Joint Capped Norm Minimization Subspace Clustering Algorithm

With the development of network technology,a large amount of high-dimensional complex data,such as images and videos,are generated in the real world all the time.To label and classify these data is not only time-consuming and laborious,but also has very serious subjectivity problems.Therefore,the problem of unlabeled data clustering has become a research hotspot and difficulty in the fields of machine learning and computer vision.In this paper,we propose two robust subspace clustering algorithms for general data and sequence data,jointly Capped norm respectively.The specific content is as follows:In Chapter 1,the research background,significance,status and application of subspace clustering are introduced briefly.Then the basic principle of subspace clustering and some problems still exist are discussed.Finally,the main work and content arrangement of this paper are briefly described.In Chapter 2,a joint Cappedl₂norm and Capped kernel norm minimization subspace clustering algo-rithm is proposed for general data.Firstly,the Capped kernel norm is defined as a better approximation of the rank function to improve the accuracy of subspace clustering.Then,in order to improve the robustness of the proposed algorithm,Cappedl₂norm is used to describe the prior information of data noise,and a subspace clustering model(CNSC)is established for the joint Cappedl₂norm and Capped kernel norm.Inspired by the reweighting technique,a reweighting iterative method is proposed to solve the model by constructing aux-iliary variables,and the convergence of the algorithm is proved.Finally,the experimental results of synthetic data and real data show that the proposed method is effective and superior to the existing methods.In Chapter 3,for the sequence data,we propose the joint Cappedl₂norm andi_2,pnorm minimization algorithm of ordered subspace clustering.Firstly,the Cappedl₂norm is introduced to reduce the influence of noise and outliers in clustering.Then,the non-convexi_2,p(0<p<1)norm is used as the regular term of time series information to mine the local similarity of data in time dimension.Then,the Cappedl₂norm andi_2,pnorm are combined to build the ordered subspace clustering model(JCi²M).Finally,an iterative reweighting algorithm with guaranteed convergence is proposed.Numerical experiments on video,motion and face data show that the proposed algorithm is effective and highly competitive.