Multilinear Discriminant Analysis for Face Recognition

In this paper, we present a novel approach to solving the supervised dimensionality reduction problem by encoding an image object as a general tensor of 2nd or higher order. First, we propose a discriminant tensor criterion (DTC), whereby multiple interrelated lower-dimensional discriminative subspaces are derived for feature selection. Then, a novel approach called k-mode cluster-based discriminant analysis is presented to iteratively learn these subspaces by unfolding the tensor along different tensor dimensions. We call this algorithm discriminant analysis with tensor representation (DATER), which has the following characteristics: 1) multiple interrelated subspaces can collaborate to discriminate different classes; 2) for classification problems involving higher-order tensors, the DATER algorithm can avoid the curse of dimensionality dilemma and overcome the small sample size problem; and 3) the computational cost in the learning stage is reduced to a large extent owing to the reduced data dimensions in generalized eigenvalue decomposition. We provide extensive experiments by encoding face images as 2nd or 3rd order tensors to demonstrate that the proposed DATER algorithm based on higher order tensors has the potential to outperform the traditional subspace learning algorithms, especially in the small sample size cases.

This paper presents a novel approach to solve the supervised dimensionality reduction problem and feature extraction by encoding an image object as a general tensor of 2-D/3-D order. In this paper a multilinear principal component analysis (MPCA) for tensor object feature extraction and then a multilinear discriminant analysis (MDA), to find the best subspaces have been proposed. It should be noted that both of the algorithms work with tensor objects so the structure of the objects has been never broken. Therefore we achieve a better result than the result of the traditional methods. The focus of these algorithms is avoiding the curse of dimensionality. Finally, a comprehensive experiments on ORL and FERET databases has been provided by encoding face images as 2-D or 3-D tensors to demonstrate that MPCA+MDA algorithm based on higher order tensors has the potential to outperform the traditional vector-based subspace learning algorithms such as Eigenface and Fisherface, especially in the cases with small sample sizes and curse of dimensionality dilemma.

Recent research has demonstrated the success of tensor based subspace learning in both unsupervised and supervised configurations (e.g., 2-D PCA, 2-D LDA, and DATER). In this correspondence, we present a new semi-supervised subspace learning algorithm by integrating the tensor representation and the complementary information conveyed by unlabeled data. Conventional semi-supervised algorithms mostly impose a regularization term based on the data representation in the original feature space. Instead, we utilize graph Laplacian regularization based on the low-dimensional feature space. An iterative algorithm, referred to as adaptive regularization based semi-supervised discriminant analysis with tensor representation (ARSDA/T), is also developed to compute the solution. In addition to handling tensor data, a vector-based variant (ARSDA/V) is also presented, in which the tensor data are converted into vectors before subspace learning. Comprehensive experiments on the CMU PIE and YALE-B databases demonstrate that ARSDA/T brings significant improvement in face recognition accuracy over both conventional supervised and semi-supervised subspace learning algorithms.

Discriminant non-negative graph embedding for face recognition

In this paper, we propose using adaptive pixel/patch-based stereo matching for 2D face recognition. We don’t perform 3D reconstruction but define a measure of the similarity of two 2D face images. After rectifying the two images by epipolar geometry, we match them using the similarity for face recognition. The proposed approach has been tested on the CMU PIE and FERET database and demonstrates superior performance compared to existing methods in real-world situations including changes in pose and illumination.

A novel Gabor-Kernel face recognition method is proposed in this paper. This involves convolving a face image with a series of Gabor wavelets at different scales, locations, and orientations and extracting features from resulting Gabor filtered images. kernel discriminant analysis (KDDA) is then applied to the feature vectors for dimension reduction as well as class separability enhancement. A database of 600 frontal-view face images from the FERET face database is used to test the method. Experimental results demonstrate the advantage of KDDA over other Kernel methods such as kernel principal component analysis (KPCA) and general discriminant analysis (GDA). Significant improvements are also observed when features are extracted from Gabor filtered images instead of the original images. A 94% accuracy has been observed for the novel Gabor + KDDA method on the FERET database using a simple classifier, which could be further improved by employing a more complex classifier and distance measurer.

Sparse regularization discriminant analysis for face recognition

In this paper, we present a Sub-pattern based Multi-manifold Discriminant Analysis (SpMMDA) algorithm for face recognition. Unlike existing Multi-manifold Discriminant Analysis (MMDA) approach which is based on holistic information of face image for recognition, SpMMDA operates on sub-images partitioned from the original face image and then extracts the discriminative local feature from the sub-images separately. Moreover, the structure information of different sub-images from the same face image is considered in the proposed method with the aim of further improve the recognition performance. Extensive experiments on three standard face databases (Extended YaleB, CMU PIE and AR) demonstrate that the proposed method is effective and outperforms some other sub-pattern based face recognition methods.

