A multi-manifold semi-supervised Gaussian mixture model for pattern classification

•A multi-manifold semi-supervised Gaussian mixture model is proposed.•The model can classify data sets residing on multiple hybrid nonlinear manifolds.•We design a graph with local and geometric consistency to detect the multi-manifold.•Our model is naturally inductive and able to handle new data points.

Semi-supervised Gaussian mixture model (SGMM) has been successfully applied to a wide range of engineering and scientific fields, including text classification, image retrieval, and biometric identification. Recently, many studies have shown that naturally occurring data may reside on or near manifold structures in ambient space. In this paper, we study the use of SGMM for data sets containing multiple separated or intersecting manifold structures. We propose a new multi-manifold regularized, semi-supervised Gaussian mixture model (M2SGMM) for classifying multiple manifolds. Specifically, we model the data manifold using a similarity graph with local and geometrical consistency properties. The geometrical similarity is measured by a novel application of local tangent space. We regularize the model parameters of the SGMM by incorporating the enhanced Laplacian of the graph. Experiments demonstrate the effectiveness of the proposed approach.