An information theoretic approach to hierarchical clustering combination

In Hierarchical Clustering, a set of patterns are partitioned into a sequence of groups represented as a dendrogram. The dendrogram is a tree representation where each node is associated with merging of two (or more) partitions and hence each partition is nested into the next partition. Hierarchical representation has properties that are useful for visualization and interpretation of clustering results. On one hand, different hierarchical clustering algorithms usually produce different dendrograms. On the other hand, clustering combination methods have received considerable interest in recent years and they yield superior results for clustering problems. This paper proposes a framework for combining various hierarchical clustering results which preserves the structural contents of input hierarchies. In this method, first a description matrix is created for each hierarchy, and then the description matrices of the input hierarchies are aggregated to form a consensus matrix from which the final hierarchy is derived. In this framework, we use two new measures for aggregating the description matrices, namely Rényi and Jensen-Shannon Divergences. The experimental and comparative analysis of our proposed framework shows the effectiveness of these two aggregators in hierarchical clustering combination. Keywords– Clustering Combination, Dendrogram descriptor, Divergence Measure, Hierarchical Clustering.