Coherence Density Peak Clustering (CDCP) is a novel data-driven approach for detecting short-term fMRI brain activity patterns. Exploiting a novel analysis technique developed in Alessandro Laio's group, density peak clustering (Rodriguez and Laio, Science 322:1492-1496, 2015), our approach discovers well localized clusters by identifying and grouping together voxels that are coherent, i.e., voxels whose time-series are similar, irrespective of their brain location. The approach can be applied even when very short time windows (~10 volumes) are used.
The goal of CDPC is to group voxels in clusters that have a similar time development, and it proceeds according to to following steps:
(A) one defines a measure of dissimilarity dij between the time-series of two voxels i and j in a time window T; dij is small if the time-series of the intensity of the two voxels is similar, and large otherwise, irrespective of the brain location of the two voxels
(B) one computes a "density" ρi as the number of voxels j whose dissimilarity from i is smaller than a cutoff, as well as the minimum dissimilarity δi=minρj < ρi d ij between a voxel i and any other voxel with a larger density; by plotting δ as a function of ρ one obtains the "decision graph" where cluster centers (defined as local maxima in the density distribution) stand out as isolated points with a large value ρ of and δ
(C) all brain voxels are assigned to a cluster through a recursive procedure that goes from one voxel to the most similar voxel with a higher density, until a cluster center is reached. In order to remove noise, isolated voxels that are dissimilar from their spatial neighbors are removed from the analysis and not assigned to any cluster; The resulting clusters are well-ordered (based on their average density) and they are not necessarily localized in a single area of the brain but often split in two or more spatially separated regions
CDPC is a fully automatized and unsupervised procedure.
CDPC in a simple motor task: a demonstration video
Here is a video showing CDPC at work. We recorded fMRI images from a simple motor task requiring participants to perform clenches with either the left or the right hand. The video shows the results of analyzing successive 12-volume time-windows for a single participant. Each frame of the video corresponds to a 12-volume (25 s) time window. Voxels highlighted in color are the voxels that behave coherently in the time-window, and are thus assigned to a cluster. Voxels have a different color code denpending on their "density" ρ (which is a measure of how much the time series of the voxel is representative of the dominant time series in a cluster), with red voxels corresponding to the density peaks.
The MATLAB implementation of our code is available HERE.
It is meant to be used as an SPM Toolbox.
Michele Allegra (SISSA), Daniele Amati (SISSA), Fahimeh Baftizadeh (MIT), Alessandro Laio (SISSA), Marta Maieron (S. Maria della Misericordia Hospital, Udine), Fabrizio Pizzagalli (USC), Carlo Reverberi (University of Milan Bicocca), Shima Seyed-Allaei (University of Milan Bicocca)