Information-theoretic criteria for the design of compressive subspace classifiers

Using Shannon theory, we derive fundamental, asymptotic limits on the classification of low-dimensional subspaces from compressive measurements. We identify a syntactic equivalence between the classification of subspaces and the communication of codewords over non-coherent, multiple-antenna channels, from which we derive sharp bounds on the number of classes that can be discriminated with low misclassification probability as a function of the signal dimensionality and the signal-to-noise ratio. While the bounds are asymptotic in the limit of high dimension, they provide intuition for classifier design at finite dimension. We validate this intuition via an application to face recognition.