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Flexible Discriminant Analysis by Optimal Scoring (1993)
| Venue: | JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION |
| Citations: | 142 - 11 self |
BibTeX
@ARTICLE{Hastie93flexiblediscriminant,
author = {Trevor Hastie and Robert Tibshirani and Andreas Buja},
title = {Flexible Discriminant Analysis by Optimal Scoring},
journal = {JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION},
year = {1993},
volume = {89},
pages = {1255--1270}
}
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Abstract
Fisher's linear discriminant analysis is a valuable tool for multigroup classification. With a large number of predictors, one can nd a reduced number of discriminant coordinate functions that are "optimal" for separating the groups. With two such functions one can produce a classification map that partitions the reduced space into regions that are identified with group membership, and the decision boundaries are linear. This paper is about richer nonlinear classification schemes. Linear discriminant analysis is equivalent to multi-response linear regression using optimal scorings to represent the groups. We obtain nonparametric versions of discriminant analysis by replacing linear regression by any nonparametric regression method. In this way, any multi-response regression technique (such as MARS or neural networks) can be post-processed to improve their classification performence.
Keyphrases
flexible discriminant analysis discriminant analysis reduced number nonlinear classification scheme multi-response linear regression classification map multi-response regression technique optimal scoring linear discriminant analysis nonparametric regression method group membership valuable tool reduced space nonparametric version large number discriminant coordinate function decision boundary classification performence linear regression neural network multigroup classification
