A new correlation‐based fuzzy logic clustering algorithm for FMRI

Fuzzy logic clustering algorithms are a new class of processing strategies for functional MRI (fMRI). In this study, the ability of such methods to detect brain activation on application of a stimulus task is demonstrated. An optimization of the selected algorithm with regard to different parameters is proposed. These parameters include (a) those defining the pre-processing procedure of the data set; (b) the definition of the distance between two time courses, considered as p-dimensional vectors, where p is the number of sequential images in the fMRI data set; and (c) the number of clusters to be considered. Based on the assumption that such a clustering algorithm should cluster the pixel time courses according to their similarity and not their proximity (in terms of distance), cross-correlation-based distances are defined. A clear mathematical description of the algorithm is proposed, and its convergence is proven when similarity measures are used instead of conventional Euclidean distance. The differences between the membership function given by the algorithm and the probability are clearly exposed. The algorithm was tested on artificial data sets, as well as on data sets from six volunteers undergoing stimulation of the primary visual cortex. The fMRI maps provided by the fuzzy logic algorithm are compared to those achieved by the well established cross-correlation technique.