Separating populations with wide data: A spectral analysis

Abstract

In this paper, we consider the problem of partitioning a small data sample drawn from a mixture of $k$ product distributions. We are interested in the case that individual features are of low average quality $\gamma$, and we want to use as few of them as possible to correctly partition the sample. We analyze a spectral technique that is able to approximately optimize the total data size--the product of number of data points $n$ and the number of features $K$--needed to correctly perform this partitioning as a function of $1/\gamma$ for $K>n$. Our goal is motivated by an application in clustering individuals according to their population of origin using markers, when the divergence between any two of the populations is small.

Published in at http://dx.doi.org/10.1214/08-EJS289 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• A Two-round Variant of EM for Gaussian Mixtures
• Concentration of norms and eigenvalues of random matrices

Cited by in corpus (2)

• Learning Mixtures of Gaussians using the k-means Algorithm
• Learning Balanced Mixtures of Discrete Distributions with Small Sample