Separating Populations with Wide Data: a Spectral Analysis

Avrim Blum, Amin Coja-Oghlan, Alan Frieze, and Shuheng Zhou

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.