice of the optimal kernel functions. There has been a lot of research over the last few years on algorithms to help choose the exact type of kernel for a given problem with a certain set of features. Most of these methods are based on simple heuristics based on the knowledge of the input data and there has not been any standardized method to obtain the best kernel. Hence, the choice of the optimal kernel has reduced to a trial and error procedure in most scenarios. 3. SIMULATION RESULTS In this section, we present the simulation results for the gender classification problem with support vector machines.

4 3.1. Simulation setup We use the gender classification database given in class that has been adopted from [15]. This database has a total of 265 images. The first 150 of them are male and the remaining are female subjects. It has two images per person each of dimension These image have been cropped and aligned to produce only the face region. Some sample images from the database are shown in Fig. 1. The image intensity values were used as features for classification. In the following sections, we present results with the SVM tested under different kinds of scenario and under different kinds of kernel types. We start with the simple linear kernel based SVM. Fig. 1. Sample inputs for the Gender classification Problem 3.2. Simulation Results with Linear Support Vector Machine In our study, we first use the linear SVM kernel. We use 30 images from each gender for training and test it with 30 different images from each class. In each case, the number of female faces classified as male and the number of male classified as female are noted. The experiment was repeated numerous times by choosing a different set of images in training and testing set and the average performance was computed. The average confusion matrix is shown in Table 1. We notice that around 2.4% of the males are wrongly classified as females. In the case of female images, we observe a larger error and around 29.4% of the female faces are classified as males. On closer examination, we observe that there are 46 different support faces 24 of which are males

5 Table 1. Average Confusion Matrix when classified with the SVM with Linear kernel Male Female Male 97.60% 2.40% Female 29.60% 70.40% and the remaining 22 are females. Some of the support faces are shown in Fig. 2. Fig. 2. Sample Support faces obtained using Linear SVM Next, we study the performance as the number of training images in each class is increased. In all cases, we fix the number of testing images to 30. The percentage accuracies for male and female face classification are shown in Fig. 3. These results again indicate that there is considerable more error in classifying female faces. Further, we notice that the percentage accuracy does not improve much on increasing the size of training set. In Table 2, we show the average number of support faces when the number of training images are increased. We notice that when the number of training images is small, almost all the faces become support faces. Thus, in this case all the images in the training set has a very high influence on the performance during testing.

6 100 Classification Accuracy with Linear SVM Percentage Accuracy Male Female Average No. of Training images Fig. 3. Probability of Correct classification for SVM with Linear kernel with the number of training images (a) Males shown in blue (b) Females in red (c) Average performance shown in black. Table 2. Average Number of Support Faces as a function of Number of training images Num Train (per class) No. Male SVs No. Female SVs Simulation Results with SVM with Polynomial kernel We noticed from the previous subsection that the SVM with the linear kernel performed quite well for classification of males. But, it did not do quite well with females and gave a lot of errors. In most cases, the percentage accuracy for females was only around 75% and the performance did not improve much on increasing the size of the training set. Next, we study the performance with the polynomial kernel is used. The simple polynomial kernel can be expressed as K(x i, x j ) = (1+x T i x j ) p. First, we study the performance as the degree of the polynomial kernel is changed. The results are shown in Fig. 4. We observe that the classification performance improves as the degree of the polynomial kernel is increased initially and the polynomial kernel with

