The Annals of Statistics
- Ann. Statist.
- Volume 33, Number 5 (2005), 2042-2065.
The topography of multivariate normal mixtures
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.
Ann. Statist. Volume 33, Number 5 (2005), 2042-2065.
First available in Project Euclid: 25 November 2005
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62E10: Characterization and structure theory 62H05: Characterization and structure theory
Secondary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]
Ray, Surajit; Lindsay, Bruce G. The topography of multivariate normal mixtures. Ann. Statist. 33 (2005), no. 5, 2042--2065. doi:10.1214/009053605000000417. https://projecteuclid.org/euclid.aos/1132936556