Convergence analysis of consensus-based distributed clustering

This paper deals with clustering of spatially distributed data using wireless sensor networks. A distributed low-complexity clustering algorithm is developed that requires one-hop communications among neighboring nodes only, without local data exchanges. The algorithm alternates iterations over the variables of a consensus-based version of the global clustering problem. Using stability theory for time-varying and time-invariant systems, the distributed clustering algorithm is shown to be bounded-input bounded-output stable with an output arbitrarily close to a fixed point of the algorithm. For distributed hard K-means clustering, convergence to a local minimum of the centralized problem is guaranteed. Numerical examples confirm the merits of the algorithm and its stability analysis.