Improved discriminant bases using empirical probability density estimation, (with R. R. Coifman), 1996 Proc. Computing Section of Amer. Statist. Assoc., pp.312-321, 1997.


The authors developed the so-called Local Discriminant Bases (LDB) method for signal and image classification problems a few years back. The original LDB method relies on the difference in time-frequency energy distributions of the signal classes: it selects the subspaces where these energy distributions are well separated by some measure such as the Kullback-Leibler divergence. Through our experience and experiments on various datasets, however, we realized that the time-frequency energy distribution is not always the best quantity to analyze for classification. In this presentation, we propose to use empirical probability densities of coordinates for discrimination instead of the time-frequency energy distributions. That is, we estimate the probability density of each class in each coordinate in the wavelet packet/local trigonometric bases after expanding signals into such bases. Then, evaluate a power of discrimination of each subspace by selecting the K most discriminant coordinates in terms of the "distance" among the corresponding densities (e.g., by the Kullback-Leibler divergence among the densities). Then, this information is used for selecting a basis for classification. We can view this algorithm as a special and rapid version of the Projection Pursuit. We will demonstrate this algorithm using a few examples.

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