@MISC{Givoni_hierarchicalaffinity, author = {Inmar Givoni and Brendan Frey}, title = {Hierarchical Affinity Propagation}, year = {} }

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Abstract

Affinity Propagation (AP) [1] is a recently introduced algorithm for exemplar-based clustering. The goal of the algorithm is to find good partitions of data and associate each partition with its most prototypical data point (‘exemplar’) such that the similarity between points to their exemplar is maximized, and the overall cost associated with making a point an exemplar is minimized. The solution proposed to this NP-hard problem was to formulate it as inference in a factor-graph, and find approximate MAP assignment using the max-product algorithm. In their paper [2], Xiao et al describe a greedy heuristic hierarchical clustering variant of the AP clustering algorithm. The objective function it optimizes does not correspond to a natural objective for an exemplar-based hierarchical structure, and viewed under such natural objectives, due to its greedy nature it may find suboptimal solutions. We describe two alternative graphical models for hierarchical exemplar-based clustering that correspond to what we believe to be possible natural objectives. While one variant we propose is directly motivated by [2], the other can also be seen as closely related to a hierarchical version of the facility location problem (hierarchical facility location) – a