##
Separating Populations with Wide Data: a Spectral Analysis

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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.