An adaptation of homology theory to problems of topological pattern recognition

• Grant number: 16/25659-3
• Support Opportunities: Scholarships in Brazil - Master
• Start date: May 01, 2017
• End date: February 28, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: Alice Kimie Miwa Libardi
• Grantee: Marco Antonio de Freitas Contessoto
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil

Abstract

Gunnar Carlsoon discusses the adaptation of the theory of homology from the Algebraic Topology to topological pattern recognition problems in point cloud data sets. This adaptation leads to the concept of persistence homology and bar codes. Several applications have been obtained using this method. We will present several cases where persistence homology is used, illustrating different ways in which the method can be applied. We will also describe a new method to study the persistence of topological features through point cloud data sets, called zig-zag persistence. This method generalizes the homology theory of persistence and we will pay attention to several situations that are not covered by the other theory. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

CONTESSOTO, Marco Antonio de Freitas. An adaptation of homology theory to problems of topological pattern recognition. 2018. Master's Dissertation - Universidade Estadual Paulista (Unesp). Instituto de Biociências Letras e Ciências Exatas. São José do Rio Preto São José do Rio Preto.