Results 11  20
of
3,983
Consensus and cooperation in networked multiagent systems
 Proceedings of the IEEE
"... Summary. This paper provides a theoretical framework for analysis of consensus algorithms for multiagent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, timedelays, and performance guarantees. An over ..."
Abstract

Cited by 279 (2 self)
 Add to MetaCart
Summary. This paper provides a theoretical framework for analysis of consensus algorithms for multiagent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, timedelays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in smallworld networks, Markov processes and gossipbased algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with latticetype nearest neighbor interactions. Simulation results are presented that demonstrate the role of smallworld effects on the speed of consensus algorithms and cooperative control of multivehicle formations.
Fading relay channels: Performance limits and spacetime signal design
 IEEE J. SELECT. AREAS COMMUN
, 2004
"... Cooperative diversity is a transmission technique where multiple terminals pool their resources to form a virtual antenna array that realizes spatial diversity gain in a distributed fashion. In this paper, we examine the basic building block of cooperative diversity systems, a simple fading relay ch ..."
Abstract

Cited by 258 (4 self)
 Add to MetaCart
Cooperative diversity is a transmission technique where multiple terminals pool their resources to form a virtual antenna array that realizes spatial diversity gain in a distributed fashion. In this paper, we examine the basic building block of cooperative diversity systems, a simple fading relay channel where the source, destination and relay terminals are each equipped with single antenna transceivers. We consider three different TDMAbased cooperative protocols that vary the degree of broadcasting and receive collision. The relay terminal operates in either the amplifyandforward (AF) or decodeandforward (DF) modes. For each protocol, we study the ergodic and outage capacity behavior (assuming Gaussian code books) under the AF and DF modes of relaying. We analyze the spatial diversity performance of the various protocols and find that full spatial diversity (secondorder in this case) is achieved by certain protocols provided that appropriate power control is employed. Our analysis unifies previous results reported in the literature and establishes the superiority (both from a capacity as well as a diversity pointofview) of a new protocol proposed in this paper. The second part of the paper is devoted to (distributed) spacetime code design for fading relay channels operating in the AF mode. We show that the corresponding code design criteria consist of the traditional rank and determinant criteria for the case of colocated antennas as well as appropriate power control rules. Consequently spacetime codes designed for the case of colocated multiantenna channels can be used to realize cooperative diversity provided that appropriate power control is employed.
Think Globally, Fit Locally: Unsupervised Learning of Low Dimensional Manifolds
 Journal of Machine Learning Research
, 2003
"... The problem of dimensionality reduction arises in many fields of information processing, including machine learning, data compression, scientific visualization, pattern recognition, and neural computation. ..."
Abstract

Cited by 252 (8 self)
 Add to MetaCart
The problem of dimensionality reduction arises in many fields of information processing, including machine learning, data compression, scientific visualization, pattern recognition, and neural computation.
Shape fluctuations and random matrices
, 1999
"... We study a certain random growth model in two dimensions closely related to the onedimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the TracyWidom largest eigenvalue distribution for the Gaussian Uni ..."
Abstract

Cited by 240 (10 self)
 Add to MetaCart
We study a certain random growth model in two dimensions closely related to the onedimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the TracyWidom largest eigenvalue distribution for the Gaussian Unitary Ensemble (GUE).
Nineteen Dubious Ways to Compute the Exponential of a Matrix
 SIAM Review
, 1978
"... Abstract. In principle, the exponential of a matrix could be computed in many ways. Methods involving approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polynomial have been proposed. In practice, consideration of computational stability and efficienc ..."
Abstract

Cited by 228 (0 self)
 Add to MetaCart
Abstract. In principle, the exponential of a matrix could be computed in many ways. Methods involving approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polynomial have been proposed. In practice, consideration of computational stability and efficiency indicates that some of the methods are preferable to others but that none are completely satisfactory. Most of this paper was originally published in 1978. An update, with a separate bibliography, describes a few recent developments.
Guaranteed minimumrank solutions of linear matrix equations via nuclear norm minimization
, 2007
"... The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative ..."
Abstract

