Coresets vs clustering: comparison of methods for redundancy reduction in very large white matter fiber sets

Recent advances in Diffusion Weighted Magnetic Resonance Imaging (DW-MRI) of white matter in conjunction with improved tractography produce impressive reconstructions of White Matter (WM) pathways. These pathways (fiber sets) often contain hundreds of thousands of fibers, or more. In order to make fiber based analysis more practical, the fiber set needs to be preprocessed to eliminate redundancies and to keep only essential representative fibers. In this paper we demonstrate and compare two distinctive frameworks for selecting this reduced set of fibers. The first framework entails pre-clustering the fibers using k-means, followed by Hierarchical Clustering and replacing each cluster with one representative. For the second clustering stage seven distance metrics were evaluated. The second framework is based on an efficient geometric approximation paradigm named coresets. Coresets present a new approach to optimization and have huge success especially in tasks requiring large computation time and/or memory. We propose a modified version of the coresets algorithm, Density Coreset. It is used for extracting the main fibers from dense datasets, leaving a small set that represents the main structures and connectivity of the brain. A novel approach, based on a 3D indicator structure, is used for comparing the frameworks. This comparison was applied to High Angular Resolution Diffusion Imaging (HARDI) scans of 4 healthy individuals. We show that among the clustering based methods, that cosine distance gives the best performance. In comparing the clustering schemes with coresets, Density Coreset method achieves the best performance.