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MAP Classifier with BDA Features

In this paper, we derive a maximum a posteriori (MAP) classifier using the features extracted by biased discriminant analysis (BDA) in multi-class classification problems. Using the one-against-the-rest scheme we construct several feature spaces, where the MAP classifier is formulated. Although the maximum likelihood (ML) classifier is generally equivalent to the MAP classifier when the prior probability of each class is the same, an additional assumption is needed for the ML classifier to have the same results as the MAP classifier using the features extracted by BDA. We also show that the ML classifier is the same as the nearest to the mean classifier under some assumption. In order to estimate the distribution of negative samples in each reduced space, we can use the Parzen window density estimation or the Gaussian mixture model. Experimental results on several data sets indicate that the MAP classifier with BDA features provides better classification result than using the features extracted by linear discriminant analysis (LDA) or LDA using the Chrenoff criterion.