Research On Latent Subspace Clustering Method Based On Schatten-p Norm

The advent of the era of big data is accompanied by the complexity and diversity of data,which poses great challenges to traditional clustering algorithms.In the field of data mining,cluster analysis is the breakthrough of high-dimensional data processing.Faced with the problem of high-dimensional data,the subspace clustering algorithm was proposed as the key technology to deal with high-dimensional data clustering,and has received the attention of many researchers.The effectiveness of subspace clustering algorithms in processing high-dimensional data has been confirmed,but traditional subspace clustering algorithms have not coordinated the relationship between mining data hiding effects and solving low rank minimization problems.Aiming at the function approximation problem in the subspace clustering algorithm,this paper has conducted an in-depth study on the subspace clustering algorithm based on the Schatten-p norm.The main research contents include:?1?The effectiveness of Schatten-p norm approximating rank function is studied.Aiming at the study of rank minimization,we searched for a more accurate low-dimensional representation for subspace learning,and analyzed the ability of Schatten-p norm as a common rank relaxation function to recover low rank matrices.The robustness of Schatten-p norm approximation rank minimization problem is verified through experiments.?2?A latent low-rank subspace clustering algorithm based on Schatten-p norm is proposed:In the existing subspace clustering algorithm,the subspace clustering of latent low rank representation can contain hidden data samples,which solves the problem of insufficient samples of low rank representation.However,in the latent low rank representation,since finding the low rank solution of the matrix is an NP-hard problem,the nuclear norm is usually used to approximate the rank.In order to obtain a better low-rank representation matrix while being able to consider the problem of insufficient samples,this paper proposes a latent low-rank subspace clustering model based on the Schatten-p norm,using the Schatten-p norm as an approximation of the rank function.At the same time,in order to improve the robustness of the clustering performance enhancement algorithm,the7)norm is introduced against the error term.Experimental results show that the algorithm can effectively improve the performance of subspace clustering.?3?The latent multi-view subspace clustering algorithm is studied.It analyzes how to maximize the use of the original feature information when it is assumed that each view is derived from a latent representation.Compared with the single view,due to the complementarity of multiple views,the latent representation can describe the data itself more comprehensively,thereby making the subspace more accurate and robust.In this paper,the Schatten-p norm is applied to the multi-view clustering algorithm.By mining latent complementary information from multiple data points and improving the quality of low-dimensional representation,the purpose of maximizing the use of original feature information is achieved.The experimental results show that good results are obtained on the five data sets.