On Pairwise Clustering with Side Information

Pairwise clustering, in general, partitions a set of items via a known similarityfunction. In our treatment, clustering is modeled as a transductive predictionproblem. Thus rather than beginning with a known similarity function, the functioninstead is hidden and the learner only receives a random sample consisting of asubset of the pairwise similarities. An additional set of pairwise side-informationmay be given to the learner, which then determines the inductive bias of ouralgorithms. We measure performance not based on the recovery of the hiddensimilarity function, but instead on how well we classify each item. We give tightbounds on the number of misclassifications. We provide two algorithms. The firstalgorithm SACA is a simple agglomerative clustering algorithm which runs in nearlinear time, and which serves as a baseline for our analyses. Whereas the secondalgorithm, RGCA, enables the incorporation of side-information which may lead toimproved bounds at the cost of a longer running time.