A Method for Generating Consensus Partitions and its Application to Community Classification

Abstract

An efficient heuristic method called MINGFC (for MINimization of Global Fusion Criterion) is proposed to select approximately optimal consensus partitions from the consensus interval defined by Neumann and Norton. The method utilizes a dissimilarity measure, the number of partitions in which two objects belong to different classes. A new consensus index is defined as the ratio of the average of all within-class dissimilarities to the average of all between-class dissimilarities. The lower this ratio, the more appropriate a given partition is as a consensus of the alternative classifications. This consensus index serves as the fusion criterion in the agglomerative clustering algorithm of MINGFC which generates a series of consensus partitions. The result is represented by a set of at least two trees, in graph theoretical terms: a consensus forest. To obtain a unique solution for any consensus problem, two procedures are suggested to resolve ties encountered during the clustering process. If a particular level of the consensus forest is of primary concern, the partition into the given number of classes may be further improved by an iterative relocation procedure. Artificial partitions and actual vegetation data provide the basis for illustrating MINGFC and iterative relocation, for evaluating the tie-breaking procedures, and for comparing MINGFC with two other hierarchical methods of consensus generation.