International Journal of Automation and Computing 05(), April 008, 193-197 DOI: 10.1007/s11633-008-0193-x A Novel Face Recognition Algorithm for Distinguishing FaceswithVariousAngles Yong-Zhong Lu School of Software Engineering, Huazhong University of Science and Technology, Wuhan 430074, PRC Abstract: In order to distinguish faces of various angles during face recognition, an algorithm of the combination of approximate dynamic programming (ADP) called action dependent heuristic dynamic programming (ADHDP) and particle swarm optimization (PSO) is presented. ADP is used for dynamically changing the values of the PSO parameters. During the process of face recognition, the discrete cosine transformation (DCT) is first introduced to reduce negative effects. Then, Karhunen-Loève (K-L) transformation can be used to compress images and decrease data dimensions. According to principal component analysis (PCA), the main parts of vectors are extracted for data representation. Finally, radial basis function (RBF) neural network is trained to recognize various faces. The training of RBF neural network is exploited by ADP-PSO. In terms of ORL Face Database, the experimental result gives a clear view of its accurate efficiency. Keywords: Face recognition, approximate dynamic programming (ADP), particle swarm optimization (PSO). 1 Introduction In the last decade, there existed a variety of successful methods in face recognition such as subspace analysis, elastic graph matching, local characteristic analysis, neural network, shaping brightness curve plane, and so forth. However, face recognition is rather complex and difficult to describe because of the influence of the factors including angle, illumination, expression, scale, rotation, cloak, and hairstyle. At present, a majority of research works still focus on limited conditional recognition [1]. In previous research, principal component analysis (PCA) is often adopted []. However, the characteristic matching algorithm based on gray value is less resistant to disturbance, so the same image of different angle for an individual is often regarded as another one. The neural network system is complicated and is composed of a large number of simply and widely interrelated nerve cells. It can reach a rather good classification effect and plays an important role in pattern recognition. In order to distinguish the faces of different angles during face recognition more effectively, an algorithm on approximate dynamic programming - particle swarm optimization (ADP-PSO) is put forward in which ADP, called action dependent heuristic dynamic programming (ADHDP), is applied for dynamically changing the value of the PSO parameters, inertia weight w, cognitive and social acceleration constants, c 1 and c, respectively, thereby giving it the flexibility to optimize its own performance. Moreover, it is utilized in the training of a radial basis function (RBF) neural network. PSO is an algorithm based on swarm intelligence developed by Kennedy and Eberhart [3]. This algorithm is modeled on the behavior of a school of fish / flock of birds. PSO has also been used in a variety of applications including generator maintenance scheduling and Manuscript received December 1, 006; revised October 3, 007 This work was supported by Natural Science Foundation of Huazhong University of Science and Technology of PRC (No. 007Q006B). E-mail address: hotmailuser@163.com electro-magnetics [4]. ADP is a concept that tries to find the optimum solution to problems where a method to find the exact solutions is difficult. ADP approximates an optimal solution to a problem based on a utility function. It combines the concepts of dynamic programming and reinforcement learning [5]. A novel hybrid genetic algorithm/pso algorithm, breeding swarms, combining the strengths of particle swarm optimization with genetic algorithms, was proposedin[6,7]. DaandGe [8] presented a modified PSO with simulated annealing (SA) technique. An improved PSObased artificial neural network (ANN) was developed. Feng et al. [9] developed an evolutional fuzzy particle swarm optimization (FPSO) learning algorithm to selfextract the near optimum codebook of vector quantization (VQ) for carrying out image compression. The fuzzy particle swarm optimization vector quantization (FPSOVQ) learning schemes, which combined advantages of the adaptive fuzzy inference method (FIM), the simple VQ concept and the efficient PSO, were considered at the same time to automatically create a near optimum codebook to achieve the application of image compression. However, few literature discussed about the above-mentioned ADP-PSO. During the process of face recognition, the DCT is first introduced to reduce negative effects. Then, Karhunen- Loève (K-L) transformation can be used to compress images and decrease data dimensions. According to PCA, the main parts of vectors are extracted for data representation. Finally, the RBF neural network is trained to recognize various faces. The training of the RBF neural network is exploited by ADP-PSO. In terms of ORL face database, the result of the experiment shows its accurate efficiency. The rest of the paper is given as follows. Section gives a brief description of ADP-PSO. Section 3 describes the algorithm of distinguishing the faces of various angles. Section 4 presents some experimental results by the ORL Face Database. Finally, the conclusions and future work are given in Section 5.
