Residual metric learning with class-specific consistency for multiclass classification.

Least squares regression (LSR) has been widely used in pattern recognition due to its concise form and ease of solution. However, inadequate exploration of inter-class margin and intra-class similarity limits its discriminative ability. To this end, we present a novel method called residual metric learning with class-specific consistency for multiclass classification (RMLCC). Specifically, RMLCC jointly learns a projection matrix and a metric matrix for the regression residuals in a compact framework. This joint learning mechanism makes the inter-class margin of the projected instances as large as possible in the learned metric space, prompting the instances of different classes to be separated. To further improve the generalization, the class-specific consistency constraint that stimulate intra-class similarity is cleverly embedded into the joint learning framework. To solve the proposed model, we propose an alternative optimization algorithm which guarantees weak convergence. With the interactive optimization of the projection matrix and metric matrix, RMLCC can fully exploit the structure and supervised information of the data and thus has the potential to outperform other methods. Extensive experiments on several benchmark datasets demonstrate the validity of the proposed method.