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We revisit the problem of robust principal component analysis with featuresacting as prior side information. To this aim, a novel, elegant, non-convexoptimization approach is proposed to decompose a given observation matrix intoa low-rank core and the corresponding sparse residual. Rigorous theoreticalanalysis of the proposed algorithm results in exact recovery guarantees withlow computational complexity. Aptly designed synthetic experiments demonstratethat our method is the first to wholly harness the power of non-convexity overconvexity in terms of both recoverability and speed. That is, the proposednon-convex approach is more accurate and faster compared to the best availablealgorithms for the problem under study. Two real-world applications, namelyimage classification and face denoising further exemplify the practicalsuperiority of the proposed method.

Informed Non-convex Robust Principal Component Analysis with Features