2D Feature Selection by Sparse Matrix Regression

Abstract

For many image processing and computer vision problems, data points are in matrix form. Traditional methods often convert a matrix into a vector and then use vector-based approaches. They will ignore the location of matrix elements and the converted vector often has high dimensionality. How to select features for 2D matrix data directly is still an uninvestigated important issue. In this paper, we propose an algorithm named sparse matrix regression (SMR) for direct feature selection on matrix data. It employs the matrix regression model to accept matrix as input and bridges each matrix to its label. Based on the intrinsic property of regression coefficients, we design some sparse constraints on the coefficients to perform feature selection. An effective optimization method with provable convergence behavior is also proposed. We reveal that the number of regression vectors can be regarded as a tradeoff parameter to balance the capacity of learning and generalization in essence. To examine the effectiveness of SMR, we have compared it with several vector-based approaches on some benchmark data sets. Furthermore, we have also evaluated SMR in the application of scene classification. They all validate the effectiveness of our method.

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

“…Hence, when D (v) is fixed, we can decompose the problem (12) into the following c independent sub-problems min…”

“…Next, we briefly analyze the computational complexity of the iterative optimization procedure of the proposed DGRLR-SMR algorithm. In each iteration of the algorithm, the time cost focuses on updating {U k } c k=1 , {V k } c k=1 , M and W. Since 1 ≤ d ≤ min(m, n) holds [12], the computational complexity of updating…”

“…In order to verify the effectiveness of the proposed method, we will compare it with seven existing methods. These methods include Fisher score ( Fisher -Scor ) [1], global and local structure preservation framework for feature selection (GLSPFS) [5], local and global structure preservation for robust unsupervised spectral feature selection(LGSP) [6], discriminative least squares regressions(DLSR) [10], sparse matrix regression (SMR) [12], regularized label relaxation linear regression (RLR) [21] and general bilinear regression (GBR) [27].…”

“…To address these problems, it is necessary to directly study the problem of feature selection for matrix data. For example, Hou et al [12] measured the relationship between matrix data and the class labels by deploying left and right regression matrices and propose an algorithm named sparse matrix regression (SMR) for two-dimensional supervised feature selection. Yuan et al [13] present a joint sparse matrix regression and nonnegative spectral analysis (JSMRNS) model for image unsupervised feature selection.…”

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

“…He et al [13] study the problem of robust feature extraction based on regularised correntropy. Hou et al [14] proposed an algorithm named sparse matrix regression (SMR) for two‐dimensional (2D) supervised feature selection. To directly select the features on matrix data, SMR measures the relationship between matrix data and the class labels by deploying left and right regression matrices.…”