Consensus-based distributed expectation-maximization algorithm for density estimation and classification using wireless sensor networks

Abstract

The present paper develops a decentralized expectation-maximization (EM) algorithm to estimate the parameters of a mixture density model for use in distributed learning tasks performed with data collected at spatially deployed wireless sensors. The E-step in the novel iterative scheme relies on local information available to individual sensors, while during the M-step sensors exchange information only with their onehop neighbors to reach consensus and eventually percolate the global information needed to estimate the wanted parameters across the wireless sensor network (WSN). Analysis and simulations demonstrate that the resultant consensus-based distributed EM (CB-DEM) algorithm matches well the resourcelimited characteristics of WSNs and compares favorably with existing alternatives because it has wider applicability and remains resilient to inter-sensor communication noise.

A diffusion-based distributed em algorithm for density estimation in wireless sensor networks

“…Finally, Fig. 3 depicts the log-likelihood function Qpθ t¡1 ;θ t¡1 q computed as in (5) for the DB-DEM estimator (solid line) along with the curves for the centralized EM solution (dashed-dotted line) and a consensus-based EM (dashed line) [6][7][8]. In order to make a fair comparison, and since the curves for the DB-DEM and for the centralized EM have converged after approximately 100 and 10 iterations respectively, we run a consensus-based EM with 10 averaging iterations at each M-step.…”

“…[16,17], we consider here time-varying step-sizes in order to converge to the desired values. The advantage of the DB-DEM with respect to the consensus-based EM algorithm in [6][7][8] is a significant reduction in the total number of iterations, since only one averaging operation is performed at each M-step. This reduction in the number of iterations can be translated into energy savings, a critical issue specially in large-scale deployments.…”

“…A distributed implementation of the algorithm for a wireless sensor network (WSN) entails therefore a reformulation of the computations such that they can be performed locally at each node. Related contributions to the literature propose distributed EM implementations where the global sufficient statistics are computed using for instance aggregation [2][3][4][5], or using a consensus-based scheme [6][7][8]. Aggregation strategies require the assignment of routing paths or junction trees within the network, whereas consensus type strategies result in an increase in the total number of iterations until convergence, since a consensus algorithm [9,10] is fully executed at each M-step.…”

Cooperative Localization in WSNs Using Gaussian Mixture Modeling: Distributed ECM Algorithms

“…On the other hand, its synchronous nature facilitates our subsequent analyses on the computational complexity and communication overhead. However, we note that Algorithm 2 can be reformulated asynchronously (known as the "pair-wise gossip algorithm" [39]) or replaced with other consensus based methods [40] or diffusion based methods [41]. Lastly, we note that in the distributed algorithms P (η) l,i,j in (16)- (18) has to be replaced bỹ…”

Target Tracking in Wireless Sensor Networks

“…For a linear data model and under mild assumptions aligned with those considered in the centralized LMS, stability of the novel D-LMS algorithm is established to guarantee that local sensor estimation error norms remain bounded most of the time. Forero et al develop a decentralized expectation-maximization (EM) algorithm to estimate the parameters of a mixture density model for use in distributed learning tasks performed with data collected at spatially deployed wireless sensors (Forero et al, 2008). The E-step in the novel iterative scheme relies on local information available to individual sensors, while during the M-step sensors exchange information only with their single hop neighbours to reach consensus and eventually percolate the global information needed to estimate the wanted parameters across the WSN.…”