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ORL
2011

Convex approximations to sparse PCA via Lagrangian duality

12 years 10 months ago
Convex approximations to sparse PCA via Lagrangian duality
We derive a convex relaxation for cardinality constrained Principal Component Analysis (PCA) by using a simple representation of the L1 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.
Ronny Luss, Marc Teboulle
Added 29 May 2011
Updated 29 May 2011
Type Journal
Year 2011
Where ORL
Authors Ronny Luss, Marc Teboulle
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