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| Author(s): |
Marco Antônio de Freitas Contessoto
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São José do Rio Preto. 2018-06-19. |
| Institution: | Universidade Estadual Paulista (Unesp). Instituto de Biociências Letras e Ciências Exatas. São José do Rio Preto |
| Defense date: | 2018-03-09 |
| Advisor: | Alice Kimie Miwa Libardi |
| Abstract | |
The main goal of this work is to present a part of the Gunnar Carlsson paper [2], where the adaptation of the theory of usual homology to topological pattern recognition problems in point cloud data sets is discussed. This adaptation leads to the concepts of persistence homology and barcodes. Several applications have been obtained using this method. We will present some cases where persistence homology is used, illustrating different ways in which the method can be applied. We will describe,alsobasedintheCarlsson’spaper,anewmethodtostudythepersistence oftopologicalfeaturesthroughpointclouddatasets,calledzig-zagpersistence. This method generalizes the homology persistent theory and we will pay attention to situations that are not covered by the other theory. In addition, some applications of this tool are presented to obtain information from some data sets. (AU) | |
| FAPESP's process: | 16/25659-3 - An adaptation of homology theory to problems of topological pattern recognition |
| Grantee: | Marco Antonio de Freitas Contessoto |
| Support Opportunities: | Scholarships in Brazil - Master |