Tensor subspace tracking via Kronecker structured projections (TeTraKron)

We present a framework for Tensor-based subspace Tracking via Kronecker-structured projections (TeTraKron). TeTraKron allows to extend arbitrary matrix-based subspace tracking schemes to track the tensor-based subspace estimate. The latter can be computed via a structured projection applied to the matrix-based subspace estimate which enforces the multi-dimensional structure in a computationally efficient fashion. This projection is tracked by considering all matrix rearrangements of the signal tensor jointly, which can be efficiently realized via parallel processing. In time-varying scenarios, the TeTraKron-based tracking schemes outperform the original algorithms as well as the batch solutions provided by the SVD and the HOSVD.