We propose a dimensionality reducing matrix design based on training data with constraints on its Frobenius norm and number of rows. Our design criteria is aimed at preserving the distances between the data points in the dimensionality reduced space as much as possible relative to their distances in original data space. This approach can be considered as a deterministic Bi-Lipschitz embedding of the data points. We introduce a scalable learning algorithm, dubbed AMUSE, and provide a rigorous estimation guarantee by leveraging game theoretic tools. We also provide a generalization characterization of our matrix based on our sample data. We use compressive sensing problems as an example application of our problem, where the Frobenius norm design constraint translates into the sensing energy.
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