2012/10/02 by Clemens Hage, Hage, Clemens, Martin Kleinsteuber +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Statistical Methods and Models #Blind Source Separation Techniques #FOS: Computer and information sciences #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques #Structural Health Monitoring Techniques #stat.ML
paper · pdf · doi:10.48550/arxiv.1210.0805
openalex publication_date 2012/10/02 · arxiv created 2013/01/17 · arxiv updated 2013/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.