Approximation Bounds for Sparse Principal Component Analysis

Alexandre d'Aspremont (1, 2) , Francis Bach (1, 2) , Laurent El Ghaoui (3)

1 LIENS - Laboratoire d'informatique de l'école normale supérieure
2 SIERRA - Statistical Machine Learning and Parsimony
3 EECS - Department of Electrical Engineering and Computer Science [Berkeley]

We produce approximation bounds on a semidefinite programming relaxation for sparse principal component analysis. These bounds control approximation ratios for tractable statistics in hypothesis testing problems where data points are sampled from Gaussian models with a single sparse leading component.

Domaines: Optimisation et contrôle [math.OC]

Alexandre d'Aspremont, Francis Bach, Laurent El Ghaoui. Approximation Bounds for Sparse Principal Component Analysis. Mathematical Programming, 2014, 148 (1-2), pp.89-110. ⟨hal-00907531⟩