7 degree 2 performs better than the kernel with degree 1. Further, we notice that the performance almost saturates and does not change much as the degree is further increased. In this case, our results indicate that we have on an average about 16.2 male support faces and around 14.3 female support faces. Hence, the total number of faces in the boundary is 30.5 which is much less than 44 which was observed for the linear kernel. This indicates that the polynomial kernel is able to better fit the data Male Female Average Percentage Accuracy Degree of Polynomial kernel Fig. 4. Probability of Correct classification for various degrees of polynomial kernels for the case (a) Males shown in blue (b) Females in red (c) Average performance shown in black. Next, we study the performance of the polynomial kernel (with degree 3) as the number of training images is increased. The results are shown in Fig. 5. We notice that the performance improves as the number of training images is increased. We also observe that the performance in this case is much better compared to the linear SVM case explored in the previous subsection. The mediocre performance obtained with the linear SVM seems to indicate that a linear decision surface is not able to capture the properties of the dataset Simulation Results with SVM with RBF kernel In this subsection, we study the performance with the radial basis function kernel. The RBF kernel can be expressed as K(x i, x j ) = (exp( γ x i x j 2 )). First, we study the performance as the value of γ is changed. The results are shown in Fig. 6. We

8 96 Percentage Accuracies for SVM with Polynomial kernel with degree Percentage Accuracy Male Female Average Number of Training images Fig. 5. Probability of Correct classification for SVM with polynomial kernel with the number of training images for the case of (a) Males shown in blue (b) Females in red (c) Average performance shown in black. observe that the classification performance does not change much as the value of γ is changed. In this case, we use 30 images under each gender for training and 30 for testing. We notice that the average performance of the SVM with the RBF kernel is not as good as the SVM with polynomial kernel. This seems to indicate that the polynomial kernel is able to better fit the data in this case. Further, our results indicate that we have on an average about 19.8 male support faces and around 18.6 female support faces. Hence, the total number of faces in the boundary is higher than the polynomial kernel case where it was about This indicates that the polynomial kernel is able to better fit the data. Next, we study the performance of the RBF kernel (with γ = 0.5) as the number of training images is increased. The results are shown in Fig. 7. We notice that the performance does not change much as the size of the training set is increased Simulation Results with SVM with Sigmoid kernel Finally, we study the performance with the sigmoid kernel. The sigmoid kernel can be expressed as K(x i, x j ) = tanh(γ x T i x j + c). First, we study the performance as the value of γ is changed. The results are shown in Fig. 8. We observe that the classification performance changes drastically as the value of γ is changed. As the value

9 100 Percentage Accuracy for SVM with RBF kernel Percentage Accuracy Male Female Average γ Fig. 6. Probability of Correct classification for SVM with RBF kernel with the parameter γ for the case of (a) Males shown in blue (b) Females in red (c) Average performance shown in black. is increased, we notice that the classification performance for males decreases and the corresponding performance for females increases. The average performance is almost a constant. Thus, on increasing the value of γ the sigmoid kernel is able to better learn the female faces. We also see that the performance of the sigmoid kernel is not as good as the polynomial kernel which seems to provide the best performance. Further, our results indicate that we have on an average about 29.8 male support faces and around 28.6 female support faces. Hence, the total number of faces in the boundary is higher than the polynomial kernel case where it was about This indicates that the polynomial kernel is able to better fit the data. Next, we study the performance of the RBF kernel (with γ = 1.6) as the number of training images is increased. The results are shown in Fig. 9. We notice that the performance does not change much as the size of the training set is increased Comparison under Different Kernel types In this subsection, we compare the performance for all the four types of kernels considered, namely, linear, polynomial, RBF and sigmoid. The comparison results for 30 training images are shown in Table 3. The corresponding average number of support vectors are shown in Table 4. We notice from the

10 100 Results for RBF kernel Percentage Accuracy Male Female Average No. of Training images per class Fig. 7. Probability of Correct classification for SVM with RBF kernel with the number of training images for the case of (a) Males shown in blue (b) Females in red (c) Average performance shown in black. results that the SVM with the polynomial kernel provides the best classification accuracies. Thus, it is able to better represent the data. This is also evident from Table 4 where it is clear that the SVM with polynomial kernel uses the least number of support vectors. Thus, after elaborate and detailed comparison studies, we notice that the polynomial kernel performs the best for gender classification. Table 3. Average Accuracies for SVM classifier with different kernels Classifier % Overall Male Female Linear Polynomial with degree Radial Basis Function Sigmoid GENDER CLASSIFICATION USING PRINCIPAL COMPONENT ANALYSIS The Principal Component Analysis method functions by projecting a face onto a multi-dimensional feature space that spans the gamut of human faces. A set of basis images is extracted from the database presented to the system by Eigenvalue-Eigenvector decomposition. Any face in the feature space is then

