In machine learning problems with tens of thousands of features and only dozens or hun- dreds of independent training examples, di- mensionality reduction is essential for good learning performance. In previous work, many researchers have treated the learning problem in two separate phases: first use an algorithm such as singular value decomposi- tion to reduce the dimensionality of the data set, and then use a classification algorithm such as naıve Bayes or support vector ma- chines to learn a classifier. We demonstrate that it is possible to combine the two goals of dimensionality reduction and classification into a single learning objective, and present a novel and efficient algorithm which optimizes this objective directly. We present experi- mental results in fMRI analysis which show that we can achieve better learning perfor- mance and lower-dimensional representations than two-phase approaches can.
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