Margin-based discriminant embedding guided sparse matrix regression for image supervised feature selection

Abstract

Matrix regression uses matrix data as input and directly selects the features from matrix data by employing several couples of left and right regression matrices. However, the existing matrix regression methods do not consider the relationship between different classes of data and cannot get discriminant left/right regression matrix, which results in poor classifications. In this paper, a margin-based discriminant embedding sparse matrix regression (MDESMR) model for image supervised feature selection is proposed. For each matrix data, a margin is first defined as the difference between two types of distances determined by the left/right regression matrix. Maximizing the average margin for all training matrix data can get the nonlinear discriminant embedding. Thus, a nonlinear embedding and its linear approximation can be obtained simultaneously. An alternative iterative optimization algorithm for solving the proposed model is also designed and the corresponding closed-form solutions in each iteration are found. Some experiments on several datasets demonstrate the superiority of our method.