Self-Adjusted Consensus Clustering with Agglomerate Algorithms

Abstract

This paper reports of theoretical and computational results related to an original concept of consensus clustering involving what we call the projective distance between partitions. This distance is defined as the squared difference between a partition incidence matrix and its image over the orthogonal projection in the linear space spanning the other partition incidence matrix. It appears, provided that the ensemble clustering is of a sufficient size, agglomerate clustering with the semi-average within-cluster similarity criterion effectively solves the problem of consensus partition and, moreover, of the number of clusters in it.