Cluster aggregate inequality and multi-level hierarchical clustering

Authors:
Chris Ding;Xiaofeng He
Affiliations:
Lawrence Berkeley National Laboratory, Berkeley, California;Lawrence Berkeley National Laboratory, Berkeley, California
Venue:
PKDD'05 Proceedings of the 9th European conference on Principles and Practice of Knowledge Discovery in Databases
Year:
2005

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Abstract

We show that (1) in hierarchical clustering, many linkage functions satisfy a cluster aggregate inequality, which allows an exact O(N2) multi-level (using mutual nearest neighbor) implementation of the standard O(N3) agglomerative hierarchical clustering algorithm. (2) a desirable close friends cohesion of clusters can be translated into kNN consistency which is guaranteed by the multi-level algorithm; (3) For similarity-based linkage functions, the multi-level algorithm is naturally implemented as graph contraction. The effectiveness of our algorithms is demonstrated on a number of real life applications.