Robust graph regularised sparse matrix regression for two‐dimensional supervised feature selection

Abstract

Bilinear matrix regression based on matrix data can directly select the features from matrix data by deploying several couples of left and right regression matrices. However, the existing matrix regression methods do not consider the local geometric structure of the samples, which results in poor classification performance. This study proposes a robust graph regularised sparse matrix regression method for two‐dimensional supervised feature selection, where the intra‐class compactness graph based on the manifold learning is used as the regularisation item, and the ‐norm as loss functions to establish the authors’ matrix regression model. An alternating optimisation algorithm is also devised to solve it and give its closed‐form solutions in each iteration. The proposed method not only can learn the left and right regression matrices, but also can preserve the intrinsic geometry structure by using the label information. Extensive experiments on several data sets demonstrate the superiority of the proposed method.