Robust Subspace Tracking Algorithms in Signal Processing: A Brief Survey

Abstract

Principal component analysis (PCA) and subspace estimation (SE) are popular data analysis tools and used in a wide range of applications. The main interest in PCA/SE is for dimensionality reduction and low-rank approximation purposes. The emergence of big data streams have led to several essential issues for performing PCA/SE. Among them are (i) the size of such data streams increases over time, (ii) the underlying models may be time-dependent, and (iii) problem of dealing with the uncertainty and incompleteness in data. A robust variant of PCA/SE for such data streams, namely robust online PCA or robust subspace tracking (RST), has been introduced as a good alternative. The main goal of this paper is to provide a brief survey on recent RST algorithms in signal processing. Particularly, we begin this survey by introducing the basic ideas of the RST problem. Then, different aspects of RST are reviewed with respect to different kinds of non-Gaussian noises and sparse constraints. Our own contributions on this topic are also highlighted.

Robust Subspace Tracking with Contamination Mitigation via α-Divergence

“…where f (x, U * ) is the "nominal" one, h(x) is to represent contamination in the data, and δ is to control the contamination proportion. The authors in [20] indicated that when data samples are corrupted, the underlying principal subspace can be obtained by minimizing α-divergence D α (g(x, U * )||f (x, U)) which is defined as in (10). In practice g(x, U * ) is not known generally, we can solve the following optimization instead…”

“…Particularly, RST requires not only robustness against data corruption together with high subspace estimation accuracy but also fast implementation. Over the years, many RST methods have been proposed for specific scenarios (e.g., sparse outliers and missing data) and we refer the readers to [7][8][9][10] for good surveys. Most of the existing (robust) subspace trackers are, however, not designed for dealing with contaminated noises (i.e., non-standard Gaussian noises) which have been observed in several signal processing applications [11].…”

“…Most of the existing (robust) subspace trackers are, however, not designed for dealing with contaminated noises (i.e., non-standard Gaussian noises) which have been observed in several signal processing applications [11]. In the literature, there exist some RST methods capable of tracking the underlying subspace in contaminated environments [10]. To deal with impulsive noises for example, a few of them were developed by incorporating robust statistics into the well-known projection approximation subspace tracking (PAST) algorithm [12], such as RPAST [13], MCC-PAST [14], and BNC-PAST [15].…”

A robust DOA tracking algorithm for monostatic nested array MIMO radar

“…The research on DOA tracking of MIMO radar has some foundations [10][11][12] , but most of them are carried out in the case of additive white Gaussian noise, which is not robust for non-Gaussian noise. Aiming at the problem of DOA tracking in the case of non-Gaussian noise, a main research direction is to study the robust subspace tracking algorithm [13][14] . The αFAPI algorithm proposed in reference [15] combines α-divergence with fast approximate power iteration (FAPI) algorithm, which is robust to outliers and contaminated mixed noise.…”