Clustering by transitive propagation

We present a global optimization algorithm for clustering data given the ratio of likelihoods that each pair of data points is in the same cluster or in different clusters. To define a clustering solution in terms of pairwise relationships, a necessary and sufficient condition is that belonging to the same cluster satisfies transitivity. We define a global objective function based on pairwise likelihood ratios and a transitivity constraint over all triples, assigning an equal prior probability to all clustering solutions. We maximize the objective function by implementing max-sum message passing on the corresponding factor graph to arrive at an O(N^3) algorithm. Lastly, we demonstrate an application inspired by mutational sequencing for decoding random binary words transmitted through a noisy channel.