Sequential clustering with particle filters-estimating the number of clusters from data

Abstract

In this paper we develop a particle filtering approach for grouping observations into an unspecified number of clusters. Each cluster corresponds to a potential target from which the observations originate. A potential clustering with a specified number of clusters is represented by an association hypothesis. Whenever a new report arrives, a posterior distribution over all hypotheses is iteratively calculated from a prior distribution, an update model and a likelihood function. The update model is based on an association probability for clusters given the probability of false detection and a derived probability of an unobserved target. The likelihood of each hypothesis is derived from a cost value of associating the current report with its corresponding cluster according to the hypothesis. A set of hypotheses is maintained by Monte Carlo sampling. In this case, the state-space, i.e., the space of all hypotheses, is discrete with a linearly growing dimensionality over time. To lower the complexity further, hypotheses are combined if their clusters are close to each other in the observation space. Finally, for each time-step, the posterior distribution is projected into a distribution over the number of clusters. Compared to earlier information theoretic approaches for finding the number of clusters this approach does not require a large number of trial clusterings, since it maintains an estimate of the number of clusters along with the cluster configuration.