博士生讨论班2025[11]
时间：2025-04-24
阅读量：11次
- 演讲人： 金寅
- 时间：2025年4月29日15:30
- 地点：浙江大学紫金港校区行政楼1417报告厅
报告文章：Fast fitting of Gaussian mixture model via dimension reduction
摘要：The Gaussian Mixture Model (GMM) stands out as a widely applied clustering framework. Commonly, the maximal likelihood approach to fit GMM requires solving a non-convex optimization, which is computationally challenging especially for large-dimensional data. To address the problem, we propose a two-step approach to utilize the intrinsic low-dimensional structure in GMM under additional constraints on the heterogeneity of GMM. In the first step, we use a simple method to recover the low-dimensional data, given which the rest of data are normally distributed and thus redundant for clustering. We then fit GMM 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, our approach can be generalized under the ultrahigh-dimensional settings. 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 show that our algorithm significantly accelerates the computation compared to the existing methods.