Dynamic Graph Regularization and Label Relaxation-Based Sparse Matrix Regression for Two-Dimensional Feature Selection

Abstract

Sparse matrix regression (SMR) is a two-dimensional supervised feature selection method that can directly select the features on matrix data. It uses several couples of left and right regression vectors for each classifier and integrates them in formulating the regression function. However, SMR does not consider the local geometry of image samples, and it assumes that the training samples should exactly fit a linear model or a strict binary label matrix by left and right regression matrices. In order to enlarge margins between different classes and preserve the intrinsic geometry structure of samples in the transformed space, we will propose dynamic graph regularization and label relaxation-based SMR (abbreviated as DGRLR-SMR) method for two-dimensional supervised feature selection. First, the label relaxation SMR is established by relaxing the strict binary label matrix into a slack variable matrix via a nonnegative label relaxation matrix by the $\varepsilon $ -dragging technique. Second, we construct a dynamic graph matrix learning model, rather than using the heat kernel function to obtain a fixed graph matrix, to capture the discriminative information and the local manifold structure of the image samples. Therefore, the proposed model not only enlarges margins between different classes, but also obtains a sparse transformation matrix and avoids the problem of over-fitting. An optimization algorithm is devised to solve this model, and it has closed-form solutions in each iteration so that it can be implemented easily in real application. Extensive experiments on several data sets demonstrate the superiority of our method.