11 Percentage Accuracies with Sigmoid Kernel Male Female Average Percentage Accuracy γ Fig. 8. Probability of Correct classification for SVM with sigmoid kernel with the parameter γ for the case of (a) Males shown in blue (b) Females in red (c) Average performance shown in black. Table 4. Average Number of Support Vectors for SVM classifier with different kernels Classifier % Male Female Linear Polynomial with degree Radial Basis Function Sigmoid characterized by a weight vector obtained by projecting it onto the set of basis images. When a new face is presented to the system, its weight vector is calculated and a SVM based classifier is used for classification. The full details of the algorithm can be found in [1]. In this section, we present the results for the gender classification algorithm after PCA was done on the data set. The correlation matrix of the input data was first computed and its eigenvectors were found. The training data was then projected on to these basis vectors and the projection coefficients were estimated. These coefficients were then used for classification. The SVM was used for classifying the data and all the four kernel functions were tried. The results are shown in Table 5. Here, we show the results both with and without PCA for comparison. We notice that the classification performance improves after doing PCA. The improvement is especially pronounced for female data where it is around 8-9% in most cases. This indicates that the female faces are better

12 Male Female Average Percentage Accuracies for Sigmoid Kernel Percentage Accuracy No. of training images for each class Fig. 9. Probability of Correct classification for SVM with sigmoid kernel with the number of training images for the case of (a) Males shown in blue (b) Females in red (c) Average performance shown in black. represented and classified accurately when the projection coefficients are used in classification. There is also an overall enhancement of about 1-2%. Again, we notice that the polynomial kernel with degree 3 performs best for classification. Our results indicate that the polynomial kernel is better able to fit the face data. Table 5. Average Accuracies for SVM classifier with different kernels with and without doing PCA on the test data Features SVM Kernel Type % Overall Male Female Image Pixels Linear SVM Polynomial with degree Radial Basis Function Sigmoid PCA coefficients Linear SVM Polynomial with degree Radial Basis Function Sigmoid

13 5. GENDER CLASSIFICATION USING FISHER LINEAR DISCRIMINANT The PCA takes advantage of the fact that, under admittedly idealized conditions, the variation within class lies in a linear subspace of the image space [2]. Hence, the classes are convex, and, therefore, linearly separable. One can perform dimensionality reduction using linear projection and still preserve linear separability. However, when the variation in classes is large, there is a lot of variance in the observed features and this leads to wrong classification results. This problem can be offset by considering a modified set of optimization leading to a different set of basis vectors. Instead of finding the best set of basis vectors to minimize the representation error, a modified cost function is considered to improve classification accuracy. More specifically, the basic idea behind Fisher Linear discriminant analysis is to find the best set of vectors that can minimize the intra cluster variability while maximizing the inter cluster distances. The simulation results for FLD are shown in Table 6. Here, we show the results using PCA and direct image features also for comparison purposes. We use 60 images for training and test it with 60 other images to generate our simulation results. Out of these, 30 are male and the remaining 30 are females. These 60 images are chosen in a random order and a different set of faces is chosen each time. The experiment is repeated over a 100 times and the average performance is recorded as shown in the table. In the case of FLD, we first do a PCA to reduce the dimensionality of the input space to 60. The within class scatter and the between class scatter matrix is computed. The top 5 eigenvectors corresponding to the solution of the generalized eigenvalue problem are found. The input data is then projected on to these top 5 fisher basis. These 5 coefficients are used for classification. The results of our study and the overall performance is shown in Table 6. We notice a slight improvement in performance with compared with directly using the image pixel intensities as features. However, it to be noted that while using the image pixel values, the length of our feature vector was around 9750 compared to 5 in the case of FLD. Thus, the FLD was able to achieve a much better performance even under a highly reduced dimensional space. Again, in this case like in PCA, we notice that the average classification accuracy for females improved tremendously in comparison with using image pixel values as features. This is expected in the light of the fact that we are using better set of features by projecting the input faces on to a set of basis vectors. Our results also indicate that the SVM with polynomial kernel with degree 3 seems to give the best results.

