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12
Distributed principal subspace estimation in wireless sensor networks
 IEEE J. Sel. Topics Signal Process
, 2011
"... Abstract—Motivated by applications in multisensor array detection and estimation, this paper studies the problem of tracking the principal eigenvector and the principal subspace of a signal’s covariance matrix adaptively in a fully decentralized wireless sensor network (WSN). Sensor networks are tr ..."
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Abstract—Motivated by applications in multisensor array detection and estimation, this paper studies the problem of tracking the principal eigenvector and the principal subspace of a signal’s covariance matrix adaptively in a fully decentralized wireless sensor network (WSN). Sensor networks are traditionally designed to simply gather raw data at a fusion center, where all the processing occurs. In large deployments, this model entails high networking cost and creates a computational and storage bottleneck for the system. By leveraging both sensors ’ abilities to communicate and their local computational power, our objective is to propose distributed algorithms for principal eigenvector and principal subspace tracking. We show that it is possible to have each sensor estimate only the corresponding entry of the principal eigenvector or corresponding row of thedimensional principal subspace matrix and do so by iterating a simple computation that combines data from its network neighbors only. This paper also examines the convergence properties of the proposed principal eigenvector and principal subspace tracking algorithms analytically and by simulations. Index Terms—Asynchronous time, average consensus, distributed algorithm, gossiping, signal detection, stochastic approximation, subspace estimation, subspace tracking, synchronous time. I.
Distributed size estimation in anonymous networks
"... The knowledge of the size of a network, i.e. of the number of nodes composing it, is important for maintenance and organization purposes. In networks where the identity of the nodes or is not unique or cannot be disclosed for privacy reasons, the sizeestimation problem is particularly challenging s ..."
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The knowledge of the size of a network, i.e. of the number of nodes composing it, is important for maintenance and organization purposes. In networks where the identity of the nodes or is not unique or cannot be disclosed for privacy reasons, the sizeestimation problem is particularly challenging since the exchanged messages cannot be uniquely associated with a specific node. In this work, we propose a totally distributed anonymous strategy based on statistical inference concepts. In our approach, each node starts generating a vector of independent random numbers from a known distribution. Then nodes compute a common function via some distributed consensus algorithms, and finally they compute the Maximum Likelihood (ML) estimate of the network size exploiting opportune statistical inferences. In this work we study the performance that can be obtained following this computational scheme when the consensus strategy is either the maximum or the average. In the maxconsensus scenario, when data come from absolutely continuous distributions, we provide a complete characterization of the ML estimator. In particular, we show that the squared estimation error decreases as 1/M, where M is the amount of random numbers locally generated by each node, independently of the chosen probability distribution. Differently, in the averageconsensus scenario, we show that if the locally generated data are independent Bernoulli trials, then the probability for the ML estimator to return a wrong answer decreases exponentially in M. Finally, we provide a discussion as how the numerical errors may affect the estimators performance under different scenarios.
Finitetime and Asymptotic Convergence of Distributed Averaging and Maximizing Algorithms
, 2012
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Distributed estimation of diameter, radius and eccentricities in anonymous networks
 in "3rd IFAC Workshop on Distributed Estimation and Control in Networked Systems (NecSys’12)", Santa Barbara (CA), ÉtatsUnis
"... Abstract: We consider how a set of collaborating agents can distributedly infer some of the properties of the communication network that they form. We specifically focus on estimating quantities that can characterize the performance of other distributed algorithms, namely the eccentricities of the n ..."
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Abstract: We consider how a set of collaborating agents can distributedly infer some of the properties of the communication network that they form. We specifically focus on estimating quantities that can characterize the performance of other distributed algorithms, namely the eccentricities of the nodes, and the radius and diameter of the network. We propose a strategy that can be implemented in any network, even under anonymity constraints, and has the desirable properties of being fully distributed, parallel and scalable. We analytically characterize the statistics of the estimation error, and highlight how the performance of the algorithm depends on a parameter tuning the communication complexity.
