Study On Matrix Regression Based Image Classification

With the rapid development of modern science and technology,a large amount of data in scientific research and social life are represented as matrix,which brings opportunities and challenges for the development of computer vision,pattern recognition and machine learning.As an important method of machine learning,regression analysis has been widely used in image classification.However,the actual image data is complex and interfered by factors such as occlusion and light change,which brings challenges to describe this relationship.The traditional regression methods are all vector-based regression model.That is,we have to convert twodimensional images into vectors for processing,which often destroys the structural information contained in these data.In this paper,we present a two-dimensional image matrix based regression model,i.e.matrix regression,to directly carry out the image representation and classification.This matrix regression model does not need the matrix-to-vector converting procedure.Meanwhile,such matrix data is usually a low-rank structure,or it can be approximated to a low-rank structure very well.The nuclear norm,as the best convex approximation of the rank function,can be used to characterize the low-rank structure information.Finally,we evaluate our proposed matrix regression algorithm on image datasets.The main work of this paper is as follows:1.We propose a nuclear norm sparse coding algorithm with Laplacian regularization.Based on the two-dimensional image matrix,this algorithm makes full use of the low-rank structure information of the error image.At the same time,Laplacian is used for regularization,which can make the model smoother,and ADMM is used for optimization.The experimental results on two databases show that this algorithm can improve the performance of image classification.2.A logistic matrix regression algorithm based on nuclear norm regularization is proposed.Our work is motivated by the matrix regression algorithm based on the generalized linear model.We adopt the logistic loss function,which is smooth and can be used for image classification effectively,and the nuclear norm is used as the regular term to maintain the inherent structure information in the matrix data.Experimental results from two databases prove that this algorithm can further improve the accuracy of image classification...