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The robust PCA of covariance matrices plays an essential role when isolatingkey explanatory features. The currently available methods for performing such alow-rank plus sparse decomposition are matrix specific, meaning, thosealgorithms must re-run for every new matrix. Since these algorithms arecomputationally expensive, it is preferable to learn and store a function thatnearly instantaneously performs this decomposition when evaluated. Therefore,we introduce Denise, a deep learning-based algorithm for robust PCA ofcovariance matrices, or more generally, of symmetric positive semidefinitematrices, which learns precisely such a function. Theoretical guarantees forDenise are provided. These include a novel universal approximation theoremadapted to our geometric deep learning problem and convergence to an optimalsolution to the learning problem. Our experiments show that Denise matchesstate-of-the-art performance in terms of decomposition quality, while beingapproximately $2000\times$ faster than the state-of-the-art, principalcomponent pursuit (PCP), and $200 \times$ faster than the currentspeed-optimized method, fast PCP.

Denise: Deep Robust Principal Component Analysis for Positive Semidefinite Matrices