Uncovering the Topology of Time-Varying fMRI Data using Cubical Persistence

Abstract

Functional magnetic resonance imaging (fMRI) is a crucial technology for gaining insights into cognitive processes in humans. Data amassed from fMRI measurements result in volumetric data sets that vary over time. However, analysing such data presents a challenge due to the large degree of noise and person-to-person variation in how information is represented in the brain. To address this challenge, we present a novel topological approach that encodes each time point in an fMRI data set as a persistence diagram of topological features, i.e. high-dimensional voids present in the data. This representation naturally does not rely on voxel-byvoxel correspondence and is robust towards noise. We show that these time-varying persistence diagrams can be clustered to find meaningful groupings between participants, and that they are also useful in studying within-subject brain state trajectories of subjects performing a particular task. Here, we apply both clustering and trajectory analysis techniques to a group of participants watching the movie 'Partly Cloudy'. We observe significant differences in both brain state trajectories and overall topological activity between adults and children watching the same movie.

Image analysis for Alzheimer's disease prediction: Embracing pathological hallmarks for model architecture design

“…Topological features For 3D MR images, topological features can occur in dimen-sions 0 (connected components), 1 (cycles), and 2 (voids). We follow recent work (Rieck et al, 2020), which proposed: 1. calculating persistent homology, and 2. vectorising the resulting descriptors via persistence images (Adams et al, 2017, PI), thus simplifying their integration into neural networks; we refer to Edelsbrunner and Harer (2010) for a comprehensive introduction to TDA. Classification based on topological features was performed using a 2D-CNN as outlined in Figure 1.…”

PersGNN: Applying Topological Data Analysis and Geometric Deep Learning to Structure-Based Protein Function Prediction

“…However, these approaches turn topological information into feature vectors and rely on the construction of ad hoc handcrafted summaries. More recently, vectorizing persistence diagrams in ways that require minimal processing and retain more of the information, such as to persistence images [19], have been used in machine learning applications for scientific domains [20,21,22,23]. However, these vectorized representations are static -in contrast, the approach outlined here processes the topological information through an automatically differentiable layer, thereby continuing to learn the representation over the training process.…”