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
diversity order
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
classification capacity
, 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
Kronecker-structured learning of discriminative dictionaries
(K-SLD
$^2$
). 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
$^2$
on synthetic and real-world datasets showing that the K-SLD
$^2$
balances compact signal representation and good classification performance.