Learning Robust and Discriminative Subspace With Low-Rank Constraints

Abstract

Abstract-In this paper, we aim at learning robust and discriminative subspaces from noisy data. Subspace learning is widely used in extracting discriminative features for classification. However, when data are contaminated with severe noise, the performance of most existing subspace learning methods would be limited. Recent advances in low-rank modeling provide effective solutions for removing noise or outliers contained in sample sets, which motivates us to take advantage of low-rank constraints in order to exploit robust and discriminative subspace for classification. In particular, we present a discriminative subspace learning method called the supervised regularizationbased robust subspace (SRRS) approach, by incorporating the low-rank constraint. SRRS seeks low-rank representations from the noisy data, and learns a discriminative subspace from the recovered clean data jointly. A supervised regularization function is designed to make use of the class label information, and therefore to enhance the discriminability of subspace. Our approach is formulated as a constrained rank-minimization problem. We design an inexact augmented Lagrange multiplier optimization algorithm to solve it. Unlike the existing sparse representation and low-rank learning methods, our approach learns a low-dimensional subspace from recovered data, and explicitly incorporates the supervised information. Our approach and some baselines are evaluated on the COIL-100, ALOI, Extended YaleB, FERET, AR, and KinFace databases. The experimental results demonstrate the effectiveness of our approach, especially when the data contain considerable noise or variations.

Modal-Regression-Based Structured Low-Rank Matrix Recovery for Multiview Learning

“…Problem (1) is hard to optimize due to the discrete nature of the rank function [37]. A common practice to handle this problem is to replace rank function with nuclear norm [36], [38], and then Eq. (1) can be substituted with the following convex optimization [39], [40]:…”

Discriminative Elastic-Net Regularized Linear Regression

“…discrete targets, and then exploit the projection matrix to make image classification or regression [3], [4]. In addition, discriminative methods can achieve impressive performance when constructing robust projection matrix and providing sufficient training samples [5], [6].…”

“…Latent low-rank representation (LatLRR) [26] explores the unobserved hidden information of data, and can robustly extract salient features from noise or corrupted data. Subsequently, many variations of the low-rank minimization have been applied to solve different problems [3], [27]- [29]. For example, Li and Fu [3] proposed a supervised regularization-based robust subspace learning method by jointly removing noise term with low-rank constraint and learning a discriminate subspace from the clean data.…”

“…Subsequently, many variations of the low-rank minimization have been applied to solve different problems [3], [27]- [29]. For example, Li and Fu [3] proposed a supervised regularization-based robust subspace learning method by jointly removing noise term with low-rank constraint and learning a discriminate subspace from the clean data. Wei et al [27] designed a method of low-rank matrix recovery method by embedding the structure incoherence (LRSI) information for robust face recognition.…”

Face representation learning and its applications on social media

“…To evaluate the scalability of our method and competing methods, we separately utilize samples of 20, 40, 60, 80 and 100 objects in this dataset. Several subspace methods (NPE [55], LSDA [56] and SRRS [60]) and latest DL based classification methods, i.e. [59], LCLRD [29] are compared in this dataset.…”