A robust, heteroskedastic matrix factorization method generalizes PCA to handle per-feature uncertainties, missing data, and outlier detection via Student-t likelihood iterative reweighting.
Accelerated Alternating Projections for Robust Principal Component Analysis
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abstract
We study robust PCA for the fully observed setting, which is about separating a low rank matrix $\boldsymbol{L}$ and a sparse matrix $\boldsymbol{S}$ from their sum $\boldsymbol{D}=\boldsymbol{L}+\boldsymbol{S}$. In this paper, a new algorithm, dubbed accelerated alternating projections, is introduced for robust PCA which significantly improves the computational efficiency of the existing alternating projections proposed in [Netrapalli, Praneeth, et al., 2014] when updating the low rank factor. The acceleration is achieved by first projecting a matrix onto some low dimensional subspace before obtaining a new estimate of the low rank matrix via truncated SVD. Exact recovery guarantee has been established which shows linear convergence of the proposed algorithm. Empirical performance evaluations establish the advantage of our algorithm over other state-of-the-art algorithms for robust PCA.
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Robust Heteroskedastic Matrix Factorization: A Generalization of PCA that Flags Outliers and Handles Missing Data
A robust, heteroskedastic matrix factorization method generalizes PCA to handle per-feature uncertainties, missing data, and outlier detection via Student-t likelihood iterative reweighting.