An investigation of computational and informational limits in Gaussian mixture clustering

Abstract

We investigate under what conditions clustering by learning a mixture of spherical Gaussians is (a) computationally tractable; and (b) statistically possible. We show that using principal component projection greatly aids in recovering the clustering using EM; present empirical evidence that even using such a projection, there is still a large gap between the number of samples needed to recover the clustering using EM, and the number of samples needed without computational restrictions; and characterize the regime in which such a gap exists.