Document details

Selecção de variáveis em estatística multivariada

Author(s): Minhoto, Manuel Joaquim Piteira

Date: 2009

Persistent ID: http://hdl.handle.net/10400.5/1877

Origin: Repositório da UTL

Subject(s): variable selection; multivariate statistics; combinatorial optimization; Heuristics; Pareto optimal


Description

The problem of variable selection consists in identifying a k-subset of a set of original variables that is optimal for a given criterion of adequate approximation to the whole data set. In this work we present and we discuss some new optimization criteria and others that are suggested by the literature. We present and we discuss the algorithms for the optimization problems resulting from the different criteria, as well as the calculated computational results. The criteria and algorithms are available in the package Subselect that is called from statistical program R. This package is in permanent update, with varied contributions, between which, this work is included. Package and program are of the public domain and meet available in the Internet. In this work we also discuss a multiple criteria optimization for the problem of identifying subsets of variables. In this approach, we are looking for subsets that are optimal for some criteria simultaneously. The induced total order for an only criterion gives place to a partial order, with which is associated a set of solutions that cannot simultaneously be improved in all the criteria. Usually they are called maximal, efficient solutions or Pareto optimal.

Doutoramento em Matemática e Estatística - Instituto Superior de Agronomia

Document Type Doctoral thesis
Language Portuguese
Advisor(s) Cadima, Jorge Landerset; Cerdeira, Jorge Orestes
Contributor(s) Minhoto, Manuel Joaquim Piteira
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