Separating populations with wide data: A spectral analysis

Details Separating populations with wide data: A spectral analysis Separating populations with wide data: A spectral analysis

2007-06-25

arxiv.org/abs/0706.3434v2

Electronic Journal of Statistics 2009, Vol. 3, 76-113

Statistics

Machine Learning

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

Scientific paper

10.1214/08-EJS289

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.

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