Discriminative low-rank dictionary learning for face recognition

Abstract

Based on Low-Rank Representation (LRR), this paper presents a novel dictionary learning method to learn a discriminative dictionary which is more suitable for face recognition. Specifically, in order to make the dictionary more discriminating, we introduce an ideal regularization term with label information of training data to obtain low-rank coefficients. In the dictionary learning process, by optimizing the within-class reconstruction error and minimizing of between-class sub dictionaries, the learned dictionary has good representation ability for the training samples. In addition, we also suggest each sub dictionary is low-rank, which can violate with noise contained in training samples and make the dictionary more pure and compact. The learned dictionary and structured discriminative low-rank representation then will be used for classification. The proposed Discriminative Low-Rank Dictionary Learning (DLR_DL) method is evaluated on public face databases in comparison with previous dictionary learning under the same learning conditions. The experimental results demonstrate the effectiveness and robustness of our approach.

Introduction

In recent years, dictionary learning has been successfully applied in the field of computer vision. Many dictionary learning methods have been proposed and have achieved state-of-the-art performances for image processing [1], [2], [3] and classification [4], [5], [6], [7], [8], [9], [10], [11]. The dictionary learning is usually used for sparse representation or approximation of signals, and it aims to learn a dictionary from training samples in which only a few atoms can be linearly combined to well approximate given test samples.

The most basic way to build a dictionary is directly to use the training samples. Wright et al. [12] introduced sparse representation based classification (SRC) algorithm, where all the training samples are used to form a dictionary, and a test image is classified by finding its sparse representation with respect to this dictionary. Many methods have been proposed to improve the performance of SRC [13], [14], [15]. However, in these methods if the number of training images is very large, this will result in a big size dictionary which requires much memory and high computational cost. In addition, using original training samples as a dictionary could not exploit the discriminating information hidden in the training samples.

Several methods have been proposed to learn a small-sized dictionary from the training samples. KSVD [2] is proposed to efficiently learn an over-complete dictionary by updating dictionary atoms and sparse representations iteratively. This method has been applied in image compression and denoising. KSVD only considers the representational power of the learned dictionary but ignores its capability dicrimination. Marial et al. [4] proposed the dictionary learning model by adding a discriminative reconstruction constraint to gain the discriminative ability. Marial et al. [16] prpoposed an online dictionary learning algorithm for digit recognition and texture classification. By incorporating the classification error into the objective function, Zhang and Li [8] proposed discriminative KSVD (D-KSVD) algorithm for face recognition. Pham and Venkatesh [6] obtained a discriminative dictionary for object categorization and utilized a linear predictive classier to realize face recognition. The above methods learn a common dictionary shared by all classes as a classifier of coefficients for classification. However, the learned dictionary shared by all classes can easily lose the corresponding information between dictionary atoms and the class label, and hence they are not really effective while using the reconstruction error associated with each class for the classification. Some methods use the reconstruction error of each class as the discriminative information for classification are proposed. Yang et al. [11] learned a dictionary of each class for face recognition and achieved better results than SRC. Jiang et al. [17] add a label consistence term on K-SVD algorithm (LC-KSVD) to make the dictionary more discriminative for sparse coding. To reduce the computational complexity, Lee et al. [18] and Wang et al. [19] emphasized specific discriminative criteria to learn an over-complete dictionary. Ramirez et al. [9] learned the dictionaries with structure incoherence and shared features. Yang et al. [20] proposed a Fisher Discriminative Dictionary Learning (FDDL) for sparse representation. Studer and Baraniuk [21] investigated dictionary learning from sparsely corrupted signals. These above methods can learn concurrently the optimal dictionary and improve the discriminative capability of coding vectors. However, in the case of training samples corrupted with large noise, the dictionary atoms will also get corrupted.

In recent years, based on low-rank matrix recovery and completion [22], [23], [24], Wright et al. [25] proposed the Robust Principal Component Analysis (RPCA) to recover the underlying low-rank structure in the data. It has been successfully applied to applications including salient object detection [26], segmentation and grouping [27], [28], background subtraction [29], and tracking [30]. In image classification, Chen et al. [31] use low rank matrix recovery to remove noise from the training sample class by class for face recognition. Furthermore, Liu et al. [32], [33] established a low-rank representation (LRR) as an efficient way to perform noise correction and subspace segmentation simultaneously. Based on low-rank representation, a number of dictionary learning methods for image classification have been proposed. Ma et al. [34] presented a discriminative low-rank dictionary for sparse representation (DLRD_SR). By integrating rank minimization into sparse representation for dictionary learning, this method achieved impressive face recognition results especially when corruption existed. Zhang et al. [35] proposed a structure low-rank representation for image classification, by adding a regularization term to the objective function. Recently, Li et al. [36] proposed discriminative dictionary learning with low-rank regularization (D²L²R²) for image classification that can handle training samples corrupted with large noise. D²L²R² combines the Fisher discrimination function with low-rank on the sub dictionary to make the learned dictionary more discerning and pure.

In this paper, we propose a Discriminative Low-Rank Dictionary Learning (DLR_DL) method for face recognition. To improve the discriminative power of the dictionary, we use an ideal regularization term with label information of training samples, which is incorporated into the objective function as a discrimination regularization term. When the training samples are corrupted with large noise, the dictionary atoms will get corrupted. Therefore, to reduce the effect of noise contained in training samples, we suggest each sub dictionary is low-rank, which can violate with noise contained in training samples and make the dictionary more pure and compact. In the dictionary learning process, we make each class specific in the whole structured discriminative dictionary which has good representation ability for the training samples from the associated class but poor for other class. The low-rank sparse coefficients and discriminate low-rank dictionary learned then will be used for classification.

Unlike DLRD_SR algorithm proposed in Ref. [34], the low-rank regularization can cause losses of certain information, however, our approach can still perform well by combining label information with low-rank representation. Different from the recently proposed algorithm in Ref. [35], which improves the representation power of the dictionary while ignoring its discriminative capacity, our method has superior performance by optimizing the reconstruction error of each class in the dictionary learning process. Compared with the SRC and DLRD_SR, DLR_DL not only get higher classification accuracy, but also learns a smaller dictionary. Experimental results show that our approach has competitive performance in pattern recognition tasks.

The remainder of this paper is organized as follows: Section 2 gives a brief review of some related work. Section 3 introduces a Discriminative Low-Rank Dictionary Learning approach. Section 4 presents the optimization of the proposed model. Section 5 describes the classification scheme. Experimental results are given in Section 6. Finally, Section 7 concludes this paper.