The Study Of Low-Rank Coding And Representation Learning Algorithms For Subspace Recovery

Real-world visual data(such as facial images)can usually be represented by using the low-dimensional or low-rank subspaces for feature extracttion.Therefore,low-rank coding based subspace learning methods can be widely utilized in the areas of image recovey,denoising,compression and classification.However,existing low-rank coding algorithms still cannot obtain the promising performance due to the insufficient representation and discriminating abilities,the setting of learning features in original space directly,inaccurate similarity measures and the single-layer learning structure.To improve the epresentation and discriminating abilities,this thesis mainly proposes innovative solutions,and verifies the effectiveness of the proposed algorithms on the popular real image datasets.The main contriutions of this thesis are summarized as follows:(1)Most existing low-rank representation methods perform the representation learning and dictionary learning in the original input space,but most real data contains noise and even gross corruptions,so the recovery performance may be decreased in practice.Therefore,we proposed a new Robust Projective Low-Rank&Sparse Representation by Joint Robust Factorization and Projective Dictionary Learning,called J-RFDL.J-RFDL investigates the robust factorization based dictionary learning problem for recovering low-rank and sparse subspace structures for robust representations.Specifically,J-RFDL clearly integrates the L1-norm based robust factorization and robust low-rank&sparse representation by robust dictionary learning into a unified framework.By performing the joint low-rank and sparse representation based on the sparse low-dimensional representation by the L1-norm based robust factorization,J-RFDL can achieve more accurate results.J-RFDL regularizes the sparse L2,1-norm on the reconstruction errors over the factorization and dictionary learning to make the factorization and representation procedures robust to noise and outliers in the input data.(2)To enable the coefficients to deliver strict block-diagonal structures for enhancing the representations,a new learning framework called Robust Block-Diagonal Adaptive Locality-constrained Latent Representation(rBDLR)is proposed.rBDLR clearly integrates the block diagonal structure representation and salient feature extraction based on adaptive locality into a unified model.To reduce the computational complexity,Frobenius-norm is used to constrain the low-rank coding coefficients.To improve the robustness of the model,rBDLR performs the latent representation and adaptive weighting in a recovered clean data space.To make the coefficients have a strict block-diagonal structure,rBDLR performs the auto-weighting by minimizing the reconstruction error based on robust adaptive locality-constrained features,constrained by a block-diagonal regularizer over adaptive weights.(3)We propose a new deep low-rank representation framework called Progressive Deep Latent Low-Rank Fusion Network termed DLRF-Net to uncover deep features and the clustering structures embedded in the latent subspace.The basic idea of DLRF-Net in each layer is to refine the principal and salient features progressively from the previous layers by fusing the subspaces,which can potentially learn more accurate features and subspaces for image representation learning and clustering.To learn deep hidden information,DLRF-Net inputs the shallow features from the last layers into the subsequent layers.Then,it recovers hierarchical information and deeper features by respectively congregating the projective subspaces and representation subspaces in each layer.As such,one can learn deeper subspaces and can also ensure the representation learning of deeper layers to remove the noise and discover the underlying clean subspaces.It is noteworthy that the framework of our DLRF-Net is applicable to most existing latent low-rank representation models,i.e.,existing latent models can be easily extended to multilayer scenario using our DLRF-Net.(4)In this thesis,we will also design an interactive image recognition platform based on the proposed low-rank representation models,which can complete the image recognition task and training data extraction from the interface operations.On one hand,the feasibility and effectiveness of the proposed algorithms can be verified;on the other hand,this thesis also provide new technologies for image representation and recognition.