Topical issue

Self-adjusted consensus clustering with agglomerate algorithms

B. G. Mirkin^ab, A. A. Parinov<sup>a

a</sup> National Research University Higher School of Economics, Moscow
^b Birkbeck, University of London

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.

Keywords: consensus clustering, agglomerate clustering, consensus matrix, semi-average criterion, shifting data.

Presented by the member of Editorial Board: A. A. Galyaev

Received: 08.07.2023
Revised: 21.10.2023
Accepted: 20.01.2024

DOI: 10.31857/S0005231024030014

 English version: Automation and Remote Control, 2024, 85:3, 241–251