Semi-Naive Mixture Model for Consensus Clustering

Abstract

Consensus clustering is a powerful method to combine multiple partitions obtained through different runs of clustering algorithms. The goal is to achieve a robust and stable partition of the space through a consensus procedure which exploits the diversity of multiple clusterings outputs. Several methods have been proposed to tackle the consensus clustering problem. Among them, the algorithm which models the problem as a mixture of multivariate multinomial distributions in the space of cluster labels gained high attention in the literature. However, to make the problem tractable, the theoretical formulation takes into account a Naive Bayesian conditional independence assumption over the components of the vector space in which the consensus function acts (i.e., the conditional probability of a $d-$dimensional vector space is represented as the product of conditional probability in an one dimensional feature space). In this paper we propose to relax the aforementioned assumption, heading to a Semi-Naive approach to model some of the dependencies among the components of the vector space for the generation of the final consensus partition. The Semi-Naive approach consists in grouping in a random way the components of the labels space and modeling the conditional density term in the maximum-likelihood estimation formulation as the product of the conditional densities of the finite set of groups composed by elements of the labels space. Experiments are performed to point out the results of the proposed approach.