Research On Multiple Change Points Test Method Of High Dimensional Data Based On Sparse Projection

The change point problem is one of the classic problems in statistics,which has been widely used in financial industry,Internet security,biomedicine,hydrologic analysis and other fields.In this paper,we study the multiple change points test problem of high dimensional data,and give two algorithms of sparse projection(SOP)combined with seeded binary segmentation(Seed BS)and narrowest over threshold method(NOT),which are called SOP-Seed BS and SOP-NOT method,respectively.This paper mainly studies the problem of multiple change points test for highdimensional data by using the data dimensionality reduction method based on sparse projection and the univariate multiple change points test method.The main work is as follows:Firstly,this paper considers the multiple change points of high dimensional data from the perspective of data dimensionality reduction.After the high dimensional data is projected into one-dimensional data by using the sparse projection method(SOP),the multiple change points test is carried out by combining the Seed BS and NOT method,and the algorithm steps of SOP-Seed BS and SOP-NOT methods are given.Simulation experiments show that SOP-Seed BS and SOP-NOT methods have better accuracy in the change point test.Secondly,the SOP-Seed BS and SOP-NOT are compared with other multiple change points test methods for high dimensional data: SBS,Inspect,E-Divisive,and Geom CP.Simulation experiments are carried out under different parameter settings,such as the amount of data,dimension,sparsity and mean jump size.The experimental results show that the test accuracy of SOP-Seed BS and SOP-NOT is better than the other four methods in many cases,and also has advantages in computation speed.Considering the test accuracy and calculation efficiency,the SOP-Seed BS and SOPNOT presented in this paper have better test performance in many cases.Finally,the SOP-Seed BS and SOP-NOT algorithms are applied to the ACGH dataset and the S&P500 dataset.The results show that SOP-Seed BS and SOP-NOT methods are highly similar with other methods on ACGH data set.On the S&P500 data set,the results of change points test conducted by SOP-Seed BS and SOP-NOT methods mostly correspond to the occurrence of real events.