Matrix variate distribution-induced sparse representation for robust image classification

Consensus Sparsity: Multi-Context Sparse Image Representation via L∞-Induced Matrix Variate

The sparsity is an attractive property that has been widely and intensively utilized in various image processing fields (e.g., robust image representation, image compression, image analysis, etc.). Its actual success owes to the exhaustive mining of the intrinsic (or homogenous) information from the whole data carrying redundant information. From the perspective of image representation, the sparsity can successfully find an underlying homogenous subspace from a collection of training data to represent a given test sample. The famous sparse representation (SR) and its variants embed the sparsity by representing the test sample using a linear combination of training samples with $L_{0}$ -norm regularization and $L_{1}$ -norm regularization. However, although these state-of-the-art methods achieve powerful and robust performances, the sparsity is not fully exploited on the image representation in the following three aspects: 1) the within-sample sparsity, 2) the between-sample sparsity, and 3) the image structural sparsity. In this paper, to make the above-mentioned multi-context sparsity properties agree and simultaneously learned in one model, we propose the concept of consensus sparsity (Con-sparsity) and correspondingly build a multi-context sparse image representation (MCSIR) framework to realize this. We theoretically prove that the consensus sparsity can be achieved by the $L_{\infty }$ -induced matrix variate based on the Bayesian inference. Extensive experiments and comparisons with the state-of-the-art methods (including deep learning) are performed to demonstrate the promising performance and property of the proposed consensus sparsity.

Enhanced Group Sparse Regularized Nonconvex Regression for Face Recognition

Regression analysis based methods have shown strong robustness and achieved great success in face recognition. In these methods, convex l₁-norm and nuclear norm are usually utilized to approximate the l₀-norm and rank function. However, such convex relaxations may introduce a bias and lead to a suboptimal solution. In this paper, we propose a novel Enhanced Group Sparse regularized Nonconvex Regression (EGSNR) method for robust face recognition. An upper bounded nonconvex function is introduced to replace l₁-norm for sparsity, which alleviates the bias problem and adverse effects caused by outliers. To capture the characteristics of complex errors, we propose a mixed model by combining γ-norm and matrix γ-norm induced from the nonconvex function. Furthermore, an l_2,γ-norm based regularizer is designed to directly seek the interclass sparsity or group sparsity instead of traditional l_2,1-norm. The locality of data, i.e., the distance between the query sample and multi-subspaces, is also taken into consideration. This enhanced group sparse regularizer enables EGSNR to learn more discriminative representation coefficients. Comprehensive experiments on several popular face datasets demonstrate that the proposed EGSNR outperforms the state-of-the-art regression based methods for robust face recognition.

Locality-Constrained Discriminative Matrix Regression for Robust Face Identification

Regression-based methods have been widely applied in face identification, which attempts to approximately represent a query sample as a linear combination of all training samples. Recently, a matrix regression model based on nuclear norm has been proposed and shown strong robustness to structural noises. However, it may ignore two important issues: the label information and local relationship of data. In this article, a novel robust representation method called locality-constrained discriminative matrix regression (LDMR) is proposed, which takes label information and locality structure into account. Instead of focusing on the representation coefficients, LDMR directly imposes constraints on representation components by fully considering the label information, which has a closer connection to identification process. The locality structure characterized by subspace distances is used to learn class weights, and the correct class is forced to make more contribution to representation. Furthermore, the class weights are also incorporated into a competitive constraint on the representation components, which reduces the pairwise correlations between different classes and enhances the competitive relationships among all classes. An iterative optimization algorithm is presented to solve LDMR. Experiments on several benchmark data sets demonstrate that LDMR outperforms some state-of-the-art regression-based methods.

Weighted Mixed-Norm Regularized Regression for Robust Face Identification

Face identification (FI) via regression-based classification has been extensively studied during the recent years. Most vector-based methods achieve appealing performance in handing the noncontiguous pixelwise noises, while some matrix-based regression methods show great potential in dealing with contiguous imagewise noises. However, there is a lack of consideration of the mixture noises case, where both contiguous and noncontiguous noises are jointly contained. In this paper, we propose a weighted mixed-norm regression (WMNR) method to cope with the mixture image corruption. WMNR reveals certain essential characteristics of FI problems and bridges the vector- and matrix-based methods. Particularly, WMNR provides two advantages for both theoretical analysis and practical implementation. First, it generalizes possible distributions of the residuals into a unified feature weighted loss function. Second, it constrains the residual image as low-rank structure that can be quantified with general nonconvex functions and a weight factor. Moreover, a new reweighted alternating direction method of multipliers algorithm is derived for the proposed WMNR model. The algorithm exhibits great computational efficiency since it divides the original optimization problem into certain subproblems with analytical solution or can be implemented in a parallel manner. Extensive experiments on several public face databases demonstrate the advantages of WMNR over the state-of-the-art regression-based approaches. More specifically, the WMNR achieves an appealing tradeoff between identification accuracy and computational efficiency. Compared with the pure vector-based methods, our approach achieves more than 10% performance improvement and saves more than 70% of runtime, especially in severe corruption scenarios. Compared with the pure matrix-based methods, although it requires slightly more computation time, the performance benefits are even larger; up to 20% improvement can be obtained.

