Positional and confidence voting-based consensus functions for fuzzy cluster ensembles

Consensus clustering, i.e. the task of combining the outcomes of several clustering systems into a single partition, has lately attracted the attention of researchers in the unsupervised classification field, as it allows the creation of clustering committees that can be applied with multiple interesting purposes, such as knowledge reuse or distributed clustering. However, little attention has been paid to the development of algorithms, known as consensus functions, especially designed for consolidating the outcomes of multiple fuzzy (or soft) clustering systems into a single fuzzy partition - despite the fact that fuzzy clustering is far more informative than its crisp counterpart, as it provides information regarding the degree of association between objects and clusters that can be helpful for deriving richer descriptive data models. For this reason, this paper presents a set of fuzzy consensus functions capable of creating soft consensus partitions by fusing a collection of fuzzy clusterings. Our proposals base clustering combination on a cluster disambiguation process followed by the application of positional and confidence voting techniques. The modular design of these algorithms makes it possible to sequence their constituting steps in different manners, which allows to derive versions of the proposed consensus functions optimized from a computational standpoint. The proposed consensus functions have been evaluated in terms of the quality of the consensus partitions they deliver and in terms of their running time on multiple benchmark data sets. A comparison against several representative state-of-the-art consensus functions reveals that our proposals constitute an appealing alternative for conducting fuzzy consensus clustering, as they are capable of yielding high quality consensus partitions at a low computational cost.