Feature extraction using the Bhattacharyya distance

The Bhattacharyya distance provides valuable information in determining the effectiveness of a feature set and has been used as a separability measure for feature selection. In Lee (1997), it has been shown that it is feasible to predict the classification error accurately using the Bhattacharyya distance. The new formula makes it possible to estimate classification error between two classes within 1-2% margin. In this paper, we propose a new feature extraction method utilizing the result. Initially, we start with an arbitrary feature vector. Assuming that the feature vector is used for classification, we estimate the classification error using the error estimation formula. Then we move the feature vector slightly in the direction so that the estimated classification error is decreased most rapidly. This can be done by taking a gradient. Experiments show that the proposed method compares favorably with the conventional methods.