Cited by 218 (15 self)
 Add to MetaCart
The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative filtering. Although specific instances can often be solved with specialized algorithms, the general affine rank minimization problem is NPhard, because it contains vector cardinality minimization as a special case. In this paper, we show that if a certain restricted isometry property holds for the linear transformation defining the constraints, the minimum rank solution can be recovered by solving a convex optimization problem, namely the minimization of the nuclear norm over the given affine space. We present several random ensembles of equations where the restricted isometry property holds with overwhelming probability, provided the codimension of the subspace is sufficiently large. The techniques used in our analysis have strong parallels in the compressed sensing framework. We discuss how affine rank minimization generalizes this preexisting concept and outline a dictionary relating concepts from cardinality minimization to those of rank minimization. We also discuss several algorithmic approaches to solving the norm minimization relaxations, and illustrate our results with numerical examples.
Randomized Gossip Algorithms
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2006
"... Motivated by applications to sensor, peertopeer, and ad hoc networks, we study distributed algorithms, also known as gossip algorithms, for exchanging information and for computing in an arbitrarily connected network of nodes. The topology of such networks changes continuously as new nodes join a ..."
Abstract

Cited by 208 (5 self)
 Add to MetaCart
Motivated by applications to sensor, peertopeer, and ad hoc networks, we study distributed algorithms, also known as gossip algorithms, for exchanging information and for computing in an arbitrarily connected network of nodes. The topology of such networks changes continuously as new nodes join and old nodes leave the network. Algorithms for such networks need to be robust against changes in topology. Additionally, nodes in sensor networks operate under limited computational, communication, and energy resources. These constraints have motivated the design of “gossip ” algorithms: schemes which distribute the computational burden and in which a node communicates with a randomly chosen neighbor. We analyze the averaging problem under the gossip constraint for an arbitrary network graph, and find that the averaging time of a gossip algorithm depends on the second largest eigenvalue of a doubly stochastic matrix characterizing the algorithm. Designing the fastest gossip algorithm corresponds to minimizing this eigenvalue, which is a semidefinite program (SDP). In general, SDPs cannot be solved in a distributed fashion; however, exploiting problem structure, we propose a distributed subgradient method that solves the optimization problem over the network. The relation of averaging time to the second largest eigenvalue naturally relates it to the mixing time of a random walk with transition probabilities derived from the gossip algorithm. We use this connection to study the performance and scaling of gossip algorithms on two popular networks: Wireless Sensor Networks, which are modeled as Geometric Random Graphs, and the Internet graph under the socalled Preferential Connectivity (PC) model.
Restoration of a Single Superresolution Image from Several Blurred, Noisy, and Undersampled Measured Images
, 1997
"... The three main tools in the single image restoration theory are the maximum likelihood (ML) estimator, the maximum a posteriori probability (MAP) estimator, and the set theoretic approach using projection onto convex sets (POCS). This paper utilizes the above known tools to propose a unified methodo ..."
Abstract

Cited by 207 (20 self)
 Add to MetaCart
The three main tools in the single image restoration theory are the maximum likelihood (ML) estimator, the maximum a posteriori probability (MAP) estimator, and the set theoretic approach using projection onto convex sets (POCS). This paper utilizes the above known tools to propose a unified methodology toward the more complicated problem of superresolution restoration. In the superresolution restoration problem, an improved resolution image is restored from several geometrically warped, blurred, noisy and downsampled measured images. The superresolution restoration problem is modeled and analyzed from the ML, the MAP, and POCS points of view, yielding a generalization of the known superresolution restoration methods. The proposed restoration approach is general but assumes explicit knowledge of the linear space and timevariant blur, the (additive Gaussian) noise, the different measured resolutions, and the (smooth) motion characteristics. A hybrid method combining the simplicity of the ML and the incorporation of nonellipsoid constraints is presented, giving improved restoration performance, compared with the ML and the POCS approaches. The hybrid method is shown to converge to the unique optimal solution of a new definition of the optimization problem. Superresolution restoration from motionless measurements is also discussed. Simulations demonstrate the power of the proposed methodology.