A Distributed Higher-Order $k$-Medoids Clustering Algorithm for Network Partition

In this paper, we develop a distributed higher-order
k
-medoids clustering algorithm for networks using hop count as the distance metric, typical examples include social networks, wireless sensor networks and etc. Different than the classical
k
-medoids clustering where each cluster is assigned with one medoid (representative nodes in the network), the proposed algorithm is capable of partitioning the nodes into clusters dominated by multiple medoids. In this algorithm, a higher-order shortest path algorithm is first adopted to assign each node the clustering set comprising of its
h
(
${h} \geq 1$
) closest medoids using the hop count metric, then an aggregation algorithm collects the local information from each node to the medoids in its clustering set, based on which a medoids update mechanism helps each medoid decide whether to keep its medoid status or assign the status to one of its neighbors, so as to improve the clustering quality. The clustering performance of the proposed algorithm is proved to monotonically converge to a local optimum after running the algorithm finite times. Simulations results show that the proposed algorithm can achieve superior performance compared with several centralized
$k$
-medoids clustering algorithms and scale well as the number of nodes increases.