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October 2005 The topography of multivariate normal mixtures
Surajit Ray, Bruce G. Lindsay
Ann. Statist. 33(5): 2042-2065 (October 2005). DOI: 10.1214/009053605000000417


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.


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Surajit Ray. Bruce G. Lindsay. "The topography of multivariate normal mixtures." Ann. Statist. 33 (5) 2042 - 2065, October 2005.


Published: October 2005
First available in Project Euclid: 25 November 2005

zbMATH: 1086.62066
MathSciNet: MR2211079
Digital Object Identifier: 10.1214/009053605000000417

Primary: 62E10 , 62H05
Secondary: 62H30

Keywords: clustering , Dimension reduction , Manifold , mixture , modal cluster , multivariate mode , topography

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 5 • October 2005
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