194 International Journal of Automation and Computing 05(), April 008 ADP based PSO PSO is a population-based search strategy. A problem space is initialized with a population of random solutions in which it searches for the optimum over a number of generations/iterations and reproduction is based on prior generations. The concept of PSO is that each particle randomly searches through the problem space by updating itself with its own memory and the social information gathered from other particles [3]. Fig. 1 gives the vector representation of the PSO search space. In Fig. 1, V pd and V ld represent the effect of P best and G best on the individual. The basic PSO velocity and position update equations are given by (1) and (), respectively. V new =w V old + c 1 rand (P best P old )+ c rand (G best P old ) (1) P new = P old + V new () where V new is the new velocity value calculated for each particle, V old is the old velocity value of the particle from the previous iteration, P new is the new position value calculated for each particle, P old is the old position value of the particle from the previous iteration, w is inertia weight constant, c 1 and c are cognitive and social acceleration constants, and rand generates a random value in the range [0, 1]. Fig. Block diagram of ADP-PSO As seen in Fig., G fit a function of the fitness value of the PSO process, is taken as the input to the action and critic networks. The action network gives out the values of the PSO parameters w, c 1,andc which drive the application. These values are also fed to the critic network. The output of the action network is given by (3). A(k) =[w(k),c 1(k),c (k)]. (3) Fig. 3 shows the block diagram for the training of the critic network. The critic network is initially trained without the action network. The critic network can be trained for different values of the w, c 1,andc. They can be constants, linearly increasing or decreasing or randomly generated. w is generated in the range [0., 1.], and c 1 and c are generated in the range [0.4, ]. γ is a discount factor and is in the range [0, 1]. These inputs are fed to both the PSO application as well as the critic network. The error signal generated at the output is back-propagated and the weights of the critic network are updated. Fig. 1 Vector representation of PSO (T is the target.) ADP, called ADHDP here, is used to determine the optimal control law for a dynamic process [5]. It adopts two neural networks successively to learn the dynamics of the process. These are namely the action neural network which provides the control signal for the process and the critic neural network which evaluates the performance of the action network. The action network dispenses a control signal in order to optimize (minimize or maximize) the output of the critic. The action network may learn this control signal through a model network or directly through the critic s performance. Thus, the two neural networks together learn the system dynamics and are able to achieve an optimal control law for the process dynamically. The initialization of the weights of the neural networks does not affect the final results. The action and the critic networks need to be trained for the problem at hand before the ADP-PSO can be applied directly to the problem. Fig. shows the block diagram for ADP-PSO. Fig. 3 Block diagram for the critic training The cost-to-go function is given by (4). The objective of ADP is to develop an optimal control strategy. U(x(k)) is called the utility function where x(k) is k-th position value corresponding to P in (). The utility function is custom to the application and is chosen by the designer and it embodies the design requirements of the system. Equation (5)
Y. Z. Lu / A Novel Face Recognition Algorithm for Distinguishing Faces with Various Angles 195 gives the error value for which the critic network is trained. Equation (6) gives the value of the utility function. The critic network needs to be trained for a number of runs of the PSO applications. The fitness function of the PSO application is fed to the critic network in order to tune the network for the application at hand. This training is carried out till the output of the critic follows the target as closely as possible. J(x(k)) = γ k (U(x(k))) (4) k=0 E c = γ J(k)+U(k) J(k 1) (5) U(k) =f(g fit (k)). (6) The action network provides the control action for the PSO based system. This value is given as the input to the critic network instead of the random values of w, c 1,and c as described above. The critic responds to this signal by generating the output J function. The action network is trained in such a way that the output of the critic is minimized. Thus, the outputs of the action network will eventually drive the system efficiently. Fig. 4 shows the block diagram for the training of the action network. Fig. 4 Block diagram of the action network training The action can be trained for the different inputs. Fig. 4 shows two different sets of inputs. One set gives random values of w, c 1,andc and the other set is the output of the action network itself. The action network is trained with an error signal taken from the critic network. This is given by J/ A, where A is the output of the action network. 