Multi-manifold clustering: A graph-constrained deep nonparametric method

Abstract

For multi-manifold clustering, it is still a challenging problem on how to learn the cluster number automatically from data. This paper presents a novel nonparametric Bayesian model to cluster the multi-manifold data and estimate the number of submanifolds simultaneously. Our model firstly assumes that every submanifold is a probability distribution defined in the manifold space. Then, we approximate the manifold distribution with a deep neural network. To maintain the data similarity among data, we regularize the data generation process with a modified k-nearest neighbor graph. Though the posterior inference is hard, our model leads to a very efficient deterministic optimization algorithm, which incorporates the mean field variational inference with the Graph regularized Variational Auto-Encoder (Graph-VAE). By applying the Graph-VAE, our model exhibits another advantage of realistic image generation which overcomes the conventional clustering methods. Furthermore, we expand our proposed manifold algorithm with the Dirichlet Process Mixture (DPM) to model the real datasets, in which the manifold data and non-manifold data are coexisting. Experiments on synthetic data verify our theoretical analysis. Clustering results on motion segmentation, coil20 and 3D pedestrian show that our approach can significantly improve the clustering accuracy. The handwritten database experiment demonstrates the image generation capability.