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On Local Orthonormal Bases For Classification And Regression (1995)
| Venue: | Comptes Rendus Acad. Sci. Paris, Serie I |
BibTeX
@ARTICLE{Schlumberger-Doll95onlocal,
author = {Naoki Saito Schlumberger-Doll and Naoki Saito and Ronald R. Coifman},
title = {On Local Orthonormal Bases For Classification And Regression},
journal = {Comptes Rendus Acad. Sci. Paris, Serie I},
year = {1995},
volume = {319},
number = {319},
pages = {191--196}
}
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Abstract
We describe extensions to the "best-basis" method to select orthonormal bases suitable for signal classification and regression problems from a large collection of orthonormal bases. For classification problems, we select the basis which maximizes relative entropy of time-frequency energy distributions among classes. For regression problems, we select the basis which tries to minimize the regression error. Once these bases are selected, the most significant coordinates are fed into a traditional classifier or regression method such as Linear Discriminant Analysis (LDA) or Classification and Regression Tree (CART TM ). The performance of these statistical methods is enhanced since the proposed methods reduce the dimensionality of the problems without losing important information for the problem at hand by using the basis functions which are welllocalized in the time-frequency plane as feature extractors. Finally, we compare their performance with the traditional methods using a synthe...
Keyphrases
local orthonormal base regression problem orthonormal base regression error regression tree traditional classifier feature extractor important information linear discriminant analysis significant coordinate cart tm regression method time-frequency plane time-frequency energy distribution statistical method classification problem traditional method best-basis method large collection relative entropy signal classification basis function
