Feasibility of topological data analysis for event-related fMRI

Abstract

Recent fMRI research shows that perceptual and cognitive representations are instantiated in high-dimensional multivoxel patterns in the brain. However, the methods for detecting these representations are limited. Topological data analysis (TDA) is a new approach, based on the mathematical field of topology, that can detect unique types of geometric features in patterns of data. Several recent studies have successfully applied TDA to study various forms of neural data; however, to our knowledge, TDA has not been successfully applied to data from event-related fMRI designs. Event-related fMRI is very common but limited in terms of the number of events that can be run within a practical time frame and the effect size that can be expected. Here, we investigate whether persistent homology—a popular TDA tool that identifies topological features in data and quantifies their robustness—can identify known signals given these constraints. We use fmrisim, a Python-based simulator of realistic fMRI data, to assess the plausibility of recovering a simple topological representation under a variety of conditions. Our results suggest that persistent homology can be used under certain circumstances to recover topological structure embedded in realistic fMRI data simulations. How do we represent the world? In cognitive neuroscience it is typical to think representations are points in high-dimensional space. In order to study these kinds of spaces it is necessary to have tools that capture the organization of high-dimensional data. Topological data analysis (TDA) holds promise for detecting unique types of geometric features in patterns of data. Although potentially useful, TDA has not been applied to event-related fMRI data. Here we utilized a popular tool from TDA, persistent homology, to recover topological signals from event-related fMRI data. We simulated realistic fMRI data and explored the parameters under which persistent homology can successfully extract signal. We also provided extensive code and recommendations for how to make the most out of TDA for fMRI analysis.

Keywords

• Topological data analysis
• Persistent homology
• fMRI
• Simulation
• Event-related design
• Representation