The topography of multivariate normal mixtures

• 成果类型: Article
• 署名作者: Ray, S; Lindsay, BG
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000417
• 发表日期: 2005
• 页码: 2042-2065
• 关键词: NUMBER; modes

摘要

Multivariate normal mixtures provide a flexible method of fitting high-dimensional data. It is shown that their topography, in the sense of their key features as a density, can be analyzed rigorously in lower dimensions by use of a ridgeline manifold that contains all critical points, as well as the ridges of the density. A plot of the elevations on the ridgeline shows the key features of the mixed density. In addition, by use of the ridgeline, We uncover a function that determines the number of modes of the mixed density when there are two components being mixed. A followup analysis then gives a Curvature function that can be used to prove a set of modality theorems.