An Information-theoretic Perspective of Hierarchical Clustering
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A combinatorial cost function for hierarchical clustering was introduced by Dasgupta <cit.>. It has been generalized by Cohen-Addad et al. <cit.> to a general form named admissible function. In this paper, we investigate hierarchical clustering from the information-theoretic perspective and formulate a new objective function. We also establish the relationship between these two perspectives. In algorithmic aspect, we get rid of the traditional top-down and bottom-up frameworks, and propose a new one to stratify the sparsest level of a cluster tree recursively in guide with our objective function. For practical use, our resulting cluster tree is not binary. Our algorithm called HCSE outputs a k-level cluster tree by a novel and interpretable mechanism to choose k automatically without any hyper-parameter. Our experimental results on synthetic datasets show that HCSE has a great advantage in finding the intrinsic number of hierarchies, and the results on real datasets show that HCSE also achieves competitive costs over the popular algorithms LOUVAIN and HLP.
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