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.
@article{1132936556,
author = {Ray, Surajit and Lindsay, Bruce G.},
title = {The topography of multivariate normal mixtures},
journal = {Ann. Statist.},
volume = {33},
number = {1},
year = {2005},
pages = { 2042-2065},
language = {en},
url = {http://dml.mathdoc.fr/item/1132936556}
}
Ray, Surajit; Lindsay, Bruce G. The topography of multivariate normal mixtures. Ann. Statist., Tome 33 (2005) no. 1, pp. 2042-2065. http://gdmltest.u-ga.fr/item/1132936556/