Robust Low-rank And Sparse Representation Subspace Clustering Algorithm Based On Logarithmic Approximatio

As an unsupervised learning algorithm,clustering is an important research content in the fields of pattern recognition and machine learning,as well as an important technique to analyze and process data when label information is not available.Traditional clustering algorithms usually have far from satisfactory performance when processing highdimensional,massive and complex image data.Among various clustering methods,sparse and low-rank representation models have attracted extensive attentions since they can effectively capture the latent structural information from data,which is essentially important in further data processing.However,it should be noted that the sparse representation model focuses on the local similarity information of the data by seeking a sparse representation while omitting the global structure of the data.The low-rank representation model focuses on the global information while lacking of ability to remove irrelevant redundant information.To solve the above problems and further capture the structural information of the data,this thesis combines the advantages of sparse and lowrank representation model and develop a new Logarithm-based Robust Low-rank and Sparse Representation for Subspace Clustering.The main research is as follows:(1)A mathematical model for a robust low-rank and sparse representation subspace clustering algorithm is proposed based on logarithmic approximation.First,the model combines the advantages of the sparse and the low-rank representation models to learn the local and global representation of the data.Second,the model adopts a non-convex approach to constrain the rank and sparse of representation matrix to better reveal the structural information for the data.Then,to effectively improve the robustness of the model to noise,a new non-convex loss term is developed to measure the residual.Finally,manifold learning is introduced into the model to capture nonlinear relation of the data.(2)An efficient Logarithm-based optimization strategy is developed,with a detailed theoretical convergence analysis.Specifically,by introducing several auxiliary variables,the overall optimization problem is decomposed into several sub-problems.Among them,some are typical shrinkage problems,for which we develop an efficient strategy to calculate solutions.These solutions can be used as a general tool for element-wise sparse,columnwise sparse,and spectral-wise sparse problems.(3)Extensive experiments are carried out to evaluate the effectiveness of our method.First,experiments on six clean data sets and two noisy data sets is conducted,where the results confirm the effectiveness of the proposed method in clustering as well as its robustness to noise effects.Then,this thesis conducts representation matrix analysis,parameter sensitivity analysis,convergence analysis and ablation experiments,which suggests the effectiveness of the proposed method in recovering the latent structure and its potential applicability in real-world applications.