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Many machine learning problems, especially multi-modal learning problems,have two sets of distinct features (e.g., image and text features in news storyclassification, or neuroimaging data and neurocognitive data in cognitivescience research). This paper addresses the joint dimensionality reduction oftwo feature vectors in supervised learning problems. In particular, we assume adiscriminative model where low-dimensional linear embeddings of the two featurevectors are sufficient statistics for predicting a dependent variable. We showthat a simple algorithm involving singular value decomposition can accuratelyestimate the embeddings provided that certain sample complexities aresatisfied, without specifying the nonlinear link function (regressor orclassifier). The main results establish sample complexities under multiplesettings. Sample complexities for different link functions only differ byconstant factors.

Joint Dimensionality Reduction for Two Feature Vectors