Mining the Hierarchy of Resting-State Brain Networks: Selection of Representative Clusters in a Multiscale Structure

The hierarchical organization of brain networks can be captured by clustering time series using multiple numbers of clusters, or scales, in resting-state functional magnetic resonance imaging. However, the systematic examination of all scales is a tedious task. Here, I propose a method to select a limited number of scales that are representative of the full hierarchy. A bootstrap analysis is first performed to estimate stability matrices, which quantify the reliability of the clustering for every pair of brain regions, over a grid of possible scales. A subset of scales is then selected to approximate linearly all stability matrices with a specified level of accuracy. On real data, the method was found to select a relatively small (~7) number of scales to explain 95% of the energy of 73 scales ranging from 2 to 1100 clusters. The number of selected scales was very consistent across 43 subjects, and the actual scales also showed some good level of agreement. This approach thus provides a principled approach to mine hierarchical brain networks, in the form of a few scales amenable to detailed examination.