Discriminant feature extraction using empirical probability density estimation and a local basis library
The authors previously developed the so-called local discriminant basis (LDB) method for signal and image classification problems. The original LDB method relies on differences in the timefrequency energy distribution of each class: it selects the subspaces where these energy distributions are well separated by some measure such as the KullbackLeibler divergence. Through our experience and experiments on various datasets, however, we realized that the timefrequency energy distribution is not always the best quantity to analyze for classification. In this paper, we propose to use the discrimination of coordinates based, instead, on empirical probability densities. 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. We then evaluate a power of discrimination of each subspace by selecting the m most discriminant coordinates in terms of the distance among the corresponding densities (e.g., by the KullbackLeibler divergence among the densities). This information is then used for selecting a basis for classification. We will demonstrate the capability of this algorithm using both synthetic and real datasets.
density estimation kullbackleibler divergence local feature extraction pattern classification hellinger distance