Y. N. Singh

Sateeshkrishna Dhuli, Y. N. Singh

Average consensus algorithms compute the global average of sensor data in a distributed fashion using local sensor nodes. Simple execution, decentralized philosophy make these algorithms suitable for WSN scenarios. Most of the researchers have studied the average consensus algorithms by modeling the network as an undirected graph. But, WSNs in practice consist of asymmetric links and the undirected graph cannot model the asymmetric links. Therefore, these studies fail to study the actual performance of consensus algorithms on WSNs. In this paper, we model the WSN as a directed graph and derive the explicit formulas of the ring, torus, $r$-nearest neighbor ring, and $m$-dimensional torus networks. Numerical results subsequently demonstrate the accuracy of directed graph modeling. Further, we study the effect of asymmetric links, the number of nodes, network dimension, and node overhead on the convergence rate of average consensus algorithms.

Sateeshkrishna Dhuli, Kumar Gaurav, Y. N. Singh

Average consensus algorithms can be implemented over wireless sensor networks (WSN), where global statistics can be computed using communications among sensor nodes locally. Simple execution, robustness to global topology changes due to frequent node failures and underlying distributed philosophy has made consensus algorithms more suitable to WSNs. Since these algorithms are iterative in nature, their performance is characterized by convergence speed. We study the convergence of the average consensus algorithms for WSNs using regular graphs. We obtained the analytical expressions for optimal consensus and convergence parameters which decides the convergence time for r-nearest neighbor cycle and torus networks. We have also derived the generalized expression for optimal consensus and convergence parameters for m-dimensional r-nearest neighbor torus networks. The obtained analytical results agree with the simulation results and shown the effect of network dimension, number of nodes and transmission radius on convergence time. This work provides the basic analytical tools for managing and controlling the performance of average consensus algorithm in the finite sized practical networks.

Bhaskar Mukhoty, Ruchir Gupta, Y. N. Singh

Several methods have been proposed to estimate the number of clusters in a dataset; the basic ideal behind all of them has been to study an index that measures inter-cluster separation and intra-cluster cohesion over a range of cluster numbers and report the number which gives an optimum value of the index. In this paper we propose a simple, parameter free approach that is like human cognition to form clusters, where closely lying points are easily identified to form a cluster and total number of clusters are revealed. To identify closely lying points, affinity of two points is defined as a function of distance and a threshold affinity is identified, above which two points in a dataset are likely to be in the same cluster. Well separated clusters are identified even in the presence of outliers, whereas for not so well separated dataset, final number of clusters are estimated and the detected clusters are merged to produce the final clusters. Experiments performed with several large dimensional synthetic and real datasets show good results with robustness to noise and density variation within dataset.