INVARIANTS FOR TAME PARAMETRISED CHAIN COMPLEXES

Wojciech Chacholski; Barbara Giunti; Claudia Landi

doi:10.4310/HHA.2021.v23.n2.a11

INVARIANTS FOR TAME PARAMETRISED CHAIN COMPLEXES

Wojciech Chacholski
, Barbara Giunti
, Claudia Landi

Mathematics and Statistics

University at Albany

KTH Royal Institute of Technology
University of Modena and Reggio Emilia

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We set the foundations for a new approach to Topological Data Analysis (TDA) based on homotopical methods at the chain complex level. We present the category of tame parametrised chain complexes as a comprehensive environment that includes several cases that usually TDA handles separately, such as persistence modules, zigzag modules, and commutative ladders. We extract new invariants in this category using a model structure and various minimal cofibrant approximations. Such approximations and their invariants retain some of the topological, and not just homological, aspects of the objects they approximate.

Original language	English
Pages (from-to)	183-213
Number of pages	31
Journal	Homology, Homotopy and Applications
Volume	23
Issue number	2
DOIs	https://doi.org/10.4310/HHA.2021.v23.n2.a11
State	Published - 2021

Keywords

Cofibrant approximation
Minimality
Persistence theory
Topological data analysis

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title = "INVARIANTS FOR TAME PARAMETRISED CHAIN COMPLEXES",

abstract = "We set the foundations for a new approach to Topological Data Analysis (TDA) based on homotopical methods at the chain complex level. We present the category of tame parametrised chain complexes as a comprehensive environment that includes several cases that usually TDA handles separately, such as persistence modules, zigzag modules, and commutative ladders. We extract new invariants in this category using a model structure and various minimal cofibrant approximations. Such approximations and their invariants retain some of the topological, and not just homological, aspects of the objects they approximate.",

keywords = "Cofibrant approximation, Minimality, Persistence theory, Topological data analysis",

author = "Wojciech Chacholski and Barbara Giunti and Claudia Landi",

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T1 - INVARIANTS FOR TAME PARAMETRISED CHAIN COMPLEXES

AU - Chacholski, Wojciech

AU - Giunti, Barbara

AU - Landi, Claudia

PY - 2021

Y1 - 2021

N2 - We set the foundations for a new approach to Topological Data Analysis (TDA) based on homotopical methods at the chain complex level. We present the category of tame parametrised chain complexes as a comprehensive environment that includes several cases that usually TDA handles separately, such as persistence modules, zigzag modules, and commutative ladders. We extract new invariants in this category using a model structure and various minimal cofibrant approximations. Such approximations and their invariants retain some of the topological, and not just homological, aspects of the objects they approximate.

AB - We set the foundations for a new approach to Topological Data Analysis (TDA) based on homotopical methods at the chain complex level. We present the category of tame parametrised chain complexes as a comprehensive environment that includes several cases that usually TDA handles separately, such as persistence modules, zigzag modules, and commutative ladders. We extract new invariants in this category using a model structure and various minimal cofibrant approximations. Such approximations and their invariants retain some of the topological, and not just homological, aspects of the objects they approximate.

KW - Cofibrant approximation

KW - Minimality

KW - Persistence theory

KW - Topological data analysis

UR - https://www.scopus.com/pages/publications/85099537283

U2 - 10.4310/HHA.2021.v23.n2.a11

DO - 10.4310/HHA.2021.v23.n2.a11

M3 - Article

SN - 1532-0073

VL - 23

SP - 183

EP - 213

JO - Homology, Homotopy and Applications

JF - Homology, Homotopy and Applications

IS - 2

ER -

INVARIANTS FOR TAME PARAMETRISED CHAIN COMPLEXES

Abstract

Keywords

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