A Study On Sparse And Low-rank Representation Learning Model And Methods

Sparse,low rank representation learning is the hottest research topic in recent years,including sparse representation,low rank matrix recovery,low rank tensor recovery and other issues.These series of mathematical problems have a very wide range of appli-cations in the pattern recognition,image processing,social networking and many other areas.This paper aims to solve the problem of data recovery such as face recognition and image processing,establish the relevant sparse and low rank representation learning model,design effective algorithms,and verify theirs validity through a series of numerical experiments.The details are as follows:?1?A customized extended sparse representation model is proposed to take advantage of the variational information for single sample per person face recognition.The proposed model with the mixed norm is a generalization of the extended sparse representation-based classification model.This model uses the single l₁-norm regularization to guar-antees the sparsity of representation coefficient and use the mixed norm?the convex combination of l₁-norm and l₂-norm?to improve the robustness for the variational in-formation from generic dataset.The mixed norm well fits the distribution of variational information?such as illumination,expression,poses,occlusion?and the interference in-formation?somewhat face-specific in generic dataset?simultaneously.We compare the proposed method with the related methods on several popular face databases,including AR,CMUPIE,Georgia and LFW databases.The experimental results show that the pro-posed method outperforms several popular face recognition methods.?2?A customized dictionary-based extended joint sparse representation approach is proposed to solve a special single sample face surveillance problem,we name it as the single image to image set face recognition problem?ISFR?.We first learn a customized variation dictionary from the on-location probing face images,and then propose the ex-tended joint sparse representation,which utilizes the information of both the customized dictionary and the gallery samples,to classify the probe samples.Finally,we compare the proposed method with the related methods on several popular face databases,including Yale,AR,CMU-PIE,Georgia,Multi-PIE and LFW databases.The experimental results show that the proposed method outperforms most of these popular face recognition meth-ods for the ISFR problem.?3?An iterative p-shrinkage thresholding algorithm is proposed for solving miss data recovery problem——low Tucker rank tensor recovery problem.The proposed algorithm is based on the framework of alternative direction method of multipliers.We implement the proposed algorithm both on simulation data and real data.Numerical results on simu-lation data demonstrate that our algorithm can successfully recover varieties of synthetic low Tucker rank tensors in different sampling ratios with better quality compared to the existing state-of-art tensor recovery algorithms.Experiments on real data,including col-ored image inpainting,MRI image inpainting and hyperspectral image inpainting,further illustrate the effectiveness of the proposed iterative p-shrinkage thresholding algorithm.?4?A compact discriminative model is proposed as a supervision signal to train the Convolutional Neural Network,which plays an important role for learning the compact and discriminative feature to represent the raw data.The proposed losses supervise CNN to map the raw data into the feature space,where the intra-class space is compact and inter-class spaces have sensible gaps,by constraining the intra-class variations and the inter-class variations adaptively.They can exploit existing well-performed CNNs and provide an easy way to enhance them.To illustrate the effectiveness and the adaption of the proposed losses,we conduct extensive experiments on several benchmark databases.Experimental results show that the proposed losses are effective,and can easily generate more favorable results than the existing state-of-the-art losses.