Face Recognition Based On Low Rank Representation

In the research field of face recognition,face recognition with light,occlusion and other factors is considered as a significant research topic in the field of machine learning and computer vision.Based on the low rank representation of matrices,a matrix regression and tensor regression method for face recognition is proposed,The main contributions are as follows:(1)A robust nuclear norm based face recognition method is proposed.Recent studies have shown that the image has a low rank structure,In order to make full use of the two-dimensional structure information of error matrix,the error image is no longer needed to be pulled into a vector,but the matrix regression model is constructed directly in the form of matrix.The robust nuclear norm is used as the criterion to describe the error matrix.Due to the robust function is non-convex function,this paper uses the one-step approximation of non-convex function and derive the weighted nuclear norm as the description for low rank structure of the error image matrix.The L1 norm and the L2 norm are used to constrain the coefficients to avoid overfitting.The method of alternating direction multiplier is used to calculate the regression coefficient.Compared with the traditional linear regression method,the proposed method can describe the spatial structure information of noisy images.The experiments on several databases show that the proposed method is robust to face recognition with occlusion and illumination changes compared with some recent regression based methods.(2)Inspired by the idea of robust principal component analysis,image matrix can be decomposed into two parts:low rank part and sparse error part.In this paper,we use the robust nuclear norm to characterize the low rank structure of the error matrix and use the L1 norm of the matrix to characterize the sparse error.It is considered that the noise data of each pixel is independent with the structural noise.The L1 norm and the L2 norm are used to constrain the coefficients to avoid overfitting.The method of alternating direction multiplier is used to calculate the regression coefficient.In the classifier design,the weighted nuclear norm of the error matrix is used as the criterion to measure the distance between the test image and each class of reconstructed image,the corresponding weights are obtained by using the derivative of the singular value function of the last iteration.Through the experimental comparison,we find that different non convex functions can get similar recognition results.The effectiveness of the proposed method is verified by experiments on several databases.(3)A face recognition method based on bi-weighted matrix regression model is proposed.Because of the existence of abnormal data,the weighted method is used to reduce the influence of abnormal data on the regression model,while the weighting is based on pixel level.Due to the influence of occlusion and illumination,the error has obvious structure,so we adopt the bi-weighted method to reduce the influence of structural noise.The L1 norm is used to constrain the coefficients to avoid overfitting.The method of alternating direction multiplier is used to calculate the regression co-efficient.The bi-weighted matrix are placed in the outer loop in order to save time.In the design of the classifier,the bi-weighted error matrix are used as the criterion to measure the distance between the test image and each class of reconstructed image.Through the experimental comparison,we find that different non convex functions can get similar recognition results.Experiments on several databases demonstrate the advantages of the proposed method.(4)A tensor volume based tensor regression method is proposed to recognize color face images.In this paper,the definition of tensor volume is derived from the view of matrix volume,and tensor regression model is proposed with tensor volume as constraint.Since tensor volume is non convex function,one step approximation to tensor volume can lead to the weighted nuclear norm of tensor.An alternate direction multiplier method is used for the optimal solution.This method is applied to face recognition in color images,Compared with the face recognition using gray scale images,this method can achieve better recognition results.