CONSENSUS-BASED ENSEMBLES OF SOFT CLUSTERINGS

The problem of obtaining a single “consensus” clustering solution from a multitude or ensemble of clusterings of a set of objects, has attracted much interest recently because of its numerous practical applications. While a wide variety of approaches including graph partitioning, maximum likelihood, genetic algorithms, and voting-merging have been proposed so far to solve this problem, virtually all of them work on hard partitionings, i.e., where an object is a member of exactly one cluster in any individual solution. However, many clustering algorithms such as fuzzy c-means naturally output soft partitionings of data, and forcibly hardening these partitions before applying a consensus method potentially involves loss of valuable information. In this article we propose several consensus algorithms that can be applied directly to soft clusterings. Experimental results over a variety of real-life datasets are also provided to show that using soft clusterings as input does offer significant advantages, especially when dealing with vertically partitioned data.