4,047 research outputs found
Shape Interaction Matrix Revisited and Robustified: Efficient Subspace Clustering with Corrupted and Incomplete Data
The Shape Interaction Matrix (SIM) is one of the earliest approaches to
performing subspace clustering (i.e., separating points drawn from a union of
subspaces). In this paper, we revisit the SIM and reveal its connections to
several recent subspace clustering methods. Our analysis lets us derive a
simple, yet effective algorithm to robustify the SIM and make it applicable to
realistic scenarios where the data is corrupted by noise. We justify our method
by intuitive examples and the matrix perturbation theory. We then show how this
approach can be extended to handle missing data, thus yielding an efficient and
general subspace clustering algorithm. We demonstrate the benefits of our
approach over state-of-the-art subspace clustering methods on several
challenging motion segmentation and face clustering problems, where the data
includes corrupted and missing measurements.Comment: This is an extended version of our iccv15 pape
Mathematical control of complex systems
Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
On GROUSE and Incremental SVD
GROUSE (Grassmannian Rank-One Update Subspace Estimation) is an incremental
algorithm for identifying a subspace of Rn from a sequence of vectors in this
subspace, where only a subset of components of each vector is revealed at each
iteration. Recent analysis has shown that GROUSE converges locally at an
expected linear rate, under certain assumptions. GROUSE has a similar flavor to
the incremental singular value decomposition algorithm, which updates the SVD
of a matrix following addition of a single column. In this paper, we modify the
incremental SVD approach to handle missing data, and demonstrate that this
modified approach is equivalent to GROUSE, for a certain choice of an
algorithmic parameter
Sparsity-Based Error Detection in DC Power Flow State Estimation
This paper presents a new approach for identifying the measurement error in
the DC power flow state estimation problem. The proposed algorithm exploits the
singularity of the impedance matrix and the sparsity of the error vector by
posing the DC power flow problem as a sparse vector recovery problem that
leverages the structure of the power system and uses -norm minimization
for state estimation. This approach can provably compute the measurement errors
exactly, and its performance is robust to the arbitrary magnitudes of the
measurement errors. Hence, the proposed approach can detect the noisy elements
if the measurements are contaminated with additive white Gaussian noise plus
sparse noise with large magnitude. The effectiveness of the proposed
sparsity-based decomposition-DC power flow approach is demonstrated on the IEEE
118-bus and 300-bus test systems
Matched direction detectors and estimators for array processing with subspace steering vector uncertainties
In this paper, we consider the problem of estimating and detecting a signal whose associated spatial signature is known to lie in a given linear subspace but whose coordinates in this subspace are otherwise unknown, in the presence of subspace interference and broad-band noise. This situation arises when, on one hand, there exist uncertainties about the steering vector but, on the other hand, some knowledge about the steering vector errors is available. First, we derive the maximum-likelihood estimator (MLE) for the problem and compute the corresponding Cramer-Rao bound. Next, the maximum-likelihood estimates are used to derive a generalized likelihood ratio test (GLRT). The GLRT is compared and contrasted with the standard matched subspace detectors. The performances of the estimators and detectors are illustrated by means of numerical simulations
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