3 An algorithm of distinguishing faces with various angles Face recognition is performed by the following steps: 1) DCT is used to reduce the influences which are created by a variety of different angles; ) K-L transformation and PCA are utilized to lessen the data dimension; 3) RBF neural network is implemented to recognize the faces while ADP- PSO is used to train the samples in advance. The definition of DCT were first given by Ahmed et al. [10]. DCT can reduce the influences which are created by a variety of different angles. Disperse cosine transformation of two dimensions is expressed as F (μ, 0) = F (0,ν)= F (μ, v) = N F (0, 0) = 1 N N N (x, y) cos f(x, y)cos f(x, y)cos f(x, y) (7) (x +1)μπ (x +1)μπ (y +1)νπ cos (8) (9) (y +1)vπ (10) where f(x, y) is a vector of two dimensions in the space domain, x, y =0, 1,,; F (μ, v) is a transformed coefficient matrix, μ, v =1,,,. After DCT, a directing current branch (DC coefficient) and some alternating current branches (AC coefficient) are obtained. The DC coefficient, AC coefficient of low frequency, and AC coefficient of high frequency represent the average value of pixel density in the block, abundant image texture and edge information, and image details, respectively. Majority of the transformation energy is concentrated on the coefficients of low frequency which reflect the main image and are bigger while ones of high frequency are smaller. After DCT, the part of low frequency is displaced in left-down angle and the part of high frequency is located in right-up angle among the matrix. The dimension of data that are transformed by DCT is very high. Thus, K-L transformation is exploited to lessen the dimension. K-L transformation is a special optimal perpendicular transformation. The given signal vector X =[x(0),x(1),,x(n 1)] T is transformed into N dimensional vector of which each branch vector is completely irrelative and highlights its properties to minimize the approximate average square difference. The covariance of the above-mentioned vector is defined as C x = E { (X μ x)(x μ x) T} (11) where E{ } is average value operation, μ x = E{x} is the average value vector, and C x embodies the relativity of each branch in the vector. Real symmetry matrix can be diagonalized. Thus, perpendicular matrix U is constructed to make Λ = U T C xu, where Λ is a diagonal matrix, and U =[U 1,U,,U N ]. Thus, Y is obtained by Y = U T X. A three-layer feed-forward RBF neural network has been widely adopted in pattern recognition because of its fast convergence, less ease to get into local small extremum and good robustness and so forth. There is a hidden layer in the RBF neural network where the activated function of the nodes is a radial basis function, where its radius is not only symmetric, but also smooth and arbitrarily derivative. RBF is usually the Gaussian kernel function which is [ ] x x c K x x c =exp (1) σ
196 International Journal of Automation and Computing 05(), April 008 where x c is the center and σ is the wide parameter which controls the radial functionary scope of the function respectively [11]. Moreover, an algorithm about ADP-PSO is utilized in the training of the RBF neural network in which ADP is used for dynamically changing the values of the PSO parameters, inertia weight w, cognitive and social acceleration constants c 1 and c, respectively. Thereby, PSO gains the flexibility to optimize its own performance. it is 0. Weighty values between the input layer and latent layer are all 1. 4 Experiment Twenty two individuals faces were chosen from the ORL face database [1] to carry out the experiment. In the experiment, there were 10 faces with various different angles for each person and the total number is 0. The faces are all 56 gray hue, 9 pixel width, and 11 pixel height. Meanwhile, 5 faces were used for the training of the RBF neural network and another 5 for the detection. The original faces with 10 different angles and their images after DCT are presented in Figs. 5 and 6. Fig. 7 Structure of the RBF neural network The above-mentioned algorithm about ADP-PSO is used for training the samples. Two hundreds particles are initialized in which their parameters are as follows: central vector X c in 19 hidden nodes, their square differences σ in 19 latent nodes, and their weighty values W i between the hidden layer and output layer. Each particle performs the iterative calculation 300 times to obtain the parameters with the least error in order to train the network above. Meanwhile, the fitness function and utility function are expressed below. Fig. 5 Original faces with 10 different angles Sum i = G fit = O i = M 1 j=0 { i=0 T i O i (13) 1 Sum i V i 0 Sum i V i (14) W j exp [ ] Yi Yjc σj (15) Fig. 6 The images after DCT One hundred and ten training faces were performed by K-L transformation while 19 front branch vectors of U were chosen to project. Therefore, X of 10304 dimensions is projected in Y of 19 dimensions. A three-layer feed-forward RBF neural network, which includes the input layer, hidden layer, and output layer, is built as shown in Fig. 7 and the number amounts to. There are 19 nodes in the input and Y obtained above acts as input. 