We introduce a method that learns a class-discriminative subspace or discriminative components of data. Such a subspace is useful for visualization, dimensionality reduction, feature extraction, and for learning a regularized distance metric. We learn the subspace by optimizing a probabilistic semiparametric model, a mixture of Gaussians, of classes in the subspace. The semiparametric modeling leads to fast computation (O(N) for N samples) in each iteration of optimization, in contrast to recent nonparametric methods that take O(N^2) time, but with equal accuracy. Moreover, we learn the subspace in a semi-supervised manner from three kinds of data: labeled and unlabeled samples, and unlabeled samples with pairwise constraints, with a unified objective.

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S. Kaski and J. Peltonen were supported by the Academy of Finland, decision numbers 108515 and 207467. This work was also supported in part by the IST Programme of the European Community, under the PASCAL Network of Excellence, IST-2002-506778. This publication only reflects the authors' views. All rights are reserved because of other commitments.