Decentralized Clustering on Compressed Data without Prior Knowledge of the Number of Clusters

TL;DR

This paper introduces decentralized clustering algorithms for sensor networks that operate on compressed data without prior knowledge of the number of clusters, reducing data exchange and energy consumption.

Contribution

It presents a novel theoretical framework and algorithms that estimate the number of clusters in one run, outperforming standard methods in data efficiency.

Findings

Algorithms are competitive with K-means and DB-Scan in clustering performance.

Data exchange is reduced by at least a factor of 2.

Theoretical framework guarantees convergence to cluster centroids.

Abstract

In sensor networks, it is not always practical to set up a fusion center. Therefore, there is need for fully decentralized clustering algorithms. Decentralized clustering algorithms should minimize the amount of data exchanged between sensors in order to reduce sensor energy consumption. In this respect, we propose one centralized and one decentralized clustering algorithm that work on compressed data without prior knowledge of the number of clusters. In the standard K-means clustering algorithm, the number of clusters is estimated by repeating the algorithm several times, which dramatically increases the amount of exchanged data, while our algorithm can estimate this number in one run. The proposed clustering algorithms derive from a theoretical framework establishing that, under asymptotic conditions, the cluster centroids are the only fixed-point of a cost function we introduce. This cost function depends on a weight function which we choose as the p-value of a Wald hypothesis test. This p-value measures the plausibility that a given measurement vector belongs to a given cluster. Experimental results show that our two algorithms are competitive in terms of clustering performance with respect to K-means and DB-Scan, while lowering by a factor at least $2$ the amount of data exchanged between sensors.