Image decomposition based matrix regression with applications to robust face recognition Abstract   The previous matrix regression based methods mainly focus on designing a robust error term to characterize the occlusion and illumination changes. In actually, it is very challenging to give a strong model for solving the original images directly since the images contains rich and complex structure information. To address this problem, we aim to simplify the complex images and propose a simple and robust matrix regression based classification model. In our method, we firstly employ the local gradient distribution to decompose the image into a series of gradient images (LID for short). Each gradient image reveals the local structure information in different gradient orientations. Subsequently, we consider each gradient image as the diagonal block element and construct the diagonal block matrix for image representation. Nuclear norm based matrix regression model (NMR) is then applied to complete the classification tasks. The proposed model can be called IDNMR for short. We further design a fast ADMM optimization algorithm to solve the proposed IDNMR due to the fact that the big diagonal block matrix will increase the computational load. Experimental results show that the proposed method performs favorably compared with stateoftheart regression based classification methods.

Intrinsic Dimension Estimation via Nearest Constrained Subspace Classifier We consider the problems of classification and intrinsic dimension estimation on image data. A new subspace based classifier is proposed for supervised classification or intrinsic dimension estimation. The distribution of the data in each class is modeled by a union of of a finite number ofaffine subspaces of the feature space. The affine subspaces have a common dimension, which is assumed to be much less than the dimension of the feature space. The subspaces are found using regression based on the L0norm. The proposed method is a generalisation of classical NN (Nearest Neighbor), NFL (Nearest Feature Line) classifiers and has a close relationship to NS (Nearest Subspace) classifier. The proposed classifier with an accurately estimated dimension parameter generally outperforms its competitors in terms of classification accuracy. We also propose a fast version of the classifier using a neighborhood representation to reduce its computational complexity. Experiments on publicly available datasets corroborate these claims.