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Doctoral Thesis
DOI
10.11606/T.55.2019.tde-03012019-094950
Document
Author
Full name
Sabrina Graciela Suárez Calcina
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2018
Supervisor
Committee
Gameiro, Márcio Fuzeto (President)
Castelo Filho, Antonio
Manzoli Neto, Oziride
Melo, Thiago de
Title in English
Topological data analysis: applications in machine learning
Keywords in English
Betti numbers
KNeighbors regressor
Naive Bayes classifier
Persistence diagrams
Persistent homology
PLS-DA classifier
Protein classification
SVM classifier
SVR regressor
Abstract in English
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.
Title in Portuguese
Análise topológica de dados: aplicações em aprendizado de máquina
Keywords in Portuguese
Classificação de proteínas
Classificador Naive Bayes
Classificador PLS-DA
Classificador SVM
Diagramas de persistencia
Homologia persistente
Números de Betti
Regressor KNeighbors
Regressor SVR
Abstract in Portuguese
Recentemente a topologia computacional teve um importante desenvolvimento na análise de dados dando origem ao campo da Análise Topológica de Dados. A homologia persistente aparece como uma ferramenta fundamental baseada na topologia de dados que possam ser representados como pontos num espaço métrico. Neste trabalho, aplicamos técnicas da Análise Topológica de Dados, mais precisamente, usamos homologia persistente para calcular características topológicas mais persistentes em dados. Nesse sentido, os diagramas de persistencia são processados como vetores de características para posteriormente aplicar algoritmos de Aprendizado de Máquina. Para classificação, foram utilizados os seguintes classificadores: Análise de Discriminantes de Minimos Quadrados Parciais, Máquina de Vetores de Suporte, e Naive Bayes. Para a regressão, usamos a Regressão de Vetores de Suporte e KNeighbors. Finalmente, daremos uma certa abordagem estatística para analisar a precisão de cada classificador e regressor.
 
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Publishing Date
2019-01-03
 
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