Distributed Size Estimation of Dynamic Anonymous Networks
"... Abstract We consider the problem of estimating the size of dynamic anonymous networks. The proposed algorithm exploits maxconsensus protocols and extends a previous strategy suited for static networks. A regularization term accounts apriori assumptions on the smoothness of the estimate, and we spe ..."
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Abstract We consider the problem of estimating the size of dynamic anonymous networks. The proposed algorithm exploits maxconsensus protocols and extends a previous strategy suited for static networks. A regularization term accounts apriori assumptions on the smoothness of the estimate, and we specifically consider quadratic regularization terms since they lead to closedform solutions. We explicitly derive an estimation scheme tailored for peertopeer service networks, starting from their statistical model. Numerical experiments validate the accuracy of the algorithm and show how the strategy can be implemented using finite precision arithmetics. Problem Description I dynamic network of N(t) agents I each agent wants to estimate N(t) Constraints: I can only use local information I agents are anonymous (no global unique ID) Static Estimation (N(t) = N) Algorithm: 1. every agent i generates yi,m ∼ U [0, 1], m = 1,...,M, i.i.d. 2. run max consensus: fm = maxi yi,m, f (t): = [f1,..., fM]T, 3. estimate N through MaximumLikelihood: N ̂ = arg minN − log (p (f1,..., fM; N)) = arg minN − log M∏ m=1 N · fN−1m Example:
On decentralized innetwork aggregation in realworld scenarios with crowd mobility
 in IEEE DCOSS
"... Abstract—Recently proposed applications for monitoring the behavior of realworld crowds with wireless sensor nodes rely on decentralized innetwork aggregation. Although some of the aggregation algorithms for wireless sensor networks seem appealing for such applications, we are not aware of any de ..."
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Abstract—Recently proposed applications for monitoring the behavior of realworld crowds with wireless sensor nodes rely on decentralized innetwork aggregation. Although some of the aggregation algorithms for wireless sensor networks seem appealing for such applications, we are not aware of any deployments of these algorithms in realworld scenarios with crowd mobility. As a step toward filling this gap, we thus discuss our experiences with decentralized innetwork aggregation from a few such deployments involving up to 177 nodes. We compare two main classes of algorithms for basic aggregates. We show that algorithms based on probabilistic, order and duplicateinsensitive sketches outperform algorithms based on gradual variance reduction. To this end, however, they have to be adapted considerably to minimize the traffic, latency, and errors of the aggregation process, and to account for some realworld issues. In short, while the algorithms do have a potential for the envisioned crowdmonitoring applications, deploying them is not trivial. I.
Author manuscript, published in "52nd IEEE Conference on Decision and Control (CDC 2013) (2013)" Distributed privacypreserving network size computation: A systemidentification based method
, 2013
"... Abstract — In this study, we propose an algorithm for computing the network size of communicating agents. The algorithm is distributed: a) it does not require a leader selection; b) it only requires local exchange of information, and; c) its design can be implemented using local information only, wi ..."
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Abstract — In this study, we propose an algorithm for computing the network size of communicating agents. The algorithm is distributed: a) it does not require a leader selection; b) it only requires local exchange of information, and; c) its design can be implemented using local information only, without any global information about the network. It is privacypreserving, namely it does not require to propagate identifying labels. This algorithm is based on system identification, and more precisely on the identification of the order of a suitablyconstructed discretetime linear timeinvariant system over some finite field. We provide a probabilistic guarantee for any randomly picked node to correctly compute the number of nodes in the network. Moreover, numerical implementation has been taken into account to make the algorithm applicable to networks of hundreds of nodes, and therefore make the algorithm applicable in realworld sensor or robotic networks. We finally illustrate our results in simulation and conclude the paper with discussions on how our technique differs from a previouslyknown strategy based on statistical inference. I.