Nonparametric Bayesian Correlated Group Regression With Applications to Image Classification

Sparse Bayesian learning has emerged as a powerful tool to tackle various image classification tasks. The existing sparse Bayesian models usually use independent Gaussian distribution as the prior knowledge for the noise. However, this assumption often contradicts to the practical observations in which the noise is long tail and pixels containing noise are spatially correlated. To handle the practical noise, this paper proposes to partition the noise image into several 2-D groups and adopt the long-tail distribution, i.e., the scale mixture of the matrix Gaussian distribution, to model each group to capture the intragroup correlation of the noise. Under the nonparametric Bayesian estimation, the low-rank-induced prior and the matrix Gamma distribution prior are imposed on the covariance matrix of each group, respectively, to induce two Bayesian correlated group regression (BCGR) methods. Moreover, the proposed methods are extended to the case with unknown group structure. Our BCGR method provides an effective way to automatically fit the noise distribution and integrates the long-tail attribute and structure information of the practical noise into model. Therefore, the estimated coefficients are better for reconstructing the desired data. We apply BCGR to address image classification task and utilize the learned covariance matrices to construct a grouped Mahalanobis distance to measure the reconstruction residual of each class in the design of a classifier. Experimental results demonstrate the effectiveness of our new BCGR model.

Incremental Codebook Adaptation for Visual Representation and Categorization

The bag-of-visual-words model is widely used for visual content analysis. For visual data, the codebook plays an important role for efficient representation. However, the codebook has to be relearned with the changes of training images. Once the codebook is changed, the encoding parameters of local features have to be recomputed. To alleviate this problem, in this paper, we propose an incremental codebook adaptation method for efficient visual representation. Instead of learning a new codebook, we gradually adapt a prelearned codebook using new images in an incremental way. To make use of the prelearned codebook, we try to make changes to the prelearned codebook with sparsity constraint and low-rank correlation. Besides, we also encode visually similar local features within a neighborhood to take advantage of locality information and ensure the encoded parameters are consistent. To evaluate the effectiveness of the proposed method, we apply the proposed method for categorization tasks on several public image datasets. Experimental results prove the effectiveness and usefulness of the proposed method over other codebook-based methods.

Robust Image Regression Based on the Extended Matrix Variate Power Exponential Distribution of Dependent Noise

Dealing with partial occlusion or illumination is one of the most challenging problems in image representation and classification. In this problem, the characterization of the representation error plays a crucial role. In most current approaches, the error matrix needs to be stretched into a vector and each element is assumed to be independently corrupted. This ignores the dependence between the elements of error. In this paper, it is assumed that the error image caused by partial occlusion or illumination changes is a random matrix variate and follows the extended matrix variate power exponential distribution. This has the heavy tailed regions and can be used to describe a matrix pattern of l×m dimensional observations that are not independent. This paper reveals the essence of the proposed distribution: it actually alleviates the correlations between pixels in an error matrix E and makes E approximately Gaussian. On the basis of this distribution, we derive a Schatten p -norm-based matrix regression model with L_q regularization. Alternating direction method of multipliers is applied to solve this model. To get a closed-form solution in each step of the algorithm, two singular value function thresholding operators are introduced. In addition, the extended Schatten p -norm is utilized to characterize the distance between the test samples and classes in the design of the classifier. Extensive experimental results for image reconstruction and classification with structural noise demonstrate that the proposed algorithm works much more robustly than some existing regression-based methods.

Fine-Grained Image Classification via Low-Rank Sparse Coding With General and Class-Specific Codebooks

This paper tries to separate fine-grained images by jointly learning the encoding parameters and codebooks through low-rank sparse coding (LRSC) with general and class-specific codebook generation. Instead of treating each local feature independently, we encode the local features within a spatial region jointly by LRSC. This ensures that the spatially nearby local features with similar visual characters are encoded by correlated parameters. In this way, we can make the encoded parameters more consistent for fine-grained image representation. Besides, we also learn a general codebook and a number of class-specific codebooks in combination with the encoding scheme. Since images of fine-grained classes are visually similar, the difference is relatively small between the general codebook and each class-specific codebook. We impose sparsity constraints to model this relationship. Moreover, the incoherences with different codebooks and class-specific codebooks are jointly considered. We evaluate the proposed method on several public image data sets. The experimental results show that by learning general and class-specific codebooks with the joint encoding of local features, we are able to model the differences among different fine-grained classes than many other fine-grained image classification methods.

Iterative Re-Constrained Group Sparse Face Recognition With Adaptive Weights Learning

In this paper, we consider the robust face recognition problem via iterative re-constrained group sparse classifier (IRGSC) with adaptive weights learning. Specifically, we propose a group sparse representation classification (GSRC) approach in which weighted features and groups are collaboratively adopted to encode more structure information and discriminative information than other regression based methods. In addition, we derive an efficient algorithm to optimize the proposed objective function, and theoretically prove the convergence. There are several appealing aspects associated with IRGSC. First, adaptively learned weights can be seamlessly incorporated into the GSRC framework. This integrates the locality structure of the data and validity information of the features into l_2,p -norm regularization to form a unified formulation. Second, IRGSC is very flexible to different size of training set as well as feature dimension thanks to the l_2,p -norm regularization. Third, the derived solution is proved to be a stationary point (globally optimal if p ≥ 1 ). Comprehensive experiments on representative data sets demonstrate that IRGSC is a robust discriminative classifier which significantly improves the performance and efficiency compared with the state-of-the-art methods in dealing with face occlusion, corruption, and illumination changes, and so on.