41,081 research outputs found
The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices
This paper proposes scalable and fast algorithms for solving the Robust PCA
problem, namely recovering a low-rank matrix with an unknown fraction of its
entries being arbitrarily corrupted. This problem arises in many applications,
such as image processing, web data ranking, and bioinformatic data analysis. It
was recently shown that under surprisingly broad conditions, the Robust PCA
problem can be exactly solved via convex optimization that minimizes a
combination of the nuclear norm and the -norm . In this paper, we apply
the method of augmented Lagrange multipliers (ALM) to solve this convex
program. As the objective function is non-smooth, we show how to extend the
classical analysis of ALM to such new objective functions and prove the
optimality of the proposed algorithms and characterize their convergence rate.
Empirically, the proposed new algorithms can be more than five times faster
than the previous state-of-the-art algorithms for Robust PCA, such as the
accelerated proximal gradient (APG) algorithm. Moreover, the new algorithms
achieve higher precision, yet being less storage/memory demanding. We also show
that the ALM technique can be used to solve the (related but somewhat simpler)
matrix completion problem and obtain rather promising results too. We further
prove the necessary and sufficient condition for the inexact ALM to converge
globally. Matlab code of all algorithms discussed are available at
http://perception.csl.illinois.edu/matrix-rank/home.htmlComment: Please cite "Zhouchen Lin, Risheng Liu, and Zhixun Su, Linearized
Alternating Direction Method with Adaptive Penalty for Low Rank
Representation, NIPS 2011." (available at arXiv:1109.0367) instead for a more
general method called Linearized Alternating Direction Method This manuscript
first appeared as University of Illinois at Urbana-Champaign technical report
#UILU-ENG-09-2215 in October 2009 Zhouchen Lin, Risheng Liu, and Zhixun Su,
Linearized Alternating Direction Method with Adaptive Penalty for Low Rank
Representation, NIPS 2011. (available at http://arxiv.org/abs/1109.0367
Machine Learning in Wireless Sensor Networks: Algorithms, Strategies, and Applications
Wireless sensor networks monitor dynamic environments that change rapidly
over time. This dynamic behavior is either caused by external factors or
initiated by the system designers themselves. To adapt to such conditions,
sensor networks often adopt machine learning techniques to eliminate the need
for unnecessary redesign. Machine learning also inspires many practical
solutions that maximize resource utilization and prolong the lifespan of the
network. In this paper, we present an extensive literature review over the
period 2002-2013 of machine learning methods that were used to address common
issues in wireless sensor networks (WSNs). The advantages and disadvantages of
each proposed algorithm are evaluated against the corresponding problem. We
also provide a comparative guide to aid WSN designers in developing suitable
machine learning solutions for their specific application challenges.Comment: Accepted for publication in IEEE Communications Surveys and Tutorial
Jitter-Adaptive Dictionary Learning - Application to Multi-Trial Neuroelectric Signals
Dictionary Learning has proven to be a powerful tool for many image
processing tasks, where atoms are typically defined on small image patches. As
a drawback, the dictionary only encodes basic structures. In addition, this
approach treats patches of different locations in one single set, which means a
loss of information when features are well-aligned across signals. This is the
case, for instance, in multi-trial magneto- or electroencephalography (M/EEG).
Learning the dictionary on the entire signals could make use of the alignement
and reveal higher-level features. In this case, however, small missalignements
or phase variations of features would not be compensated for. In this paper, we
propose an extension to the common dictionary learning framework to overcome
these limitations by allowing atoms to adapt their position across signals. The
method is validated on simulated and real neuroelectric data.Comment: 9 pages, 5 figures, minor correction
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