Robust PCA and subspace tracking from incomplete observations using L0-surrogates
This addresses the challenge of robust PCA and subspace tracking in data analysis, offering incremental improvements over existing methods for applications dealing with corrupted or incomplete observations.
The paper tackles the problem of robustly recovering and tracking a low-rank subspace from incomplete and corrupted data, proposing a method that uses non-convex sparsity measures and an intrinsic Conjugate Gradient approach on the Grassmannian, resulting in improved ability to handle more outliers and higher-rank matrices compared to state-of-the-art methods.
Many applications in data analysis rely on the decomposition of a data matrix into a low-rank and a sparse component. Existing methods that tackle this task use the nuclear norm and L1-cost functions as convex relaxations of the rank constraint and the sparsity measure, respectively, or employ thresholding techniques. We propose a method that allows for reconstructing and tracking a subspace of upper-bounded dimension from incomplete and corrupted observations. It does not require any a priori information about the number of outliers. The core of our algorithm is an intrinsic Conjugate Gradient method on the set of orthogonal projection matrices, the so-called Grassmannian. Non-convex sparsity measures are used for outlier detection, which leads to improved performance in terms of robustly recovering and tracking the low-rank matrix. In particular, our approach can cope with more outliers and with an underlying matrix of higher rank than other state-of-the-art methods.