Subspace Methods for Face Recognition: Singularity, Regularization, and Robustness
Wangmeng Zuo, Kuanquan Wang, Hongzhi Zhang · 2009
Previous workAt the beginning, linear unsupervised method, such as principal component analysis (PCA), was used to extract the holistic feature vectors for facial image representation and recognition (Turk & Pentland, 1991).Other unsupervised methods, such as independent component analysis (ICA) and non-negative matrix factorization (NMF), have been subsequently applied to face recognition (Bartlett et al., 2002;Zafeiriou et al., 2006).Since the unsupervised methods do not utilize the class label information in the training stage, it is generally believed that the supervised methods are more effective in dealing with recognition problems.Fisher linear discriminant analysis (LDA), which aims to find a set of optimal discriminant vectors that map the original data into a low-dimensional feature space, is then gaining popularity in face recognition.In 1996, Fisher linear discriminant analysis was applied to face recognition, and subsequently was developed into one of the most famous face recognition approaches, Fisherfaces (Swets & Weng, 1996;Belhumeur et al., 1997).In face recognition, the data dimensionality is much higher than the size of the training set, leading to the small sample size problem (the SSS problem).Currently there are two popular strategies to solve the SSS problem, the transform-based and the algorithmbased.The transform-based strategy first reduces the dimensions of the original image data and then uses LDA for feature extraction, while the algorithm-based strategy finds an algorithm to circumvent the SSS problem (Yang & Yang, 2003;Yu & Yang, 2001).Face recognition usually is highly complex and can not be regarded as a linear problem.In the last few years, a class of nonlinear discriminant analysis techniques named as kernel discriminant analysis has been widely investigated for face recognition.A number of kernelmethods, such as kernel principal component analysis (KPCA), kernel Fisher's discriminant analysis, complete kernel Fisher discriminant (CKFD), and kernel direct discriminant analysis (KDDA), have been developed (Liu, 2004;Yang, 2002; Yang et al., 2005b;Lu et al., 2003).Most recently, manifold learning methods, such as isometric feature mapping (ISOMAP), locally linear embedding (LLE), and Laplacian eigenmaps, have also shown great potential in face recognition (Tenenbaum et al., 2000;Roweis & Saul, 2000; He et al., 2005).As a generalization of vector-based methods, a number of tensor discrimination technologies have been proposed.The beginning of tensor discrimination technology can be traced back to 1993, where a 2D image matrix based algebraic feature extraction method is proposed for image recognition (Liu et al., 1993).As a new development of the 2D image matrix based straightforward projection technique, a two-Dimensional PCA (2DPCA) approach was suggested for face representation and recognition (Yang et al., 2004).To further reduce computational cost, researchers had developed several BDPCA and generalized low rank approximations of matrices (GLRAM) approaches (Ye, 2004; Zuo et al., 2005a).Motivated by multilinear generalization of singular vector decomposition (Lathauwer et al., 2000), a number of alterative supervised and unsupervised tensor analysis methods have been proposed for facial image or image sequence feature extraction (Tao et al., 2005;Yan et al., 2007). Organization of this chapterGenerally, there are three issues which should be addressed in the development of subspace methods for face recognition, singularity, regularization, and robustness.First, the dimensionality of facial image usually is higher than the size of the available training set, www.intechopen.com