On local feature extraction for signal classification, (with R. R. Coifman), in Applied Analysis (O. Mahrenholtz and R. Mennicken, eds.), Zeitschrift für Angewandte Mathematik und Mechanik, vol.76, no.S2, pp.453-456, Akademie-Verlag, Berlin, 1996


This paper reviews the local discriminant basis (LDB) method for signal classification problems and demonstrates its capability using a synthetic example. The LDB method rapidly selects an orthonormal basis suitable for signal classification problem from a large collection of orthonormal bases. The goodness of each basis in this collection is measured by the "difference" (e.g., relative entropy) of energy distributions among signal classes under that basis. Once the LDB -- which maximizes this measure -- is selected, a small number of most significant coordinates are fed into a traditional classifier such as linear discriminant analysis (LDA) or classification tree (CT). The performance of these classifiers is enhanced since the method reduces the dimensionality of the problems without losing important information for classification. Moreover, since the basis functions well-localized in the time-frequency plane are used as feature extractors, interpretation of the classification results becomes easier and more intuitive than using the conventional methods directly on the original coordinate system.

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