Convex approximations to sparse PCA via Lagrangian duality

Authors:
Ronny Luss;Marc Teboulle
Affiliations:
-;-
Venue:
Operations Research Letters
Year:
2011

Citing 8
Cited 1

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Abstract

We derive a convex relaxation for cardinality constrained Principal Component Analysis (PCA) by using a simple representation of the L"1 unit ball and standard Lagrangian duality. The resulting convex dual bound is an unconstrained minimization of the sum of two nonsmooth convex functions. Applying a partial smoothing technique reduces the objective to the sum of a smooth and nonsmooth convex function for which an efficient first order algorithm can be applied. Numerical experiments demonstrate its potential.