A Nonparametric Model for Multi-Manifold Clustering with Mixture of Gaussians and Graph Consistency

Abstract

Multi-manifold clustering is among the most fundamental tasks in signal processing and machine learning. Although the existing multi-manifold clustering methods are quite powerful, learning the cluster number automatically from data is still a challenge. In this paper, a novel unsupervised generative clustering approach within the Bayesian nonparametric framework has been proposed. Specifically, our manifold method automatically selects the cluster number with a Dirichlet Process (DP) prior. Then, a DP-based mixture model with constrained Mixture of Gaussians (MoG) is constructed to handle the manifold data. Finally, we integrate our model with the k-nearest neighbor graph to capture the manifold geometric information. An efficient optimization algorithm has also been derived to do the model inference and optimization. Experimental results on synthetic datasets and real-world benchmark datasets exhibit the effectiveness of this new DP-based manifold method.

A Novel Approach for Gaussian Mixture Model Clustering Based on Soft Computing Method

“…In model selection studies for the perspective and strategies of mixture models, Celeux et al proposed using cluster analysis based on mixture models to determine the number of components (𝑔) in the finite mixture models [5]. In multivariate data, components in the heterogeneous variable are used to determine the number and the location of clusters in the mixture model [6]. Each sub-group (component) in the variables corresponds to at least one cluster in the mixture model [7].…”