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A Primer on Topological Data Analysis and Graph Signal Processing for Neuroimaging Data

Geometry Scattering Trajectory Homology (GSTH) toolbox

Dr. Dhananjay Bhaskar, Postdoctoral Researcher, Department of Genetics, Yale School of Medicine (formerly)
Watch: Part I, Part II, Part III, Part IV:

Presentation Slides:

Part I gives an overview of aims and basics of topological data analysis.
Dhananjay Bhaskar, Ph.D, Yale School of Medicine

Part II introduces graph signal processing methods.
Rahul Singh, Ph.D, Yale Wu Tsai Neuroscience Institute, Yale University

Part III introduces the Geometry Scattering Trajectory Homology (GSTH) approach and discuss some applications for clinical research.
Dhananjay Bhaskar, Ph.D, Yale School of Medicine
Brian Zaboski, Ph.D, Yale School of Medicine

Part IV is the practical tutorial in GSTH using real data.
Dhananjay Bhaskar, Ph.D, Yale School of Medicine
Rahul Singh, Ph.D, Yale Wu Tsai Neuroscience Institute

What?

Quantitative methods in psychiatry have largely focused on static or short-duration analyses of brain activity and functional connectivity. However, the analysis of long-duration spatiotemporal dynamics is critical for understanding brain activity at rest, and in response to various stimuli, tasks, and treatments. In this 4-part series, we will introduce a technique called Geometric Scattering Trajectory Homology (GSTH), which employs graph signal processing and dimensionality reduction to generate easily interpretable low-dimensional trajectories of brain activity from neuroimaging data, e.g. EEG, fNIRS, and fMRI.

GSTH was originally developed to quantify the Ca2+ signaling dynamics of stem cells in the mouse epidermis. We later adapted it for applications in neuroscience. The technique is generally applicable to any biophysical system that exhibits complex spatiotemporal dynamics. Using techniques from topological data analysis and geometry, GSTH produces quantitative readouts that capture the overall shape of the dynamic trajectories, thus enabling the identification of ‘neural motifs’ (patterns of neural activity) associated with different stimuli, tasks and neurological disorders.

Why?

Geometry Scattering Trajectory Homology (GSTH) for Neuroimaging Data has three key strengths.

First, while other techniques for analyzing brain dynamics (e.g. wavelet coherence, phase analysis, granger causality) operate solely in the spatial or temporal domain, GSTH uses graph wavelet analysis to capture spatial information and topological data analysis to capture temporal information simultaneously. This facilitates more comprehensive understanding of complex neural dynamics in a data driven way.

Second, GSTH enables dimensionality reduction to generate easily interpretable low-dimensional trajectories of brain activity from neuroimaging data, e.g. EEG, fNIRS, and fMRI.

Third, GSTH can be used to examine a long-duration spatiotemporal dynamics on an individual level, and, thus, enables evaluating within-subject changes in neural patterns in relation to fluctuation of symptom severity or following treatment

How?

Prerequisites:

  • Basic programming skills in Python (open source),
  • Fundamentals of functional MRI
  • Basic understanding of matrix algebra and frequency analysis
  • Basic understanding of graph spectral theory and topological data analysis (both are covered in this series).

Required Tools:

  • Python (open source)
  • We will use Google Collab (free) in the hands-on tutorial.

Tutorials:

YouTube video series:

Datasets:

  • GSTH can be used to analyze multiple neuroimaging modalities, including EEG, MEG, fMRI, and fNIRS
  • In this workshop series, participants will learn to use GSTH using open-source, publicly available from OpenNeuro.

Reference publications: