7,120 research outputs found
Performance Analysis of Spectral Clustering on Compressed, Incomplete and Inaccurate Measurements
Spectral clustering is one of the most widely used techniques for extracting
the underlying global structure of a data set. Compressed sensing and matrix
completion have emerged as prevailing methods for efficiently recovering sparse
and partially observed signals respectively. We combine the distance preserving
measurements of compressed sensing and matrix completion with the power of
robust spectral clustering. Our analysis provides rigorous bounds on how small
errors in the affinity matrix can affect the spectral coordinates and
clusterability. This work generalizes the current perturbation results of
two-class spectral clustering to incorporate multi-class clustering with k
eigenvectors. We thoroughly track how small perturbation from using compressed
sensing and matrix completion affect the affinity matrix and in succession the
spectral coordinates. These perturbation results for multi-class clustering
require an eigengap between the kth and (k+1)th eigenvalues of the affinity
matrix, which naturally occurs in data with k well-defined clusters. Our
theoretical guarantees are complemented with numerical results along with a
number of examples of the unsupervised organization and clustering of image
data
Multitask Diffusion Adaptation over Networks
Adaptive networks are suitable for decentralized inference tasks, e.g., to
monitor complex natural phenomena. Recent research works have intensively
studied distributed optimization problems in the case where the nodes have to
estimate a single optimum parameter vector collaboratively. However, there are
many important applications that are multitask-oriented in the sense that there
are multiple optimum parameter vectors to be inferred simultaneously, in a
collaborative manner, over the area covered by the network. In this paper, we
employ diffusion strategies to develop distributed algorithms that address
multitask problems by minimizing an appropriate mean-square error criterion
with -regularization. The stability and convergence of the algorithm in
the mean and in the mean-square sense is analyzed. Simulations are conducted to
verify the theoretical findings, and to illustrate how the distributed strategy
can be used in several useful applications related to spectral sensing, target
localization, and hyperspectral data unmixing.Comment: 29 pages, 11 figures, submitted for publicatio
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
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