Sparse Distributed Learning Based on Diffusion Adaptation

This article proposes diffusion LMS strategies for distributed estimation over adaptive networks that are able to exploit sparsity in the underlying system model. The approach relies on convex regularization, common in compressive sensing, to enhance the detection of sparsity via a diffusive process over the network. The resulting algorithms endow networks with learning abilities and allow them to learn the sparse structure from the incoming data in real-time, and also to track variations in the sparsity of the model. We provide convergence and mean-square performance analysis of the proposed method and show under what conditions it outperforms the unregularized diffusion version. We also show how to adaptively select the regularization parameter. Simulation results illustrate the advantage of the proposed filters for sparse data recovery.Comment: to appear in IEEE Trans. on Signal Processing, 201

Diffusion Adaptation over Networks under Imperfect Information Exchange and Non-stationary Data

Adaptive networks rely on in-network and collaborative processing among distributed agents to deliver enhanced performance in estimation and inference tasks. Information is exchanged among the nodes, usually over noisy links. The combination weights that are used by the nodes to fuse information from their neighbors play a critical role in influencing the adaptation and tracking abilities of the network. This paper first investigates the mean-square performance of general adaptive diffusion algorithms in the presence of various sources of imperfect information exchanges, quantization errors, and model non-stationarities. Among other results, the analysis reveals that link noise over the regression data modifies the dynamics of the network evolution in a distinct way, and leads to biased estimates in steady-state. The analysis also reveals how the network mean-square performance is dependent on the combination weights. We use these observations to show how the combination weights can be optimized and adapted. Simulation results illustrate the theoretical findings and match well with theory.Comment: 36 pages, 7 figures, to appear in IEEE Transactions on Signal Processing, June 201

Diffusion lms strategy over wireless sensor network

The mess with distributed detection, where nodes arranged in certain topology are obliged to decideamong two speculations focused around accessible estimations.We look for completely appropriated and versatile usage, where all nodes make singular constant-choices by putting crosswise over with their quick neighbours just, and no combination focus is vital. The proffered distributed detection algorithms are based on a concept of extension of strategies that are employed for diffusion mechanism in a distributed network topology. After a large-scale systematic plan or arrangement for attaining some particular object or putting a particular idea into effect detection using diffusion LMS are fascinating in the context of sensor networksbecause of their versatility, enhanced strength to node and connection disappointment as contrasted with unified frameworks and their capability to convey vitality and correspondence assets. The proposed algorithms are inherently adaptive and can track changes in the element speculation.We examine the operation of the suggested algorithms in terms of their chances of detection and false alarm, and provide simulation results comparing with other cooperation schemes, including centralized processing and the case where there is no cooperation. In the context of digital signal processing and communication, the role of adaptive filters is very vital. In day to daywork where practical requirement is necessary,the computational complexities is the most considerable parameter in context of an adaptive filter. As it tells us about reliability of any system, agility to real time environment least mean squares (LMS) algorithm is generally utilized in light of its low computational multifaceted nature (O(N)) and easier in implementation.

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

Data-Reserved Periodic Diffusion LMS With Low Communication Cost Over Networks

In this paper, we analyze diffusion strategies in which all nodes attempt to estimate a common vector parameter for achieving distributed estimation in adaptive networks. Under diffusion strategies, each node essentially needs to share processed data with predefined neighbors. Although the use of internode communication has contributed significantly to improving convergence performance based on diffusion, such communications consume a huge quantity of power in data transmission. In developing low-power consumption diffusion strategies, it is very important to reduce the communication cost without significant degradation of convergence performance. For that purpose, we propose a data-reserved periodic diffusion least-mean-squares (LMS) algorithm in which each node updates and transmits an estimate periodically while reserving its measurement data even during non-update time. By applying these reserved data in an adaptation step at update time, the proposed algorithm mitigates the decline in convergence speed incurred by most conventional periodic schemes. For a period p, the total cost of communication is reduced to a factor of 1/p relative to the conventional adapt-then-combine (ATC) diffusion LMS algorithm. The loss of combination steps in this process leads naturally to a slight increase in the steady-state error as the period p increases, as is theoretically confirmed through mathematical analysis. We also prove an interesting property of the proposed algorithm, namely, that it suffers less degradation of the steady-state error than the conventional diffusion in a noisy communication environment. Experimental results show that the proposed algorithm outperforms related conventional algorithms and, in particular, outperforms ATC diffusion LMS over a network with noisy links.11Ysciescopu

Diffusion Strategies Outperform Consensus Strategies for Distributed Estimation over Adaptive Networks

Adaptive networks consist of a collection of nodes with adaptation and learning abilities. The nodes interact with each other on a local level and diffuse information across the network to solve estimation and inference tasks in a distributed manner. In this work, we compare the mean-square performance of two main strategies for distributed estimation over networks: consensus strategies and diffusion strategies. The analysis in the paper confirms that under constant step-sizes, diffusion strategies allow information to diffuse more thoroughly through the network and this property has a favorable effect on the evolution of the network: diffusion networks are shown to converge faster and reach lower mean-square deviation than consensus networks, and their mean-square stability is insensitive to the choice of the combination weights. In contrast, and surprisingly, it is shown that consensus networks can become unstable even if all the individual nodes are stable and able to solve the estimation task on their own. When this occurs, cooperation over the network leads to a catastrophic failure of the estimation task. This phenomenon does not occur for diffusion networks: we show that stability of the individual nodes always ensures stability of the diffusion network irrespective of the combination topology. Simulation results support the theoretical findings.Comment: 37 pages, 7 figures, To appear in IEEE Transactions on Signal Processing, 201