Robust Structured Low-Rank Approximation on the Grassmannian

TL;DR

This paper introduces a robust, online low-rank approximation method on the Grassmannian that effectively handles outliers and enables fast re-initialization for time series forecasting.

Contribution

It proposes a novel Grassmannian-based approach combining robustness to outliers with online re-initialization capabilities for structured low-rank approximation.

Findings

Effective outlier robustness demonstrated in experiments

Fast online re-initialization achieved in time series tasks

Method outperforms existing static approaches

Abstract

Over the past years Robust PCA has been established as a standard tool for reliable low-rank approximation of matrices in the presence of outliers. Recently, the Robust PCA approach via nuclear norm minimization has been extended to matrices with linear structures which appear in applications such as system identification and data series analysis. At the same time it has been shown how to control the rank of a structured approximation via matrix factorization approaches. The drawbacks of these methods either lie in the lack of robustness against outliers or in their static nature of repeated batch-processing. We present a Robust Structured Low-Rank Approximation method on the Grassmannian that on the one hand allows for fast re-initialization in an online setting due to subspace identification with manifolds, and that is robust against outliers due to a smooth approximation of the $\ell_p$-norm cost function on the other hand. The method is evaluated in online time series forecasting tasks on simulated and real-world data.