Ensemble online clustering through decentralized observations

We investigate the problem of online learning for an ensemble of agents clustering incoming data, i.e., the problem of combining online local clustering decisions made by distributed agents to improve knowledge and accuracy of implicit clusters hidden in the incoming data streams. We focus on clustering using the well-known K-means algorithm for numerical data due to its efficiency in clustering large data sets. Nevertheless, our results can be straightforwardly extended to, e.g., the K-modes variant of the K-means algorithm to handle categorical data, as well as to other clustering algorithms. We show that the proposed ensemble online solutions, which are based on a simple majority-voting scheme, converge to the centralized solutions that would be made by a fusion center, that is, the solutions resulting from one agent with access to all information across agents. Given the dimensions of the clustering model, the aforementioned convergence is demonstrated to be achievable for relatively small sizes of the ensemble.