Ghosts in Gaussian Mixture Models
Nov 30, 2011
ABSTRACT:
The sum of finitely many isotropic Gaussian kernels in 2- or highter-dimensional Euclidean space can have more modes than kernels. Even more surprising is the fact that the sum (also known as a Gaussian Mixture Model or GMM) can have an exponential number of critical values. We provide an analytical description of these critical points, focusing our attention on the extra mode.
The sum of finitely many isotropic Gaussian kernels in 2- or highter-dimensional Euclidean space can have more modes than kernels. Even more surprising is the fact that the sum (also known as a Gaussian Mixture Model or GMM) can have an exponential number of critical values. We provide an analytical description of these critical points, focusing our attention on the extra mode.