Abstract — Recently, a Two-Dimensional Principal Component Analysis (2DPCA) [1] was proposed and the authors have demonstrated its superiority over the conventional Principal Component Analysis (PCA) in face recognition. But the theoretical proof why 2DPCA is better than PCA has not been given until now. In this paper, The essence of 2DPCA is analyzed and a framework of Generalized 2D Principal Component Analysis (G2DPCA) is proposed to extend the original 2DPCA in two perspectives: a Bilateral-projection-based 2DPCA (B2DPCA) and a Kernelbased 2DPCA (K2DPCA) schemes are introduced. Experimental results in face recognition show its excellent performance. I.

Face Representation (FR) plays a typically important role in face recognition and methods such as Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) have been received wide attention recently. However, despite of the achieved successes, these FR methods will inevitably lead to poor classification performance in case of great facial variations such as expression, lighting, occlusion and so on, due to the fact that the image gray value matrices on which they manipulate are very sensitive to these facial variations. In this paper, we take notice of the facts that every image matrix can always have the well-known Singular Value Decomposition (SVD) and can be regarded as a composition of a set of base images generated by SVD, and we further point out that the leading base images (those corresponding to large singular values) on one hand are sensitive to the aforementioned facial variations and on the other hand dominate the composition of the face image. Then based on these observations, we subtly deflate the weights of the facial variation sensitive base images by a parameter α and propose a novel Fractional order Singular Value Decomposition Representation (FSVDR) to alleviate facial variations for face recognition. Finally, our experimental results show that FSVDR can: 1) effectively alleviate facial variations; and 2) form an intermediate representation for many FR methods such as PCA and LDA to significantly improve their classification performance in case of great facial variations.

Abstract. Many linear discriminant analysis (LDA) and kernel Fisher discriminant analysis (KFD) methods are based on the restrictive assumption that the data are homoscedastic. In this paper, we propose a new KFD method called heteroscedastic kernel weighted discriminant analysis (HKWDA) which has several appealing characteristics. First, like all kernel methods, it can handle nonlinearity efficiently in a disciplined manner. Second, by incorporating a weighting function that can capture heteroscedastic data distributions into the discriminant criterion, it can work under more realistic situations and hence can further enhance the classification accuracy in many real-world applications. Moreover, it can effectively deal with the small sample size problem. We have performed some face recognition experiments to compare HKWDA with several linear and nonlinear dimensionality reduction methods, showing that HKWDA consistently gives the best results. 1

Abstract. Small sample size and severe facial variation are two challenging problems for face recognition. In this paper, we propose the SIS (Single Image Subspace) approach to address these two problems. To deal with the former one, we represent each single image as a subspace spanned by its synthesized (shifted) samples, and employ a newly designed subspace distance metric to measure the distance of subspaces. To deal with the latter one, we divide a face image into several regions, compute the contribution scores of the training samples based on the extracted subspaces in each region, and aggregate the scores of all the regions to yield the ultimate recognition result. Experiments on well-known face databases such as AR, Extended YALE and FERET show that the proposed approach outperforms some renowned methods not only in the scenario of one training sample per person, but also in the scenario of multiple training samples per person with significant facial variations. 1

In high-dimensional classification problems it is infeasible to include enough training samples to cover the class regions densely. Irregularities in the resulting sparse sample distributions cause local classifiers such as Nearest Neighbors (NN) and kernel methods to have irregular decision boundaries. One solution is to “fill in the holes” by building a convex model of the region spanned by the training samples of each class and classifying examples based on their distances to these approximate models. Methods of this kind based on affine and convex hulls and bounding hyperspheres have already been studied. Here we propose a method based on the bounding hyperdisk of each class – the intersection of the affine hull and the smallest bounding hypersphere of its training samples. We argue that in many cases hyperdisks are preferable to affine and convex hulls and hyperspheres: they bound the classes more tightly than affine hulls or hyperspheres while avoiding much of the sample overfitting and computational complexity that is inherent in high-dimensional convex hulls. We show that the hyperdisk method can be kernelized to provide nonlinear classifiers based on non-Euclidean distance metrics. Experiments on several classification problems show promising results. 1.

Abstract—In this paper, covariance behavior of several features (signature identifiers) that are determined from the voltage waveform within a time window for power-quality (PQ) event detection and classification is analyzed. A feature vector using selected signature identifiers such as local wavelet transform extrema at various decomposition levels, spectral harmonic ratios, and local extrema of higher order statistical parameters, is constructed. It is observed that the feature vectors corresponding to power quality event instances can be efficiently classified according to the event type using a covariance based classifier known as the common vector classifier. Arcing fault (high impedance fault) type events are successfully classified and distinguished from motor startup events under various load conditions. It is also observed that the proposed approach is even able to discriminate the loading conditions within the same class of events at a success rate of 70%. In addition, the common vector approach provides a redundancy and usefulness information about the feature vector elements. Implication of this information is experimentally justified with the fact that some of the signature identifiers are more important than others for the discrimination of PQ event types. Index Terms—Covariance analysis, event classification, higher order statistics, power-quality (PQ) analysis. I.

In this paper, we make a study on three Linear Discriminant Analysis (LDA) based

This paper presents a new approach for face recognition based on the fusion of tensors of census transform histograms from Local Gaussian features maps. Local Gaussian feature maps encode the most relevant information from Gaussian derivative features. Census Transform (CT) histograms are calculated and concatenated to form a tensor for each class of Gaussian map. Multi-linear Principal Component Analysis (MPCA) is applied to each tensor to reduce the number of dimensions as well as the correlation between neighboring pixels due to the Census Transform. We then train Kernel Discriminative Common Vectors (KDCV) to generate a discriminative vector using the results of the MPCA. Results of recognition using MPCA of tensors-CT histograms from Gaussian features maps with KDCV is shown to compare favorably with competing techniques that use more complex features maps like for example Gabor features maps in the FERET and Yale datasets. Additional experiments were done in the Yale B+ extended Yale B Faces dataset to show the performance of Gaussian features map with hard illumination changes.

Abstract. Linear discriminant analysis (LDA) is commonly used for dimensionality reduction. In real-world applications where labeled data are scarce, LDA does not work very well. However, unlabeled data are often available in large quantities. We propose a novel semi-supervised discriminant analysis algorithm called SSDACCCP. We utilize unlabeled data to maximize an optimality criterion of LDA and use the constrained concave-convex procedure to solve the optimization problem. The optimization procedure leads to estimation of the class labels for the unlabeled data. We propose a novel confidence measure for selecting those unlabeled data points with high confidence. The selected unlabeled data can then be used to augment the original labeled data set for performing LDA. We also propose a variant of SSDACCCP, called M-SSDACCCP, which adopts the manifold assumption to utilize the unlabeled data. Extensive experiments on many benchmark data sets demonstrate the effectiveness of our proposed methods. 1

Abstract not found