Cluster significance testing using the bootstrap

Many of the statistical methods currently employed to analyze fMRI data depend on a response template. However, the true form of the hemodynamic response, and thereby the response template, is often unknown. Consequently, cluster analysis provides a complementary, template-free method for exploratory analysis of multidimensional fMRI data sets. Clustering algorithms currently being applied to fMRI data separate the data into a predefined number of clusters (k). A poor choice of k will result in erroneously partitioning well-defined clusters. Although several clustering algorithms have been successfully applied to fMRI data, techniques for statistically testing cluster separation are still lacking. To address this problem we suggest a method based on Fisher's linear discriminant and the bootstrap. Also introduced in this paper is a measure based on the projection of multidimensional data from two clusters onto the vector, maximizing the ratio of the between- to the within-cluster sums of squares. The resulting one-dimensional distribution may be readily visualized and used as a heuristic for estimating cluster homogeneity. These methods are demonstrated for the self-organizing maps clustering algorithm when applied to event-related fMRI data.