The topography of multivariate normal mixtures

Details The topography of multivariate normal mixtures The topography of multivariate normal mixtures

2006-02-11

arxiv.org/abs/math/0602238v1

Annals of Statistics 2005, Vol. 33, No. 5, 2042-2065

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053605000000417 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

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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