Doctoral Thesis
DOI
10.11606/T.45.2015.tde-03122015-155546
Document
Author
Full name
Jorge Luis Guevara Díaz
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2015
Supervisor
Committee
Hirata Junior, Roberto (President)
Carvalho, André Carlos Ponce de Leon Ferreira de
Orgambide, Alejandro César Frery
Silva, Paulo José da Silva e
Sussner, Peter
Title in Portuguese
Keywords in Portuguese
Conjunto fuzzy
Descrição de dados usando vetores de suporte
Kernel positivo definido
Máquina de vetor de suporte
Métodos de kernel
Abstract in Portuguese
Title in English
Supervised machine learning models using kernel methods, probability measures and fuzzy sets
Keywords in English
Fuzzy set
Kernel methods
Positive definite kernel
Probability measure
Support vector data description
Support vector machine
Abstract in English
This thesis proposes a methodology based on kernel methods, probability measures and fuzzy sets, to analyze datasets whose individual observations are itself sets of points, instead of individual points. Fuzzy sets and probability measures are used to model observations; and kernel methods to analyze the data. Fuzzy sets are used when the observation contain imprecise, vague or linguistic values. Whereas probability measures are used when the observation is given as a set of multidimensional points in a $D$-dimensional Euclidean space. Using this methodology, it is possible to address a wide range of machine learning problems for such datasets. Particularly, this work presents data description models when observations are modeled by probability measures. Those description models are applied to the group anomaly detection task. This work also proposes a new class of kernels, \emph{the kernels on fuzzy sets}, that are reproducing kernels able to map fuzzy sets to a geometric feature spaces. Those kernels are similarity measures between fuzzy sets. We give from basic definitions to applications of those kernels in machine learning problems as supervised classification and a kernel two-sample test. Potential applications of those kernels include machine learning and patter recognition tasks over fuzzy data; and computational tasks requiring a similarity measure estimation between fuzzy sets.

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teseJorgeGuevara.pdf (2.83 Mbytes)
Publishing Date
2015-12-08

WARNING: The material described below relates to works resulting from this thesis or dissertation. The contents of these works are the author's responsibility.
• DIAZ, J. G., JUNIOR, ROBERTO HIRATA, and CANU, S. Positive Definite Kernel Functions on Fuzzy Sets. In IEEE International Conference on Fuzzy Systems (FUZZ), Beijing, 2014. IEEE International Conference on Fuzzy Systems (FUZZ) 2014., 2014.
• DIAZ, J. G., JUNIOR, ROBERTO HIRATA, and CANU, S. Support Vector Data Description for Uncertainty Data Sets. In Machine Learning Summer School, Tübingen, 2013. Machine Learning Summer School. : Max Planck Institute for Intelligent Systems, 2013.
All rights of the thesis/dissertation are from the authors
Centro de Informática de São Carlos