Classification and Representation via Separable Subspaces: Performance Limits and Algorithms

We study the classification performance of Kronecker-structured (K-S) subpsace models in two asymptotic regimes and develop an algorithm for fast and compact K-S subspace learning for better classification and representation of multidimensional signals by exploiting the structure in the signal. First, we study the classification performance in terms of <italic>diversity order</italic> and pairwise geometry of the subspaces. We derive an exact expression for the diversity order as a function of the signal and subspace dimensions of a K-S model. Next, we study the <italic> classification capacity</italic>, the maximum rate at which the number of classes can grow as the signal dimension goes to infinity. Then, we describe a fast algorithm for <italic>Kronecker-structured learning of discriminative dictionaries</italic> (K-SLD<inline-formula><tex-math notation="LaTeX">$^2$</tex-math></inline-formula>). Finally, we evaluate the empirical classification performance of K-S models for the synthetic data, showing that they agree with the diversity order analysis. We also evaluate the performance of K-SLD<inline-formula><tex-math notation="LaTeX">$^2$ </tex-math></inline-formula> on synthetic and real-world datasets showing that the K-SLD<inline-formula> <tex-math notation="LaTeX">$^2$</tex-math></inline-formula> balances compact signal representation and good classification performance.