141 research outputs found
Accelerated Gossip in Networks of Given Dimension using Jacobi Polynomial Iterations
Consider a network of agents connected by communication links, where each
agent holds a real value. The gossip problem consists in estimating the average
of the values diffused in the network in a distributed manner. We develop a
method solving the gossip problem that depends only on the spectral dimension
of the network, that is, in the communication network set-up, the dimension of
the space in which the agents live. This contrasts with previous work that
required the spectral gap of the network as a parameter, or suffered from slow
mixing. Our method shows an important improvement over existing algorithms in
the non-asymptotic regime, i.e., when the values are far from being fully mixed
in the network. Our approach stems from a polynomial-based point of view on
gossip algorithms, as well as an approximation of the spectral measure of the
graphs with a Jacobi measure. We show the power of the approach with
simulations on various graphs, and with performance guarantees on graphs of
known spectral dimension, such as grids and random percolation bonds. An
extension of this work to distributed Laplacian solvers is discussed. As a side
result, we also use the polynomial-based point of view to show the convergence
of the message passing algorithm for gossip of Moallemi \& Van Roy on regular
graphs. The explicit computation of the rate of the convergence shows that
message passing has a slow rate of convergence on graphs with small spectral
gap
Accelerated Gossip in Networks of Given Dimension using Jacobi Polynomial Iterations
Consider a network of agents connected by communication links, where each agent holds a real value. The gossip problem consists in estimating the average of the values diffused in the network in a distributed manner. We develop a method solving the gossip problem that depends only on the spectral dimension of the network, that is, in the communication network set-up, the dimension of the space in which the agents live. This contrasts with previous work that required the spectral gap of the network as a parameter, or suffered from slow mixing. Our method shows an important improvement over existing algorithms in the non-asymptotic regime, i.e., when the values are far from being fully mixed in the network. Our approach stems from a polynomial-based point of view on gossip algorithms, as well as an approximation of the spectral measure of the graphs with a Jacobi measure. We show the power of the approach with simulations on various graphs, and with performance guarantees on graphs of known spectral dimension, such as grids and random percolation bonds. An extension of this work to distributed Laplacian solvers is discussed. As a side result, we also use the polynomial-based point of view to show the convergence of the message passing algorithm for gossip of Moallemi & Van Roy on regular graphs. The explicit computation of the rate of the convergence shows that message passing has a slow rate of convergence on graphs with small spectral gap
A unified approach to sparse signal processing
A unified view of the area of sparse signal processing is presented in tutorial form by bringing together various fields in which the property of sparsity has been successfully exploited. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described succinctly. The common potential benefits of significant reduction in sampling rate and processing manipulations through sparse signal processing are revealed. The key application domains of sparse signal processing are sampling, coding, spectral estimation, array processing, compo-nent analysis, and multipath channel estimation. In terms of the sampling process and reconstruction algorithms, linkages are made with random sampling, compressed sensing and rate of innovation. The redundancy introduced by channel coding i
Distributed Detection and Estimation in Wireless Sensor Networks
In this article we consider the problems of distributed detection and
estimation in wireless sensor networks. In the first part, we provide a general
framework aimed to show how an efficient design of a sensor network requires a
joint organization of in-network processing and communication. Then, we recall
the basic features of consensus algorithm, which is a basic tool to reach
globally optimal decisions through a distributed approach. The main part of the
paper starts addressing the distributed estimation problem. We show first an
entirely decentralized approach, where observations and estimations are
performed without the intervention of a fusion center. Then, we consider the
case where the estimation is performed at a fusion center, showing how to
allocate quantization bits and transmit powers in the links between the nodes
and the fusion center, in order to accommodate the requirement on the maximum
estimation variance, under a constraint on the global transmit power. We extend
the approach to the detection problem. Also in this case, we consider the
distributed approach, where every node can achieve a globally optimal decision,
and the case where the decision is taken at a central node. In the latter case,
we show how to allocate coding bits and transmit power in order to maximize the
detection probability, under constraints on the false alarm rate and the global
transmit power. Then, we generalize consensus algorithms illustrating a
distributed procedure that converges to the projection of the observation
vector onto a signal subspace. We then address the issue of energy consumption
in sensor networks, thus showing how to optimize the network topology in order
to minimize the energy necessary to achieve a global consensus. Finally, we
address the problem of matching the topology of the network to the graph
describing the statistical dependencies among the observed variables.Comment: 92 pages, 24 figures. To appear in E-Reference Signal Processing, R.
Chellapa and S. Theodoridis, Eds., Elsevier, 201
Distributed field estimation in wireless sensor networks
This work takes into account the problem of distributed estimation of a physical field of interest through a wireless sesnor networks
Distributed field estimation in wireless sensor networks
This work takes into account the problem of distributed estimation of a physical field of interest through a wireless sesnor networks
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