Research On Multiway P-spectral Clustering Algorithm Based On Self-adaptive Neighborhood

As an important data mining technology,spectral clustering has been widely used in computer vision,image processing,and very large scale integration(VLSI)design fields.It has rich theoretical foundation and universality,and it can successfully transform unsupervised clustering problem into optimal partition problem of undirected graph.In order to further obtain more balanced clustering results,as a generalized version of the standard spectral clustering,p-spectral clustering algorithm was proposed.By thresholding the second small eigenvector of p-Laplacian matrix,in most cases we can obtain better clustering effect compared with standard spectral clustering algorithm.How to construct similarity matrix,choose the eigenvector of the p-Laplace matrix for clustering and how to determine the value of the parameter p are the key factors affecting the performance of p-spectral clustering algorithm.In addition,there may be redundant attributes in high-dimensional data sets,and how to perform attribute reduction has been studied to improve the operating efficiency of p-spectral clustering algorithm.Therefore,this article starts from the above aspects,and studies the p-spectral clustering algorithm to improve its performance.The main research contents of paper are as follows:Firstly,in view of limitations of similarity calculation methods of p-spectral clustering,this paper studies a p-Spectral Clustering Algorithm Based on Self-adaptive(USN-p SC).The distance between the data point and some neighbor is taken as the local scale parameter of the data point to improve the similarity calculation method between the data points,and fully utilize the local distribution statistical information of the data points.Experiments show that the USN-p SC algorithm has strong adaptability and robustness,and clustering result is more balanced.Secondly,this paper studies the use of principal component analysis(PCA)to preprocess high-dimensional datasets to improve the efficiency of p-spectral clustering algorithms,and proposes A Self-adaptive p-Spectral Clustering Algorithm with P Technology(PSA-p SC).Firstly high-dimensional data set is reduced by the PCA algorithm,and then adaptive local scale parameters are introduced to optimize the similarity calculation method.Experiments show that PSA-p SC algorithm can identify complex data structures well,process high-dimensional data sets and obtain more balanced clustering results.Once again,we can calculate multiple eigenvectors of p-Laplace matrix through further research.This paper presents A Multiway p-Spectral Clustering Algorithm(MPSC).The p-spectral clustering algorithm implements clustering datasets by thresholding the second smallest eigenvector of the p-Laplacian matrix.When solving the multi-class clustering problem,we have to recursively implement two-class clustering process,which is inefficient,and clustering result isn't stable.Therefore,by introducing the idea of classical spectral clustering NJW algorithm,we study and calculate the multiple eigenvectors of p-Laplace matrix and further construct the feature space to solve the multi-class clustering problem.Finally,we summarize proposed optimized p-spectral clustering algorithm and prospect further research of p-spectral clustering algorithm.