Title: Comparing matrix factorisation approaches to fuzzy clustering
Authors: Abdul Suleman - Instituto Universitario de Lisboa ISCTE-IUL BRU Lisboa Portugal (Portugal) [presenting]
Abstract: An empirical study is presented to compare three algorithms for fuzzy clustering in the framework of nonnegative matrix factorisation: archetypal analysis (ARCH), factorised fuzzy c-means (F-FCM) and unconstrained least squares (ULSQ). As an initial step, we conduct a Monte Carlo simulation with artificial data which configure several cluster contexts according to membership degree, noise contamination and density. The goodness of fit of the estimated fuzzy partitions is assessed through a generalised version of the Dice index, given fuzzy class labels. The F-FCM performs better than others when the data have a clear cluster structure, i.e. high membership in clusters, regardless of the density pattern or amount of noise. In contrast, the other two algorithms outperform F-FCM when the data have a scattered distribution. The ARCH algorithm generally performs better than ULSQ and additionally provides more stable solutions. It is therefore preferable to use ARCH despite its higher computational effort. A second experiment is carried out using data arising from real life problems and devoted to classification task. We can further confirm the effectiveness of the F-FCM algorithm in dealing with this kind of data and thus recommend it for fuzzy clustering purposes.