Local discriminant bases and their applications, (with R. R. Coifman), J. Mathematical Imaging and Vision, vol. 5, no. 4, pp. 337-358, 1995, Invited paper.

Abstract

We describe an extension to the "best-basis" method to construct an orthonormal basis which maximizes a class separability for signal classification problems. This algorithm reduces the dimensionality of these problems by using basis functions which are well localized in time-frequency plane as feature extractors. We tested our method using two synthetic datasets: extracted features (expansion coefficients of input signals in these basis functions), supplied them to the conventional pattern classifiers, then computed the misclassification rates. These examples show the superiority of our method over the direct application of these classifiers on the input signals. As a further application, we also describe a method to extract signal component from data consisting of signal and textured background.

Keywords: wavelet packets, local trigonometric transforms, classification, feature extraction, dimensionality reduction, linear discriminant analysis, classification and regression trees

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