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Doctoral Thesis
DOI
https://doi.org/10.11606/T.85.2023.tde-06062023-143404
Document
Author
Full name
André Luiz Nogueira
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2023
Supervisor
Committee
Munita, Casimiro Jaime Alfredo Sepúlveda (President)
Barroso, Lucia Pereira
Menezes, Mário Olímpio de
Santos, José Osman dos
Title in Portuguese
Algoritmos matemáticos aplicados em resultados experimentais
Keywords in Portuguese
análise de agrupamento
aplicação web
imputação
outliers
padronização
software R
Abstract in Portuguese
Este trabalho teve como objetivo avaliar o impacto da imputação de dados (métodos: média, autoencoder, análise de agrupamento e c-médias), avaliar os métodos de detecção de outliers (métodos: Mahalanobis e Mahalanobis robusta) e padronização de dados (transformadas z-score, mínimo-máximo, mínimo-máximo melhorada, logarítmica e Box-Cox) na análise de agrupamento, assim como identificar os métodos mais adequados para a base de amostras arqueológicas estudada. A base de dados foi fornecida pelo Grupo de Estudos Arqueológicos do IPENCNEN/SP, de modo que foram analisadas 140 amostras de fragmentos cerâmicos de três sítios arqueológicos. Para análise das amostras foram utilizados 13 elementos químicos: As, Na, Ce, Cr, Eu, Fe, Hf, La, Nd, Sc, Sm, Th e U. Os resultados mostraram que não houve impacto da imputação de dados nos métodos de agrupamento hierárquicos, particionais/crisp, c-médias e c-médias com polinômio fuzzificador. A exclusão dos outliers detectados pela distância Mahalanobis teve impacto no aumento da coesão entre as amostras dos sítios B e C. As transformadas utilizadas para padronização das amostras alteraram os valores da estatística de Hopkins, bem como as imagens VAT. As funções implementadas, desenvolvidas no software estatístico R, deram origem a uma aplicação web.
Title in English
Mathematical algorithms applied to experimental results
Keywords in English
cluster analysis
imputation
outliers
R software
standardization
web application
Abstract in English
This thesis aimed to evaluate the impact of data imputation (methods: mean, autoencoder, clustering and c-means), evaluate the methods of outliers detection (methods: Mahalanobis and robust Mahalanobis), and data standardization (transforms: z-score, min-max, min-max improved, logarithmic and Box-Cox) in cluster analysis, as well as to identify the most suitable method to the test basis for the archaeological sampling researched. The basis was provided by the Group of Archaeological Studies from IPEN-CNEN/SP, so were analysed 140 samples of pottery fragments from three archaeological sites. For sample analysis, were used 13 chemical elements: As, Na, Ce, Cr, Eu, Fe, Hf, La, Nd, Sc, Sm, Th and U. The results showed that there was no impact of data imputation on the hierarchical clustering methods, crisp partitions, c-means and c-means with fuzzifier polynomial. The exclusion of outliers detected by Mahalanobis distance had the impact of increasing cohesion between the samples of sites B and C. The transforms used to standardize the samples changed the Hopkins coefficient value as well as VAT images. The implemented functions, developed in the R statistical software, resulted in a web application.
 
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Publishing Date
2023-06-13
 
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