Finding Consistent Clusters in Data Partitions

Abstract

Given an arbitrary data set, to which no particular parametrical, statistical or geometrical structure can be assumed, different clustering algorithms will in general produce different data partitions. In fact, several partitions can also be obtained by using a single clustering algorithm due to dependencies on initialization or the selection of the value of some design parameter. This paper addresses the problem of finding consistent clusters in data partitions, proposing the analysis of the most common associations performed in a majority voting scheme. Combination of clustering results are performed by transforming data partitions into a co-association sample matrix, which maps coherent associations. This matrix is then used to extract the underlying consistent clusters. The proposed methodology is evaluated in the context of k-means clustering, a new clustering algorithm-voting-k-means, being presented. Examples, using both simulated and real data, show how this majority voting combination scheme simultaneously handles the problems of selecting the number of clusters, and dependency on initialization. Furthermore, resulting clusters are not constrained to be hyper-spherically shaped.

Combining multiple classifications of chemical structures using consensus clustering

“…When the single linkage method has been used for consensus clustering it has been referred to as the majority rule or the quota rule 21,41 . The DIRECT procedure in CLUTO provided the next consensus clustering method.…”

Consensus Clustering Using kNN Mode Seeking

“…Fred and Jain [9,11,12,10] suggest to use the k-means clustering algorithm several times with random initial conditions. In each of the clustering trials, the number of clusters, k, is either fixed or chosen randomly in the range k ∈ [k min , k max ].…”

“…Each value of k is used to accumulate evidence about the clustering structure using two different approaches: -In the first approach, what we will refer to as a consensus matrix, is computed. This entails simply counting for each k whether or not pairs of data points in the data set belong to the same basin of attraction (mode), for then to compute the average over all k. Based on the consensus matrix, a hierarchical clustering approach similar to that used in [9] and [11] is utilized in order to obtain the final clustering result. -The second approach we investigate, is based on for each k to compute an information theoretic divergence measure between pairs of modes resulting in a similarity matrix between modes, for then to average over all k. Then, a spectral clustering procedure is executed on this matrix, similar to [1].…”

Clustering Similarity Comparison Using Density Profiles

“…A popular technique for merging is called 'majority voting' [11,12] which is a pair-counting method extended over multiple clusterings. Using a co-association matrix of data points, where pairs of points are given a score if they appear in the same cluster over all available clusterings.…”