Feasibility of topological data analysis for event-related fMRI.

Michael Lesnick,Bryn Keller,Jonathan D Cohen,Cameron T Ellis,Gregory Henselman-Petrusek

doi:10.1162/netn_a_00095

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.

Highlights

A fundamental construct in cognitive psychology and neuroscience is that of a representational space, within which knowledge is stored
We focus on the application of persistent homology (Zomorodian & Carlsson, 2005), one of the most widely studied and applied Topological data analysis (TDA) tools, to the analysis of representations in event-related fMRI
We chose to work with these data because many of their characteristics were representative of other fMRI studies; we note that some aspects of the design we simulated are distinct from the design of these authors

Summary

Introduction

A fundamental construct in cognitive psychology and neuroscience is that of a representational space, within which knowledge is stored. Representation: A point in a high-dimensional space where each dimension reflects features of that representation (e.g., perceptual, semantic, evaluative features). Which items of a particular type are described, in which each dimension reflects features of items of that type (e.g., perceptual, semantic, evaluative). A central goal of both cognitive psychology and neuroscience is to characterize the dimensions that define representational spaces for different types of information (e.g., objects in the world, goals, classes of actions). Progress towards this goal obviously relies on methods that can identify the structure of such spaces. Cognitive neuroscience seeks evidence for such structure in patterns of neural activity

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Conclusion