Research On RPCA Algorithm Based On Graph

With the rapid development of society and the advent of the information explosion era,a large number of irregular high-dimensional data and complex structures continue to emerge.For these high-dimensional data and complex structures,how to mine their potential features and how to reduce the dimensionality of the original information without losing the original information has become a hot research topic in recent years.Nowadays,data dimensionality reduction has become an important method to deal with irregular high-dimensional data and solve the "dimension disaster".Graph signal processing technology,as a means of processing signals in discrete irregular domains,relies on the correlation between graphs and data.It can provide an effective means for dimensionality reduction of high-dimensional data.The graph signal abstracts the topological structure between the data into a weighted graph,and then maps the signal value to the vertices of the weighted graph.The emergence of graph signals provides many new ideas for processing data with complex structures.This article is based on the correlation between data dimensionality reduction and graph signal processing.The main research work and innovations of this paper are as follows:(1)This article combines the graph smoothing theory in graph signal processing to improve the existing robust principal component analysis algorithm(RPCA)and designs a generalized non-convex regularized RPCA algorithm based on graph smoothing.This algorithm solves the problem of unsatisfactory processing effect of existing algorithms when the data is not strictly low-rank.It combines the existing RPCA algorithm based on generalized non-convex regularization with the graph smoothing operator in graph signal processing.The objective function in the algorithm is improved,and a graph smoothing regularization item is added.The algorithm uses generalized non-convex penalty and graph smoothing regularization to process the data,and successfully solves the problem of poor performance of existing algorithms in the face of non-strict low-rank data,and uses ADMM to solve the optimization problem in the algorithm.Finally,the algorithm of this paper is verified by experiments,and the results show that the algorithm of this paper has more advantages when the data is not strictly low-rank.(2)This paper combines the RPCA algorithm with the graph filtering theory in graph signal processing to design a new algorithm framework-the RPCA algorithm framework based on graph filtering.The designed algorithm framework overcomes the problem of poor processing effect of existing algorithms when the data is noisy,and combines graph filtering on the basis of the original algorithm to further improve the entire algorithm framework.The new algorithm framework introduces a graph filter on the basis of the original algorithm to preprocess the input data.After experimental verification,the results of the new framework proposed in this paper are better than those of the original algorithm.