Given a classification problem, our goal is to find a low-dimensional linear transformation of the feature vectors which retains information needed to predict the class labels. We present a method based on maximum conditional likelihood estimation of mixture models. Use of mixture models allows us to approximate the distributions to any desired accuracy while use of conditional likelihood as the contrast function ensures that the selected subspace retains maximum possible mutual information between feature vectors and class labels. Classification experiments using Gaussian mixture components show that this method compares favorably to related dimension reduction techniques. Other distributions belonging to the exponential family can be used to reduce dimensions when data is of a special type, for example binary or integer valued data. We provide an EM-like algorithm for model estimation and present visualization experiments using both the Gaussian and the Bernoulli mixture models.
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