Betti Curves of Rank One Symmetric Matrices

Carina Curto, Joshua Paik, Igor Rivin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Betti curves of symmetric matrices were introduced in [3] as a new class of matrix invariants that depend only on the relative ordering of matrix entries. These invariants are computed using persistent homology, and can be used to detect underlying structure in biological data that may otherwise be obscured by monotone nonlinearities. Here we prove three theorems that characterize the Betti curves of rank 1 symmetric matrices. We then illustrate how these Betti curve signatures arise in natural data obtained from calcium imaging of neural activity in zebrafish.

Original languageEnglish (US)
Title of host publicationGeometric Science of Information - 5th International Conference, GSI 2021, Proceedings
EditorsFrank Nielsen, Frédéric Barbaresco
PublisherSpringer Science and Business Media Deutschland GmbH
Pages645-655
Number of pages11
ISBN (Print)9783030802080
DOIs
StatePublished - 2021
Event5th International Conference on Geometric Science of Information, GSI 2021 - Paris, France
Duration: Jul 21 2021Jul 23 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12829 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference5th International Conference on Geometric Science of Information, GSI 2021
Country/TerritoryFrance
CityParis
Period7/21/217/23/21

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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