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The literature on independent component analysis (ICA)based face recognition generally evaluates its performance using standard principal component analysis (PCA) within two architectures, ICA Architecture I and ICA Architecture II. In this correspondence, we analyze these two ICA architectures and find that ICA Architecture I involves a vertically centered PCA process (PCA I), while ICA Architecture II involves a whitened horizontally centered PCA process (PCA II). Thus, it makes sense to use these two PCA versions as baselines to reevaluate the performance of ICA-based face-recognition systems. Experiments on the FERET, AR, and AT&T face-image databases showed no significant differences between ICA Architecture I (II) and PCA I (II), although ICA Architecture I (or II) may, in some cases, significantly outperform standard PCA. It can be concluded that the performance of ICA strongly depends on the PCA process that it involves. Pure ICA projection has only a trivial effect on performance in face recognition. Index Terms--Face recognition, feature extraction, image representation, independent component analysis (ICA), principal component analysis (PCA).

This paper develops an unsupervised discriminant projection (UDP) technique for dimensionality reduction of high-dimensional data in small sample size cases. UDP can be seen as a linear approximation of a multimanifolds-based learning framework which takes into account both the local and nonlocal quantities. UDP characterizes the local scatter as well as the nonlocal scatter, seeking to find a projection that simultaneously maximizes the nonlocal scatter and minimizes the local scatter. This characteristic makes UDP more intuitive and more powerful than the most up-to-date method, Locality Preserving Projection (LPP), which considers only the local scatter for clustering or classification tasks. The proposed method is applied to face and palm biometrics and is examined using the Yale, FERET, and AR face image databases and the PolyU palmprint database. The experimental results show that UDP consistently outperforms LPP and PCA and outperforms LDA when the training sample size per class is small. This demonstrates that UDP is a good choice for real-world biometrics applications. Index Terms--Dimensionality reduction, feature extraction, subspace learning, Fisher linear discriminant analysis (LDA), manifold learning, biometrics, face recognition, palmprint recognition.

The topologies of data distributions are very important for data description. Usually, it is not easy to find a description that can give us an intuitional understanding of the topologies for general distributions. In this paper, a novel concept, a topology graph, is proposed as a description for the principal topology of data distribution. The topology graph builds a one-to-one correspondence between the principal topology of the distribution and the topology itself: annularity features of the principal topology correspond to the loops of the graph, and the divarication features correspond to the branches of the graph. In general, the topology graph can be considered as the skeleton of the data distribution. A divide-and-combine learning strategy is developed to find the topology graphs for general data distributions. The learning strategy is focused on the constrained local description learning and automatic topology generation. Following the learning strategy, a cluster growing algorithm is developed. Experimental results on both artificial datasets and real-world applications show good performance of the proposed algorithm. Index Terms--Piecewise curvilinear feature detection, skeletonization, topology description, topology graph.

This paper examines the theory of kernel Fisher discriminant analysis (KFD) in a Hilbert space and develops a two-phase KFD framework, i.e., kernel principal component analysis (KPCA) plus Fisher linear discriminant analysis (LDA). This framework provides novel insights into the nature of KFD. Based on this framework, the authors propose a complete kernel Fisher discriminant analysis (CKFD) algorithm. CKFD can be used to carry out discriminant analysis in "double discriminant subspaces." The fact that, it can make full use of two kinds of discriminant information, regular and irregular, makes CKFD a more powerful discriminator. The proposed algorithm was tested and evaluated using the FERET face database and the CENPARMI handwritten numeral database. The experimental results show that CKFD outperforms other KFD algorithms. Index Terms--Kernel-based methods, subspace methods, principal component analysis (PCA), Fisher linear discriminant analysis (LDA or FLD), feature extraction, machine learning, face recognition, handwritten digit recognition.

In this paper, a new technique coined two-dimensional principal component analysis (2DPCA) is developed for image representation. As opposed to PCA, 2DPCA is based on 2D image matrices rather than 1D vectors so the image matrix does not need to be transformed into a vector prior to feature extraction. Instead, an image covariance matrix is constructed directly using the original image matrices, and its eigenvectors are derived for image feature extraction. To test 2DPCA and evaluate its performance, a series of experiments were performed on three face image databases: ORL, AR, and Yale face databases. The recognition rate across all trials was higher using 2DPCA than PCA. The experimental results also indicated that the extraction of image features is computationally more efficient using 2DPCA than PCA. Index Terms--Principal Component Analysis (PCA), Eigenfaces, feature extraction, image representation, face recognition.