Ghosts in Gaussian Mixture Models
Nov 30, 2011

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.