Merge trees decoradas e TDA

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Merge_Trees_Decordas_e_TDA-Dissertacao_Mestrado-Guilherme_de_Carvalho_Falsarella-RA_728323.pdf (1.2 MB)

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2023-08-10

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Universidade Federal de São Carlos

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In this document, first we will introduce Persistance Homology and Category Theory basic concepts. Afterwards, we will develop the Merge Tree Theory which will be useful to keep track of connected components evolution of a given dataset. Finally, we expand this Merge Tree Theory to be able to study the Decorated Merge Trees, where this decoration correspond to higher degree homology.

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Análise topológica de dados , TDA , Teoria das categorias , Persistência homologia , Topologia algébrica , Merge trees , Merge trees decoradas , Topological data analysis , Category theory , Persistent homology , Algebraic topology , Decorated merge trees

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FALSARELLA, Guilherme de Carvalho. Merge trees decoradas e TDA. 2023. Dissertação (Mestrado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2023. Disponível em: https://repositorio.ufscar.br/handle/20.500.14289/18704.

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https://repositorio.ufscar.br/handle/20.500.14289/18704

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Attribution-NonCommercial-NoDerivs 3.0 Brazil
Except where otherwise noted, this item's license is described as Attribution-NonCommercial-NoDerivs 3.0 Brazil