Joint feature weighting and adaptive graph-based matrix regression for image supervised feature Selection

Matrix regression (MR) is a regression model that can directly perform on matrix data. However, the effect of each element in matrix data on regression model is different. Taking into consideration the relevance of every original feature in the matrix data and their influence on the final estimation of the regression model, we introduce an unknown weight matrix to encode the relevance of feature in matrix data and propose a feature weighting and graph-based matrix regression (FWGMR) model for image supervised feature selection. In this model, the feature weight matrix is used to select some important features from the matrix data and preserve the relative spatial location relationship of elements in the matrix data. In addition, in order to effectively and reasonably preserve the local manifold structure of the training matrix samples, a regularization term in the model is used to adaptively learn a graph matrix on low-dimensional space. An optimization algorithm is devised to solve FWGMR model and to provide the closed-form solutions of this model in each iteration. Extensive experiments on some public datasets demonstrate the superiority of FWGMR.