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.
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