On local orthonormal bases for classification and regression,
(with R. R. Coifman), Proc. 1995 International Conference on Acoustics,
Speech, and Signal Processing, pp.1529-1532, IEEE Signal Processing Society, May 1995, Detroit, MI.
We describe extensions to the "best-basis" method which 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,
a small number of most significant coordinates are fed into a traditional
classifier or regression method such as Linear Discriminant Analysis (LDA) or
Classification and Regression Tree (CART).
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. Here, the basis functions which
are well-localized in the time-frequency plane are used as feature extractors.
We also compare their performance with the traditional methods using
a synthetic example.
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