19,327 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 Independent Component Analysis via Minimum Divergence Estimation
Independent component analysis (ICA) has been shown to be useful in many
applications. However, most ICA methods are sensitive to data contamination and
outliers. In this article we introduce a general minimum U-divergence framework
for ICA, which covers some standard ICA methods as special cases. Within the
U-family we further focus on the gamma-divergence due to its desirable property
of super robustness, which gives the proposed method gamma-ICA. Statistical
properties and technical conditions for the consistency of gamma-ICA are
rigorously studied. In the limiting case, it leads to a necessary and
sufficient condition for the consistency of MLE-ICA. This necessary and
sufficient condition is weaker than the condition known in the literature.
Since the parameter of interest in ICA is an orthogonal matrix, a geometrical
algorithm based on gradient flows on special orthogonal group is introduced to
implement gamma-ICA. Furthermore, a data-driven selection for the gamma value,
which is critical to the achievement of gamma-ICA, is developed. The
performance, especially the robustness, of gamma-ICA in comparison with
standard ICA methods is demonstrated through experimental studies using
simulated data and image data.Comment: 7 figure
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