Sparse non Gaussian component analysis by semidefinite programming

Authors:
Elmar Diederichs;Anatoli Juditsky;Arkadi Nemirovski;Vladimir Spokoiny
Affiliations:
Weierstrass Institute, Berlin, Germany 10117;LJK, Université J. Fourier, Grenoble cedex 9, France 38041;ISyE, Georgia Institute of Technology, Atlanta, USA 30332;Weierstrass Institute, Berlin, Germany 10117 and Humboldt University, Berlin, Germany and Moscow Institute of Physics and Technology, Moscow, Russia
Venue:
Machine Learning
Year:
2013

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Abstract

Sparse non-Gaussian component analysis is an unsupervised linear method of extracting any structure from high-dimensional distributed data based on estimating a low-dimensional non-Gaussian data component. In this paper we discuss a new approach with known apriori reduced dimension to direct estimation of the projector on the target space using semidefinite programming. The new approach avoids the estimation of the data covariance matrix and overcomes the traditional separation of element estimation of the target space and target space reconstruction. This allows to reduced the sampling size while improving the sensitivity to a broad variety of deviations from normality. Moreover the complexity of the new approach is limited to O(dlogd). We also discuss the procedures which allows to recover the structure when its effective dimension is unknown.