Comparisons of Null Models with Topological Data Analysis

Functional magnetic resonance imaging (fMRI) al-lows the construction of functional brain networks, offering a tool to probe the organization of neural activity. Null models have been proposed in this framework to evaluate the accuracy of new proposed approaches to discriminate network features coming from the data themselves in comparison to randomize procedure. Several models have been recently proposed and it is still complicated to choose one. We propose in this paper to compare null models and real datasets using Persistent homology (PH). PH is part of topological data analysis (TDA), and offers a framework for building multiscale summaries of networks. PH is first applied to a density-based filtration. We propose a procedure to extract label information from persistent homology summaries of labeled graphs. We then investigate its ability to discriminate between real data and surrogate data generated from null models. Interestingly, our new proposed label-informed approach is able to discriminate very accurately real datasets and classical null models opening the way to the design of new null models.