Cluster ensemble selection based on a new cluster stability measure1

Abstract

Many stability measures, such as Normalized Mutual Information (NMI), have been proposed to validate a set of partitionings. It is highly possible that a set of partitionings may contain one (or more) high quality cluster(s) but is still adjudged a bad cluster by a stability measure, and as a result, is completely neglected. Inspired by evaluation approaches measuring the efficacy of a set of partitionings, researchers have tried to define new measures for evaluating a cluster. Thus far, the measures defined for assessing a cluster are entirely based on the well-known NMI measure. The drawback of this commonly used approach is discussed in this paper, after which a new asymmetric criterion, called the Alizadeh-Parvin-Moshki-Minaei criterion (APMM), is proposed to assess the association between a cluster and a set of partitionings. The APMM criterion overcomes the deficiency in the conventional NMI measure. We also propose a clustering ensemble framework that incorporates the APMM's capabilities in order to find the best performing clusters. The framework uses Average APMM (AAPMM) as a fitness measure to select a number of clusters instead of using all of the results. Any cluster that satisfies a predefined threshold of the mentioned measure is selected to participate in an elite ensemble. To combine the chosen clusters, a co-association matrix-based consensus function (by which the set of resultant partitionings are obtained) is used. Because Evidence Accumulation Clustering (EAC) can not derive the co-association matrix from a subset of clusters, a new EAC-based method, called Extended EAC (EEAC), is employed to construct the co-association matrix from the chosen subset of clusters. Empirical studies show that our proposed approach outperforms other cluster ensemble approaches.

Ensemble cluster pruning via convex‐concave programming

“…The problem mentioned by Banerjee et al is relabeling the clusters produced with the Hungarian method, necessitated by scaling problems in the clustering of large datasets. In addition, instead of using NMI, a new asymmetric criterion has been defined, named the Alizadeh‐Parvin‐Moshki‐Minaei criterion, to avoid the elimination of high quality clusters and to produce clusters with better performance . This method has been shown to perform better than the NMI criterion .…”

“…In addition, instead of using NMI, a new asymmetric criterion has been defined, named the Alizadeh‐Parvin‐Moshki‐Minaei criterion, to avoid the elimination of high quality clusters and to produce clusters with better performance . This method has been shown to perform better than the NMI criterion . In addition to Alizadeh et al, a new study claims that edited normalized mutual information (ENMI), which is derived from a subset of total primary spurious clusters, performs better than NMI for cluster evaluation …”

“…This method has been shown to perform better than the NMI criterion . In addition to Alizadeh et al, a new study claims that edited normalized mutual information (ENMI), which is derived from a subset of total primary spurious clusters, performs better than NMI for cluster evaluation …”

SCE: A Manifold Regularized Set-Covering Method for Data Partitioning

“…Analoui and Sadighian [46] have presented a probabilistic model by a finite mixture of multinomial distributions in a space of clustering, where the consensus partition is obtained as the solution of a maximum likelihood estimation problem. Besides these, Alizadeh proposed a cluster ensemble selection mechanism by using a new cluster stability measure which was named Alizadeh-Parvin-Moshki-Minaei criterion (APMM) [47]. The framework of this work is to select as ensemble members a part of the initial partitions which satisfy APMM, and then find the final solution by using a coassociation matrix based method.…”

WoCE: A framework for Clustering Ensemble by Exploiting the Wisdom of Crowds Theory

“…After that, the evaluated results are selected by thresholding procedure. Lastly, the final clustering result is obtained by an aggregation mechanism [7], [8], [9], [10], [11].…”