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Hierarchical clustering based on pairwise similarities is a common tool usedin a broad range of scientific applications. However, in many problems it maybe expensive to obtain or compute similarities between the items to beclustered. This paper investigates the hierarchical clustering of N items basedon a small subset of pairwise similarities, significantly less than thecomplete set of N(N-1)/2 similarities. First, we show that if the intraclustersimilarities exceed intercluster similarities, then it is possible to correctlydetermine the hierarchical clustering from as few as 3N log N similarities. Wedemonstrate this order of magnitude savings in the number of pairwisesimilarities necessitates sequentially selecting which similarities to obtainin an adaptive fashion, rather than picking them at random. We then propose anactive clustering method that is robust to a limited fraction of anomaloussimilarities, and show how even in the presence of these noisy similarityvalues we can resolve the hierarchical clustering using only O(N log^2 N)pairwise similarities.

Active Clustering: Robust and Efficient Hierarchical Clustering using Adaptively Selected Similarities