Low-rank matrix recovery with discriminant regularization

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. © Springer-Verlag 2013.