Cargando…
The importance of the whole: Topological data analysis for the network neuroscientist
Data analysis techniques from network science have fundamentally improved our understanding of neural systems and the complex behaviors that they support. Yet the restriction of network techniques to the study of pairwise interactions prevents us from taking into account intrinsic topological featur...
Autores principales: | , , , |
---|---|
Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MIT Press
2019
|
Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6663305/ https://www.ncbi.nlm.nih.gov/pubmed/31410372 http://dx.doi.org/10.1162/netn_a_00073 |
_version_ | 1783439780805083136 |
---|---|
author | Sizemore, Ann E. Phillips-Cremins, Jennifer E. Ghrist, Robert Bassett, Danielle S. |
author_facet | Sizemore, Ann E. Phillips-Cremins, Jennifer E. Ghrist, Robert Bassett, Danielle S. |
author_sort | Sizemore, Ann E. |
collection | PubMed |
description | Data analysis techniques from network science have fundamentally improved our understanding of neural systems and the complex behaviors that they support. Yet the restriction of network techniques to the study of pairwise interactions prevents us from taking into account intrinsic topological features such as cavities that may be crucial for system function. To detect and quantify these topological features, we must turn to algebro-topological methods that encode data as a simplicial complex built from sets of interacting nodes called simplices. We then use the relations between simplices to expose cavities within the complex, thereby summarizing its topological features. Here we provide an introduction to persistent homology, a fundamental method from applied topology that builds a global descriptor of system structure by chronicling the evolution of cavities as we move through a combinatorial object such as a weighted network. We detail the mathematics and perform demonstrative calculations on the mouse structural connectome, synapses in C. elegans, and genomic interaction data. Finally, we suggest avenues for future work and highlight new advances in mathematics ready for use in neural systems. |
format | Online Article Text |
id | pubmed-6663305 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2019 |
publisher | MIT Press |
record_format | MEDLINE/PubMed |
spelling | pubmed-66633052019-08-13 The importance of the whole: Topological data analysis for the network neuroscientist Sizemore, Ann E. Phillips-Cremins, Jennifer E. Ghrist, Robert Bassett, Danielle S. Netw Neurosci Research Articles Data analysis techniques from network science have fundamentally improved our understanding of neural systems and the complex behaviors that they support. Yet the restriction of network techniques to the study of pairwise interactions prevents us from taking into account intrinsic topological features such as cavities that may be crucial for system function. To detect and quantify these topological features, we must turn to algebro-topological methods that encode data as a simplicial complex built from sets of interacting nodes called simplices. We then use the relations between simplices to expose cavities within the complex, thereby summarizing its topological features. Here we provide an introduction to persistent homology, a fundamental method from applied topology that builds a global descriptor of system structure by chronicling the evolution of cavities as we move through a combinatorial object such as a weighted network. We detail the mathematics and perform demonstrative calculations on the mouse structural connectome, synapses in C. elegans, and genomic interaction data. Finally, we suggest avenues for future work and highlight new advances in mathematics ready for use in neural systems. MIT Press 2019-07-01 /pmc/articles/PMC6663305/ /pubmed/31410372 http://dx.doi.org/10.1162/netn_a_00073 Text en © 2018 Massachusetts Institute of Technology This is an open-access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. For a full description of the license, please visit https://creativecommons.org/licenses/by/4.0/legalcode. |
spellingShingle | Research Articles Sizemore, Ann E. Phillips-Cremins, Jennifer E. Ghrist, Robert Bassett, Danielle S. The importance of the whole: Topological data analysis for the network neuroscientist |
title | The importance of the whole: Topological data analysis for the network neuroscientist |
title_full | The importance of the whole: Topological data analysis for the network neuroscientist |
title_fullStr | The importance of the whole: Topological data analysis for the network neuroscientist |
title_full_unstemmed | The importance of the whole: Topological data analysis for the network neuroscientist |
title_short | The importance of the whole: Topological data analysis for the network neuroscientist |
title_sort | importance of the whole: topological data analysis for the network neuroscientist |
topic | Research Articles |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6663305/ https://www.ncbi.nlm.nih.gov/pubmed/31410372 http://dx.doi.org/10.1162/netn_a_00073 |
work_keys_str_mv | AT sizemoreanne theimportanceofthewholetopologicaldataanalysisforthenetworkneuroscientist AT phillipscreminsjennifere theimportanceofthewholetopologicaldataanalysisforthenetworkneuroscientist AT ghristrobert theimportanceofthewholetopologicaldataanalysisforthenetworkneuroscientist AT bassettdanielles theimportanceofthewholetopologicaldataanalysisforthenetworkneuroscientist AT sizemoreanne importanceofthewholetopologicaldataanalysisforthenetworkneuroscientist AT phillipscreminsjennifere importanceofthewholetopologicaldataanalysisforthenetworkneuroscientist AT ghristrobert importanceofthewholetopologicaldataanalysisforthenetworkneuroscientist AT bassettdanielles importanceofthewholetopologicaldataanalysisforthenetworkneuroscientist |