On local orthonormal bases for classification and regression

We describe extensions to the \best-basis" method to select orthonormal bases suitable for signal classiica-tion and regression problems from a large collection of orthonormal bases. For classiication 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 signiicant coordinates are fed into a traditional classiier or regression method such as Linear Discriminant Analysis (LDA) or Classiication 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 well-localized in the time-frequency plane as feature extrac-tors. Finally, we compare their performance with the traditional methods using a synthetic example.