6,560 research outputs found
Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery
PCA is one of the most widely used dimension reduction techniques. A related
easier problem is "subspace learning" or "subspace estimation". Given
relatively clean data, both are easily solved via singular value decomposition
(SVD). The problem of subspace learning or PCA in the presence of outliers is
called robust subspace learning or robust PCA (RPCA). For long data sequences,
if one tries to use a single lower dimensional subspace to represent the data,
the required subspace dimension may end up being quite large. For such data, a
better model is to assume that it lies in a low-dimensional subspace that can
change over time, albeit gradually. The problem of tracking such data (and the
subspaces) while being robust to outliers is called robust subspace tracking
(RST). This article provides a magazine-style overview of the entire field of
robust subspace learning and tracking. In particular solutions for three
problems are discussed in detail: RPCA via sparse+low-rank matrix decomposition
(S+LR), RST via S+LR, and "robust subspace recovery (RSR)". RSR assumes that an
entire data vector is either an outlier or an inlier. The S+LR formulation
instead assumes that outliers occur on only a few data vector indices and hence
are well modeled as sparse corruptions.Comment: To appear, IEEE Signal Processing Magazine, July 201
Robust recursive eigendecomposition and subspace-based algorithms with application to fault detection in wireless sensor networks
The principal component analysis (PCA) is a valuable tool in multivariate statistics, and it is an effective method for fault detection in wireless sensor networks (WSNs) and other related applications. However, its online implementation requires the computation of eigendecomposition (ED) or singular value decomposition. To reduce the arithmetic complexity, we propose an efficient fault detection approach using the subspace tracking concept. In particular, two new robust subspace tracking algorithms are developed, namely, the robust orthonormal projection approximation subspace tracking (OPAST) with rank-1 modification and the robust OPAST with deflation. Both methods rely on robust M-estimate-based recursive covariance estimate to improve the robustness against the effect of faulty samples, and they offer different tradeoff between fault detection accuracy and arithmetic complexity. Since only the ED in the major subspace is computed, their arithmetic complexities are much lower than those of other conventional PCA-based algorithms. Furthermore, we propose new robust T 2 score and SPE detection criteria with recursive update formulas to improve the robustness over their conventional counterparts and to facilitate online implementation for the proposed robust subspace ED and tracking algorithms. Computer simulation and experimental results on WSN data show that the proposed fault detection approach, which combines the aforementioned robust subspace tracking algorithms with the robust detection criteria, is able to achieve better performance than other conventional approaches. Hence, it serves as an attractive alternative to other conventional approaches to fault detection in WSNs and other related applications because of its low complexity, efficient recursive implementation, and good performance. © 2012 IEEE.published_or_final_versio
Fast Robust Subspace Tracking via PCA in Sparse Data-Dependent Noise
This work studies the robust subspace tracking (ST) problem. Robust ST can be
simply understood as a (slow) time-varying subspace extension of robust PCA. It
assumes that the true data lies in a low-dimensional subspace that is either
fixed or changes slowly with time. The goal is to track the changing subspaces
over time in the presence of additive sparse outliers and to do this quickly
(with a short delay). We introduce a "fast" mini-batch robust ST solution that
is provably correct under mild assumptions. Here "fast" means two things: (i)
the subspace changes can be detected and the subspaces can be tracked with
near-optimal delay, and (ii) the time complexity of doing this is the same as
that of simple (non-robust) PCA. Our main result assumes piecewise constant
subspaces (needed for identifiability), but we also provide a corollary for the
case when there is a little change at each time.
A second contribution is a novel non-asymptotic guarantee for PCA in linearly
data-dependent noise. An important setting where this is useful is for linearly
data dependent noise that is sparse with support that changes enough over time.
The analysis of the subspace update step of our proposed robust ST solution
uses this result.Comment: To appear in IEEE Journal of Special Areas in Information Theor
Fast and robust appearance-based tracking
We introduce a fast and robust subspace-based approach to appearance-based object tracking. The core of our approach is based on Fast Robust Correlation (FRC), a recently proposed technique for the robust estimation of large translational displacements. We show how the basic principles of FRC can be naturally extended to formulate a robust version of Principal Component Analysis (PCA) which can be efficiently implemented incrementally and therefore is particularly suitable for robust real-time appearance-based object tracking. Our experimental results demonstrate that the proposed approach outperforms other state-of-the-art holistic appearance-based trackers on several popular video sequences
Robust Subspace Tracking Algorithms in Signal Processing: A Brief Survey
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
- …