The importance of the whole: Topological data analysis for the network neuroscientist
Abstract
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 01, 2019
- Source ID
- 10.1162/netn_a_00073
Entities
People
- Ann E Sizemore
- Danielle Bassett
- Jennifer E. Phillips-cremins
- Robert Ghrist
Organizations
- Alfred P. Sloan Foundation
- Army Research Office
- Eunice Kennedy Shriver National Institute of Child Health and Human Development
- Institute for Scientific Interchange
- John D. and Catherine T. MacArthur Foundation
- National Institute of Mental Health
- National Institute of Neurological Disorders and Stroke
- National Science Foundation
- Office of Naval Research
- Paul G. Allen Family Foundation
- United States Army Research Laboratory
- University of Pennsylvania