Authors:
Carlos Pardo-Aguilar
1
;
José F. Diez-Pastor
1
;
Nicolás García-Pedrajas
2
;
Juan J. Rodríguez
1
and
César García-Osorio
1
Affiliations:
1
University of Burgos, Spain
;
2
University of Córdoba, Spain
Keyword(s):
Localized sliced inverse regression, Linear discriminant analysis for regression, Weighted principal components analysis, Nonparametric discriminant regression analysis, Localized principal Hessian directions, Hybrid discriminant analysis for regression.
Related
Ontology
Subjects/Areas/Topics:
Feature Selection and Extraction
;
Pattern Recognition
;
Regression
;
Theory and Methods
Abstract:
Two contexts may be considered, in which it is of interest to reduce the dimension of a data set. One of these arises when the intention is to mitigate the curse of dimensionality, when the data set will be used for training a data mining algorithm with a heavy computational load. The other is when one wishes to identify the data set attributes that have a stronger relation with either the class, if dealing with a classification problem, or the value to be predicted, if dealing with a regression problem. Recently, various linear regression projection models have been proposed that attempt to conserve those directions that show the highest correlation with the value to be predicted: Localized Slices Inverse Regression, Weighted Principal Component Analysis and Linear Discriminant Analysis for regression. However, the papers that have presented these methods use only a small number of data sets to validate their smooth functioning. In this research, a more exhaustive study is conducted
using 30 data sets. Moreover, by applying the ideas behind these methods, a further three new methods are also presented and included in the comparative study; one of which is competitive with the methods recently proposed.
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