Topological data analysis: applications in machine learning

• Ano de defesa: 2018
• Autor(a) principal: Calcina, Sabrina Graciela Suárez
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Betti numbers; Classificação de proteínas; Classificador Naive Bayes; Classificador PLS-DA; Classificador SVM; Diagramas de persistencia; Homologia persistente; KNeighbors regressor; Naive Bayes classifier; Números de Betti; Persistence diagrams; Persistent homology; PLS-DA classifier; Protein classification; Regressor KNeighbors; Regressor SVR; SVM classifier; SVR regressor
• Link de acesso: http://www.teses.usp.br/teses/disponiveis/55/55134/tde-03012019-094950/

Recently computational topology had an important development in data analysis giving birth to the field of Topological Data Analysis. Persistent homology appears as a fundamental tool based on the topology of data that can be represented as points in metric space. In this work, we apply techniques of Topological Data Analysis, more precisely, we use persistent homology to calculate topological features more persistent in data. In this sense, the persistence diagrams are processed as feature vectors for applying Machine Learning algorithms. In order to classification, we used the following classifiers: Partial Least Squares-Discriminant Analysis, Support Vector Machine, and Naive Bayes. For regression, we used Support Vector Regression and KNeighbors. Finally, we will give a certain statistical approach to analyze the accuracy of each classifier and regressor.