On the number of clusters and the fuzziness index for unsupervised FCA application to BOLD fMRI time series

The aim of this paper is to present an exploratory data-driven strategy based on Unsupervised Fuzzy Clustering Analysis (UFCA) and its potential for fMRI data analysis in the temporal domain. The a priori definition of the number of clusters is addressed and solved using heuristics. An original validity criterion is proposed taking into account data geometry and the partition Membership Functions (MFs). From our simulations, this criterion is shown to outperform other indices used in the literature. The influence of the fuzziness index was studied using simulated activation combined with real life noise data acquired from subjects under a resting state. Receiver Operating Characteristics (ROC) methodology is implemented to assess the performance of the proposed UFCA with respect to the fuzziness index. An interval of choice around 2, a value widely used in FCA, is shown to yield the best performance.