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• W2103804774 abstract "We propose a novel convex relaxation of sparse principal subspace estimation based on the convex hull of rank-d projection matrices (the Fantope). The convex problem can be solved efficiently using alternating direction method of multipliers (ADMM). We establish a near-optimal convergence rate, in terms of the sparsity, ambient dimension, and sample size, for estimation of the principal subspace of a general covariance matrix without assuming the spiked covariance model. In the special case of d = 1, our result implies the near-optimality of DSPCA (d'Aspremont et al. [1]) even when the solution is not rank 1. We also provide a general theoretical framework for analyzing the statistical properties of the method for arbitrary input matrices that extends the applicability and provable guarantees to a wide array of settings. We demonstrate this with an application to Kendall's tau correlation matrices and transelliptical component analysis." @default.
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• W2103804774 date "2013-12-05" @default.
• W2103804774 modified "2023-10-18" @default.
• W2103804774 title "Fantope Projection and Selection: A near-optimal convex relaxation of sparse PCA" @default.
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