30 nodes are selected in the hidden layer and Gaussian kernel function is adopted. There is one node in the output and if the individual is verified correctly, the output value of the model is 1. Otherwise, U(k) =0.1 G fit (k) (16) where T i is teacher input signal, O i is the output of the i-th neural network, V i is the output threshold of the i-th neural network, W j istheweightyvaluebetweenthehiddenlayer and output layer, Y i is the input of the neural network, Y jc and σ j are considered as average value and square difference among the hidden nodes, N is equal to 110, M is equal to 30, U(k) is called the utility function. There exist output results in the network above. If the individual is tested correctly, the output value is 1 corresponding to input Y. If there are more than one output value of 1, the farthest one from the threshold is selected. During the optimization, PSO (constant w) and ADP-PSO are used respectively on a 1.7 GHz, Pentium 4 processor. The results are shown in Table 1. By detecting the 110 faces the identification ratio of the RBF based on ADP-PSO reaches the high level of 98.3%, and the algorithm reaches a high speed in practice. Table 1 Results of two PSO methods Methods Errors Iterations PSO (constant w) 4.759 300 ADP-PSO 0.309 300
Y. Z. Lu / A Novel Face Recognition Algorithm for Distinguishing Faces with Various Angles 197 5 Conclusions This paper presents a successful application of the concepts of ADP (called ADHDP) to the PSO process. The ADP-PSO algorithm greatly improves the performance of the PSO search. Moreover, it is also successfully applied to the recognition of faces with various angles. The ADP- PSO optimization-based RBF neural network algorithm is proven to be an effective identification method with high precision and fast speed. Future work can involve exploring other ADP techniques such as action dependent dual heuristic dynamic programming (ADDHP) or action dependent globalized dual heuristic dynamic programming (ADGHP) for solving these problems. The work considered here assumes that the three PSO parameters are coupled. Future work can also involve optimizing these parameters independently of each other. On the other hand, the issues on initial transformation can be improved and a reduced training period can be developed to make the identification algorithm be more efficient. References [1] Q. Yang, X. Q. Ding. Symmetric PCA and Its Application in Face Recognition. Journal of Computer, vol. 6, no. 9, pp. 1146 1151, 003. (in Chinese) [] Y. Z. Lu, J. L. Zhou, S. S. YU. A Survey of Face Detection, Extraction and Recognition. Computing and Informatics, vol., no., pp. 163 195, 003. [3] J. Kennedy, R. C. Eberhart, Y. H. Shi. Swarm Intelligence, Morgan Kauffman Publishers, San Francisco, USA, 001. [4] G. Ciuprina, D. Ioan, I. Munteanu. Use of Intelligentparticle Swarm Optimization in Electromagnetics. IEEE Transactions on Magnetics, vol. 38, no., pp. 1037 1040, 00. [5] G. K. Venayagamoorthy, R. G. Harley, D. C. Wunsch. Applications of Approximate Dynamic Programming in Power Systems Control. Handbook of Learning and Approximate Dynamic Programming, J. Si, A. Barto, W. Powell, D. C. Wunsch (eds.), Wiley Interscience/IEEE Press, Piscataway, New York, pp. 479 515, 004. [6] M. Settles, T. Soule. Breeding Swarms: A GA/PSO Hybrid. In Proceedings of the 005 Conference on Genetic and Evolutionary Computation, Washington, DC, USA, pp. 161 168, 005. [7] X.H.Shi,Y.C.Liang,H.P.Lee.AnImprovedGAanda Novel PSO-GA-based Hybrid Algorithm. Information Processing Letters, vol. 93, no. 5, pp. 55 61, 005. [8] Y. Da, X. R. Ge. An Improved PSO-based ANN with Simulated Annealing Technique. Neurocomputing, vol. 63, no. 4, pp. 57 533, 005. [9] H. M. Feng, C. Y. Chen, F. Ye. Evolutionary Fuzzy Particle Swarm Optimization Vector Quantization Learning Scheme in Image Compression. Expert Systems with Applications, vol. 3, no. 1, pp. 13, 007. [10] N. Ahmed, T. Natarajan, K. R. Rao. On Image Processing and a Discrete Cosine Transform. IEEE Transactions on Computers, vol. 3, no. 1, pp. 90 93, 1974. [11] J.B.Li,S.C.Chu,J.S.Pan,J.H.Ho.ANovelMatrix Norm Based Gaussian Kernel for Feature Extraction of Images. In Proceedings of IEEE International Conference on Intelligent Information Hiding and Multimedia Signal Processing, IEEE Press, Pasadena, California, USA, pp. 305 308, 006. [1] AT&T Laboratories Cambridge, [Online], Available: www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase. html, November 1, 006. Yong-Zhong Lu received his B. Sc. and Ph. D. degrees from the Huazhong University of Science and Technology (HUST), China, in 1993 and 001, respectively. He is currently an associate professor at the School of Software Engineering of HUST. He has published more than 50 refereed journal and conference papers. He is a member of China Computer Federation. His research interests include pattern recognition, image processing, software engineering, and industry control.