Manifold Based Bavesian Hierarchical Clusterin Analysis

Clustering analysis is one of the most important topics in unsupervised machine learning,whose goal is to segregate the dataset into subgroups with different characters.Two key issues in clustering analysis are the decision of the number of subgroups and the selection of distance measure.At the same time,when the dimensionality of the sample is very high,clustering analysis requires the preprocessing of dimensionality reduction to reduce the computation burden and discard unrelated information.While the underling structure of the high-dimensional datasets is low-dimensional,it's usually nonlinear.Traditional linear dimension reduction methods such like principle component analysis will lose the interior structure of the dataset in dimension reduction.To effectively reduce the dimension of image data and avoid the subjective choice of the number of subgroups and the distance measure,this thesis considers the manifold learning based Bayesian hierarchical clustering analysis.In the first step the dimension of the data is reduced by manifold learning and in the second step the low-dimensional data produced in the first step is clustered by the Bayesian hierarchical clustering.The simulation experiments show that manifold learning will maintain the interior structure of datasets to the maximum in reducing the dimension.Compared with traditional clustering algorithms and linear dimension reduction-based Bayesian hierarchical clustering,manifold learning-based Bayesian hierarchical clustering analysis will automatically select the nearly right number of subgroups and cluster the dataset properly.