On local orthonormal bases for classification and regression

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. 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.