Bi-2DPCA: A Fast Face Coding Method for Recognition

Face recognition has received significant attention in the past decades due to its potential applications in biometrics, information security, law enforcement, etc. Numerous methods have been suggested to address this problem [1]. Among appearance-based holistic approaches, principal component analysis (PCA) turns out to be very effective. As a classical unsupervised learning and data analysis technique, PCA was first used to represent images of human faces by Sirovich and Kirby in 1987 [2, 3]. Subsequently, Turk and Pentland [4, 5] applied PCA to face recognition and presented the well-known Eigenfaces method in 1991. Since then, PCA has been widely investigated and has become one of the most successful approaches to face recognition [6-15]. PCA-based image representation and analysis technique is based on image vectors. That is, before applying PCA, the given 2D image matrices must be mapped into 1D image vectors by stacking their columns (or rows). The resulting image vectors generally lead to a highdimensional image vector space. In such a space, calculating the eigenvectors of the covariance matrix is a critical problem deserving consideration. When the number of training samples is smaller than the dimension of images, the singular value decomposition (SVD) technique is useful for reducing the computational complexity [1-4]. However, when the training sample size becomes large, the SVD technique is helpless. To deal with this problem, an incremental principal component analysis (IPCA) technique has been proposed recently [16]. But, the efficiency of this algorithm still depends on the distribution of data. Over the last few years, two PCA-related methods, independent component analysis (ICA) [17] and kernel principal component analysis (KPCA) [18, 19] have been of wide concern. Bartlett [20], Yuen [21], Liu [22], and Draper [23] proposed using ICA for face representation and found that it was better than PCA when cosine was used as the similarity measure (however, the performance difference between ICA and PCA was not significant if the Euclidean distance is used [23]). Yang [24] and Liu [25] used KPCA for face feature extraction and recognition and showed that KPCA outperforms the classical PCA. Like PCA, ICA and KPCA both follow the matrix-to-vector mapping strategy when they are used for image analysis and, their algorithms are more complex than PCA. So, ICA and KPCA are considered to be computationally more expensive than PCA. The experimental results in 16