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Brain Representations

A repository for topological comparisons of dimension reduction algorithms applied to resting-state fMRI data.

Rough Overview

This repository contains code for/commemorates the directory tree structure of the repository underlying the analyses in

In this repository:

  1. we have several different repositories of source code; the most populated one is 'src_py', with 'src_bash' a distant second and 'src_MATLAB' an even further third
  2. we have lots of bash/slurm code meant to script resource-heavy operations on a compute cluster, plus the occasional bit of python code meant to do the same
  3. we have brain representation extraction code and figure-making code in relevant directories: code is only included in "src_*" if it is intentionally multipurpose
  4. we have directories corresponding to the computation, outputs, and feature extraction of the brain representation/dimension reduction methods we consider
  5. finally, we also have Ripser [2] and Ripser-image [3] here, upon which all of the persistence analysis is actually built

Structure of the repository

This repository is organised as follows.

Source Code

  • 'src_py': python code (this does most of the repo's work)
  • 'src_bash': bash scripts
  • 'src_MATLAB': mostly here to borrow functions from PALM, which we need to satisfy exchangeability criteria with respect to the family structure in Human Connectome Project (Young Adult) data

Experiments

  • 'datalists': lists of data files corresponding that help set conditions for specific experiments
  • 'phom_analysis': all persistent homology-based analyses in this project (with the exception of 'metric_tests' and 'bootstrap_benchmarks')
  • 'phom_analysis/full-scale-expmt': scripts, code, and tree structure corresponding to investigation in [paper] and corresponding figures
  • 'nonPH_analysis': most notably contains output of CCA analysis of shared information between pairs of brain representations
  • 'metric_tests': preliminary testing of the impact of metric choice on persistence data
  • 'bootstrap_benchmarks': benchmarking the cycle registration bootstrapping scheme to test scalability
  • 'output_benchmarks': becnhmarking the computation(al scaling) of Betti curves, Wasserstein distances, and other derivatives of persistence diagrams

Brain Representation Computation/Extraction Note that no subject data of any kind is included in this public repository! Instead, the following directories contain the extraction/computation/processing code used to standardize brain representations for persistent homology analysis.

  • profumo_reps: code for the computing FC network matrices (correlations between timecourses) and spatial correlation matrices (correlations between maps)
  • gradient_reps: code for the computing diffusion-network based gradient representations from connectivity data at both the subject and group level and derivative features of these representations
  • ICA_reps: code for computing FC network matrices, partial FC matrices, and amplitude features from extracted ICA-DR data
  • glasser: code for extracting parcellation-level timeseries from data and computing FC network matrices, partial FC matrices, and amplitude features from extracted Glasser-parcellated data
  • schaefer: code for extracting parcellation-level timeseries from data and computing FC network matrices, partial FC matrices, and amplitude features from Schaefer-parcellated data
  • yeo: code for extracting parcellation-level timeseries from data and computing FC network matrices, partial FC matrices, and amplitude features from Yeo-parcellated data

Preparations

Compiling the C++ programs (required for cycle registration)

Before running the code to perform cycle matching [1] in this repository, one needs to compile the C++ files in the modified ripser folder. For that

  • Install a C++ compiler in your computer. We recommend getting the compiler GCC.
  • The relevant Makefiles are included in the corresponding folders, so the compilation can be done by running the command line make in a terminal opened in the folder.
  • The compiled files should be in the same directory than the python scripts/notebooks in which the cycle matching [1] code is invoked.

Installing Python libraries

The analyses in this have several Python package dependencies; some are listed below according to their role in the code.

Parsing Neuroimaging Data

Canonical Correlation Analysis (regularized)

Persistent Homology

Figures and Statistics

Background

Academic use

This code is available and is fully adaptable for individual user customization. If you use the our methods, please cite as the following:

@misc{' ',
	title = {Unknown},
	publisher = {publisher?},
	author = ###############
	month = ??,
	year = {2023/4},
	note = {arXiv:####.<subj> [tag1, tag2]},
	keywords = {topological data analysis, neuroscience, computational topology, persistent homology, functional connectivity, dimension reduction},
}

References

[1] Reani, Yohai, and Omer Bobrowski. 2021. ‘Cycle Registration in Persistent Homology with Applications in Topological Bootstrap’, January. https://arxiv.org/abs/2101.00698v1.

[2] Bauer, Ulrich. 2021. ‘Ripser: Efficient Computation of Vietoris-Rips Persistence Barcodes’. Journal of Applied and Computational Topology 5 (3): 391–423. https://doi.org/10.1007/s41468-021-00071-5.

[3] Bauer, Ulrich, and Maximilian Schmahl. 2022. ‘Efficient Computation of Image Persistence’. ArXiv:2201.04170 [Cs, Math], January. http://arxiv.org/abs/2201.04170.

[4] I. García-Redondo, A. Monod, and A. Song, “Fast Topological Signal Identification and Persistent Cohomological Cycle Matching.” arXiv, Sep. 30, 2022. doi: 10.48550/arXiv.2209.15446. https://arxiv.org/abs/2209.15446

[5] G. Tauzin et al., “giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration,” in NeurIPS 2020 Workshop TDA and Beyond, 2020. Accessed: Mar. 21, 2021. [Online]. Available: https://github.com/giotto-ai/pyflagser.