A0270
Title: Fast fitting of Gaussian mixture model via dimension reduction
Authors: Yin Jin - ZheJiang University (China)
Wei Luo - Zhejiang University (China) [presenting]
Abstract: The Gaussian mixture model (GMM) is a widely applied clustering technique. Commonly, GMM is fitted by the maximal likelihood approach that involves non-convex minimization, which becomes computationally challenging, especially for large-dimensional data. A fast two-step approach is proposed to fit GMM with the aid of an intrinsic low-dimensional data structure for clustering under additional constraints on the heterogeneity of GMM. In the first step, a simple moment-based method is proposed to recover the low-dimensional data, given that the rest of the data are normally distributed and thus redundant for clustering. GMM is then fit using the reduced data in the second step, which is computationally more feasible than the original GMM due to the lower dimensionality. Under the sparsity assumption on the clustering pattern, the approach can be generalized under the ultrahigh-dimensional settings. With the aid of appropriate pseudo data, it can also be embedded under a general framework of sufficient dimension reduction, which encompasses more methods to recover the low-dimensional structure of GMM in the future. The numerical studies are presented at the end.
