Nonparametric Model and Variational Bayesian Learning for Subspace Clustering
Qing Xiang · Chinese Journal of Computers · 2007
The goal of subspace clustering is to group a given set of data represented by different feature subsets. As an unsupervised learning method, subspace clustering tries to discover the patterns of similarity examined under different presentations and has received a great deal of interest and research in the related domains. Firstly the mean and variance shift model proposed by Hoff is extended to a new nonparametric model of subspace clustering based on subsets of features.The advantage of the model is that variational Bayesian method can be applied. The model based on the integration of a Dirichlet process mixture model and a nonparametric model of selecting subsets of features can automatically choose the number of clusters and perform subspace clustering. Then posterior inference of the model is done using Markov Chain Monte Carlo. Due to computational considerations the authors propose a variational Bayesian method to learn the parameters of the model. Experimental results using simulated data and the application to the problem of clustering face images illustrate the model can simultaneously selecting the relevant features and the data points that have similar pattern under these features. Experiments on the multiple feature database from the UCI repository show that variational Bayesian method without sampling can fleetly inference the parameters of the model.