This paper introduces a novel 2D Gabor-Fisher Classifier for face recognition. The 2D-GFC method applies the 2D Fisher Linear Discriminant Analysis (2D-LDA) to the gaborfaces which is derived from the Gabor wavelets representation of face images. In our method, Gabor wavelets first derive desirable facial features characterized by spatial frequency, spatial locality, and orientation selectivity to cope with the variations due to illumination and facial expression changes. 2D-LDA is then used to enhance the face recognition performance by maximizing the Fisher's linear projection criterion. To evaluate the performance of 2D-GFC, experiments were conducted on FERET database with several other methods.

Subspace learning techniques are among the most popular methods for face recognition. In this paper, we propose a novel face recognition technique for two dimensional subspace learning which is able to exploit the symmetry nature of human faces. We extent the Two Dimensional Clustering based Discriminant Analysis (2DCDA) by incorporating an appropriate symmetry regularizer into its objective function in order to determine symmetric projection vectors. The proposed Symmetric Two Dimensional Clustering based Discriminant Analysis technique has been applied to the face recognition problem. Experimental results showed that the proposed technique achieves better classification performance in comparison to the standard one.

Incremental learning of complete linear discriminant analysis for face recognition

This paper presents a novel Gabor-based kernel Principal Component Analysis (PCA) method by integrating the Gabor wavelet representation of face images and the kernel PCA method for face recognition. Gabor wavelets first derive desirable facial features characterized by spatial frequency, spatial locality, and orientation selectivity to cope with the variations due to illumination and facial expression changes. The kernel PCA method is then extended to include fractional power polynomial models for enhanced face recognition performance. A fractional power polynomial, however, does not necessarily define a kernel function, as it might not define a positive semidefinite Gram matrix. Note that the sigmoid kernels, one of the three classes of widely used kernel functions (polynomial kernels, Gaussian kernels, and sigmoid kernels), do not actually define a positive semidefinite Gram matrix either. Nevertheless, the sigmoid kernels have been successfully used in practice, such as in building support vector machines. In order to derive real kernel PCA features, we apply only those kernel PCA eigenvectors that are associated with positive eigenvalues. The feasibility of the Gabor-based kernel PCA method with fractional power polynomial models has been successfully tested on both frontal and pose-angled face recognition, using two data sets from the FERET database and the CMU PIE database, respectively. The FERET data set contains 600 frontal face images of 200 subjects, while the PIE data set consists of 680 images across five poses (left and right profiles, left and right half profiles, and frontal view) with two different facial expressions (neutral and smiling) of 68 subjects. The effectiveness of the Gabor-based kernel PCA method with fractional power polynomial models is shown in terms of both absolute performance indices and comparative performance against the PCA method, the kernel PCA method with polynomial kernels, the kernel PCA method with fractional power polynomial models, the Gabor wavelet-based PCA method, and the Gabor wavelet-based kernel PCA method with polynomial kernels.

Locality-preserving projection (LPP) is a promising manifold-based dimensionality reduction and linear feature extraction method for face recognition. However, there exist two main issues in traditional LPP algorithm. LPP does not utilize the class label information at the training stage and its performance will be affected for classification tasks. In addition, LPP often suffers from small sample size (3S) problem, which occurs when the dimension of input pattern space is greater than the number of training samples. Under this situation, LPP fails to work. To overcome these two limitations, this paper presents a novel supervised regularization LPP (SRLPP) approach based on a supervised graph and a new regularization strategy. It theoretically proves that regularization matrix [Formula: see text] approaches to the original one as the regularized parameter tends to zero. The proposed SRLPP method is subsequently applied to face recognition. The experiments are conducted on two publicly available face databases, namely ORL database and FERET database. Compared with some existing LDA-based and LPP-based linear feature extraction approaches, experimental results show that our SRLPP approach gives superior performance.

With the improvement of security requirements of individuals, businesses and countries, the identity authentication system based on face recognition technology is applied widely. The identity methods based on single theory, due to a variety of factors, have their own inherent limitations. In order to improve the efficiency and accuracy of face recognition, based on fusion of wavelet packet sub-images, a face recognition algorithm named FW-FLD is proposed in this paper by combining PCA (Principal Component Analysis) and FLD(Fisher Linear Discriminant). Firstly, the training samples are decomposed using wavelet packet. The fusion weights of the decomposed sub-images are calculated according to their energy distribution and the weighted fusion images are obtained, which reserve the images characteristic in the frequency. Then the features of the fused images are extracted using PCA, and the optimized Fisher space is constructed using FLD. Finally, face images are classified by measuring the projection coefficients of optimized training samples and testing samples in Fisher space. Experimental results on CMU PIE, JAFFE and AR face databases show that the proposed algorithm is robust, and can adapt to face recognition with various illumination, facial expressions and gestures. Compared with other algorithms, it not only improves the face recognition rate, but also has a higher time efficiency.

Adaptive noise dictionary construction via IRRPCA for face recognition