14 Table 6. Average Accuracies for SVM classifier with different kernels and different features Features SVM Kernel Type % Overall Male Female Image Pixels Linear SVM Polynomial with degree Radial Basis Function Sigmoid PCA coefficients Linear SVM Polynomial with degree Radial Basis Function Sigmoid FLD coefficients Linear SVM Polynomial with degree Radial Basis Function Sigmoid CONCLUSIONS In this project, we consider the problem of gender classification and use the Support vector machines for our study. As a first step for gender classification, we use the image pixel intensity values as features. These are then fed into the SVM with different types of kernel functions and the classification error and accuracy are noted in each case. Our results indicate that even on using the image pixel values as features, the SVM has the potential to segregate the images into the two classes of male and female with a high accuracy. In particular, we explored the use of four different kernels namely linear, polynomial, radial basis function and sigmoid. The performance under different types of parameters was studied and tabulated. Our results indicate that that the polynomial kernel with degree 3 gives the best performance compared to all the other kernels (with different parameter settings). Next, we consider feature dimension reduction methods. More specifically, we test the performance of the SVM classifier when the principal component coefficients and the fisher linear discriminants are used as features. Again, in this case, our elaborated and detailed comparisons indicate that the FLD with polynomial kernel seems to give the best results.

15 7. REFERENCES [1] M. Turk, A. Pentland, Eigenfaces for recognition, Journal of Cognitive Neuroscience, vol. 3, pp 72-86, [2] P. Belhumeur, J. Hespanha, and D. Kriegman, Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection, IEEE Trans. PAMI, vol. 19, pp , [3] K. Etemad and R. Chellappa, Discriminant Analysis for Recognition of Human Face Images, Journal of Optical Society of America A, pp , [4] W. Zhao, R. Chellappa, A. Rosenfeld, and J. Phillips, Face Recognition: A Literature Survey, to appear ACM computing surveys, 2003 [5] S.K.Zhou and R.Chellappa, Multiple-Exemplar Discriminant Analysis for Face Recognition, ICIP. [6] M.S.Bartlett, J.R.Movellan, T.R.Sejnowski, Face recognition by Independent Component Analysis, IEEE Trans. on Neural Networks, Vol. 13, No. 6, Nov [7] B.Moghaddam, T.Jebara, A. Pentland, Bayesian Face recogition, MERL research report, Feb [8] B.Moghaddam, T.Jebara, A. Pentland, Bayesian Modeling of Facial Similarity, Adv. in Neural Info. Processing Systems 11, MIT Press, [9] B.Moghaddam, A.Pentland, Probabilisitc Visual Learning for Object Representation, Early Visual Learning, Oxford University Press, [10] S.Z.Li, J. Lu, Face Recognition Using Nearest Feature Line Method, IEEE Trans. on Neural Networks, Vol. 10, No. 2, [11] M.Ramachandran, S.K.Zhou, R.Chellappa, D.Jhalani, Methods to convert smiling face to neutral face with applications to face reognition, IEEE ICASSSP, March [12] R. Chellappa, C. Wilson, and S. Sirohey, Human and Machine Recognition of Faces: A Survey, Proceedings of IEEE, vol. 83, pp , [13] A. B. A. Graf, and F. A. Wichmann, Gender Classification of Human Faces, Technical report on MERL.

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