Random Matrix Techniques for estimation of a D dimensional covariance matrix from S samples when D > S

Steve Simon
Alcatel Lucent, Bell Labs

A sample covariance of D-dimensional data measured from S samples with S < D will necessarily have (D-S) zero eigenvalues, and does not make for a very reasonable estimate of the actual data covariance. We consider the problem of how one might improve this estimate. While some "standard approaches" are already known, we propose a novel approach where the sample data is randomly projected to a lower dimension, a covariance is estimated for this smaller dimensional data and then the data is "pseudoinversed" back to the higher dimension. We make an effort to compare the performance of this approach to the more standard approaches.

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