Two-Dimensional Quaternion Sparse Discriminant Analysis

Making the Most of Single Sensor Information: A Novel Fusion Approach for 3D Face Recognition Using Region Covariance Descriptors and Gaussian Mixture Models

Most commercially successful face recognition systems combine information from multiple sensors (2D and 3D, visible light and infrared, etc.) to achieve reliable recognition in various environments. When only a single sensor is available, the robustness as well as efficacy of the recognition process suffer. In this paper, we focus on face recognition using images captured by a single 3D sensor and propose a method based on the use of region covariance matrixes and Gaussian mixture models (GMMs). All steps of the proposed framework are automated, and no metadata, such as pre-annotated eye, nose, or mouth positions is required, while only a very simple clustering-based face detection is performed. The framework computes a set of region covariance descriptors from local regions of different face image representations and then uses the unscented transform to derive low-dimensional feature vectors, which are finally modeled by GMMs. In the last step, a support vector machine classification scheme is used to make a decision about the identity of the input 3D facial image. The proposed framework has several desirable characteristics, such as an inherent mechanism for data fusion/integration (through the region covariance matrixes), the ability to explore facial images at different levels of locality, and the ability to integrate a domain-specific prior knowledge into the modeling procedure. Several normalization techniques are incorporated into the proposed framework to further improve performance. Extensive experiments are performed on three prominent databases (FRGC v2, CASIA, and UMB-DB) yielding competitive results.

Two-dimensional Bhattacharyya bound linear discriminant analysis with its applications

The recently proposed L2-norm linear discriminant analysis criterion based on Bhattacharyya error bound estimation (L2BLDA) was an effective improvement over linear discriminant analysis (LDA) and was used to handle vector input samples. When faced with two-dimensional (2D) inputs, such as images, converting two-dimensional data to vectors, regardless of the inherent structure of the image, may result in some loss of useful information. In this paper, we propose a novel two-dimensional Bhattacharyya bound linear discriminant analysis (2DBLDA). 2DBLDA maximizes the matrix-based between-class distance, which is measured by the weighted pairwise distances of class means and minimizes the matrix-based within-class distance. The criterion of 2DBLDA is equivalent to optimizing the upper bound of the Bhattacharyya error. The weighting constant between the between-class and within-class terms is determined by the involved data that make the proposed 2DBLDA adaptive. The construction of 2DBLDA avoids the small sample size (SSS) problem, is robust, and can be solved through a simple standard eigenvalue decomposition problem. The experimental results on image recognition and face image reconstruction demonstrate the effectiveness of 2DBLDA.

Generalized two-dimensional linear discriminant analysis with regularization

Recent advances show that two-dimensional linear discriminant analysis (2DLDA) is a successful matrix based dimensionality reduction method. However, 2DLDA may encounter the singularity issue theoretically, and also is sensitive to outliers. In this paper, a generalized Lp-norm 2DLDA framework with regularization for an arbitrary p>0 is proposed, named G2DLDA. There are mainly two contributions of G2DLDA: one is G2DLDA model uses an arbitrary Lp-norm to measure the between-class and within-class scatter, and hence a proper p can be selected to achieve robustness. The other one is that the introduced regularization term makes G2DLDA enjoy better generalization performance and avoid singularity. In addition, an effective learning algorithm is designed for G2LDA, which can be solved through a series of convex problems with closed-form solutions. Its convergence can be guaranteed theoretically when 1≤p≤2. Preliminary experimental results on three contaminated human face databases show the effectiveness of the proposed G2DLDA.

Prior Knowledge Regularized Multiview Self-Representation and its Applications

To learn the self-representation matrices/tensor that encodes the intrinsic structure of the data, existing multiview self-representation models consider only the multiview features and, thus, impose equal membership preference across samples. However, this is inappropriate in real scenarios since the prior knowledge, e.g., explicit labels, semantic similarities, and weak-domain cues, can provide useful insights into the underlying relationship of samples. Based on this observation, this article proposes a prior knowledge regularized multiview self-representation (P-MVSR) model, in which the prior knowledge, multiview features, and high-order cross-view correlation are jointly considered to obtain an accurate self-representation tensor. The general concept of "prior knowledge" is defined as the complement of multiview features, and the core of P-MVSR is to take advantage of the membership preference, which is derived from the prior knowledge, to purify and refine the discovered membership of the data. Moreover, P-MVSR adopts the same optimization procedure to handle different prior knowledge and, thus, provides a unified framework for weakly supervised clustering and semisupervised classification. Extensive experiments on real-world databases demonstrate the effectiveness of the proposed P-MVSR model.

Low-Rank Preserving t-Linear Projection for Robust Image Feature Extraction

As the cornerstone for joint dimension reduction and feature extraction, extensive linear projection algorithms were proposed to fit various requirements. When being applied to image data, however, existing methods suffer from representation deficiency since the multi-way structure of the data is (partially) neglected. To solve this problem, we propose a novel Low-Rank Preserving t-Linear Projection (LRP-tP) model that preserves the intrinsic structure of the image data using t-product-based operations. The proposed model advances in four aspects: 1) LRP-tP learns the t-linear projection directly from the tensorial dataset so as to exploit the correlation among the multi-way data structure simultaneously; 2) to cope with the widely spread data errors, e.g., noise and corruptions, the robustness of LRP-tP is enhanced via self-representation learning; 3) LRP-tP is endowed with good discriminative ability by integrating the empirical classification error into the learning procedure; 4) an adaptive graph considering the similarity and locality of the data is jointly learned to precisely portray the data affinity. We devise an efficient algorithm to solve the proposed LRP-tP model using the alternating direction method of multipliers. Extensive experiments on image feature extraction have demonstrated the superiority of LRP-tP compared to the state-of-the-arts.