  In this paper, we exhibit the tradeoffs between the (training) sample,
computation and storage complexity for the problem of supervised classification
using signal subspace estimation. Our main tool is the use of tensor subspaces,
i.e. subspaces with a Kronecker structure, for embedding the data into lower
dimensions. Among the subspaces with a Kronecker structure, we show that using
subspaces with a hierarchical structure for representing data leads to improved
tradeoffs. One of the main reasons for the improvement is that embedding data
into these hierarchical Kronecker structured subspaces prevents overfitting at
higher latent dimensions.
