Low-Rank Matrix Recovery with Discriminant Regularization

Abstract

Abstract. Recently, image classification has been an active research topic due to the urgent need to retrieve and browse digital images via semantic keywords. Based on the success of low-rank matrix recovery which has been applied to statistical learning, computer vision and signal processing, this paper presents a novel low-rank matrix recovery algorithm with discriminant regularization. Standard low-rank matrix recovery algorithm decomposes the original dataset into a set of representative basis with a corresponding sparse error for modeling the raw data. Motivated by the Fisher criterion, the proposed method executes low-rank matrix recovery in a supervised manner, i.e., taking the with-class scatter and between-class scatter into account when the whole label information is available. The paper shows that the formulated model can be solved by the augmented Lagrange multipliers, and provide additional discriminating ability to the standard low-rank models for improved performance. The representative bases learned by the proposed method are encouraged to be structural coherence within the same class, and as independent as possible between classes. Numerical simulations on face recognition tasks demonstrate that the proposed algorithm is competitive with the state-of-the-art alternatives.

Learning Robust and Discriminative Subspace With Low-Rank Constraints

“…This method differs from our approach in two aspects. First, RPCA used in [43] can only model one single subspace, whereas our approach is able to discover multiple subspaces by virtue of LRR, which fits well for multiclass classification problems. Second, the method in [43] separately learns low-rank data representation and subspace, which means the obtained subspace cannot be guaranteed to be optimal, whereas our approach iteratively learns LRRs and discriminative subspaces.…”

“…In [43], a discriminant regularization term is incorporated into the formulation of RPCA. This method differs from our approach in two aspects.…”

Enhanced low-rank representation via sparse manifold adaption for semi-supervised learning

“…Based on the results of sparse manifold adaption in Section 4.2, we set (N i , γ ) as a near optimal combination (20, 1) for all data sets. As reported in Zhuang et al (2012) and Zheng, Zhang, Jia et al (2013), LRR variants are insensitive to the variation of λ provided that it is given a relatively large value (usually 10). Thus it is reasonable to set λ as a fixed value to alleviate the burden of parameter tuning, which means that the level of corruption in data could be fixed.…”

“…GLRR model employs accelerated gradient method (Ji & Ye, 2009) to update J, which is the auxiliary variable w.r.t. Z; while in our experiments, we relax the GLRR objective function as described in Zheng, Zhang, Jia et al (2013) to solve J by using the SVT operator .…”

“…Non-negative low-rank and sparse (NNLRS) graph (Zhuang, Gao, Lin, Ma, Zhang and Yu, 2012) was proposed by imposing the non-negative and sparse constraints on the low-rank representation coefficient. Zheng et al presented an algorithm to construct the graph based on low-rank representation with local constraint (LRRLC) (Zheng, Zhang, Jia, Zhao, Guo, Fu and Yu, 2013) in which the local structure is preserved by a locally constrained regularization and the global structure is preserved by LRR. A graph regularization term was added on the LRR objective and the graph regularized low-rank representation (GLRR) model was formulated for destriping of hyperspectral images in Lu, Wang, and Yuan (2013).…”