756 research outputs found
A Sparsity-Aware Adaptive Algorithm for Distributed Learning
In this paper, a sparsity-aware adaptive algorithm for distributed learning
in diffusion networks is developed. The algorithm follows the set-theoretic
estimation rationale. At each time instance and at each node of the network, a
closed convex set, known as property set, is constructed based on the received
measurements; this defines the region in which the solution is searched for. In
this paper, the property sets take the form of hyperslabs. The goal is to find
a point that belongs to the intersection of these hyperslabs. To this end,
sparsity encouraging variable metric projections onto the hyperslabs have been
adopted. Moreover, sparsity is also imposed by employing variable metric
projections onto weighted balls. A combine adapt cooperation strategy
is adopted. Under some mild assumptions, the scheme enjoys monotonicity,
asymptotic optimality and strong convergence to a point that lies in the
consensus subspace. Finally, numerical examples verify the validity of the
proposed scheme, compared to other algorithms, which have been developed in the
context of sparse adaptive learning
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
Diffusion Adaptation Strategies for Distributed Optimization and Learning over Networks
We propose an adaptive diffusion mechanism to optimize a global cost function
in a distributed manner over a network of nodes. The cost function is assumed
to consist of a collection of individual components. Diffusion adaptation
allows the nodes to cooperate and diffuse information in real-time; it also
helps alleviate the effects of stochastic gradient noise and measurement noise
through a continuous learning process. We analyze the mean-square-error
performance of the algorithm in some detail, including its transient and
steady-state behavior. We also apply the diffusion algorithm to two problems:
distributed estimation with sparse parameters and distributed localization.
Compared to well-studied incremental methods, diffusion methods do not require
the use of a cyclic path over the nodes and are robust to node and link
failure. Diffusion methods also endow networks with adaptation abilities that
enable the individual nodes to continue learning even when the cost function
changes with time. Examples involving such dynamic cost functions with moving
targets are common in the context of biological networks.Comment: 34 pages, 6 figures, to appear in IEEE Transactions on Signal
Processing, 201
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