1 research outputs found
Online Rank-Revealing Block-Term Tensor Decomposition
The so-called block-term decomposition (BTD) tensor model, especially in its
rank- version, has been recently receiving increasing attention
due to its enhanced ability of representing systems and signals that are
composed of \emph{block} components of rank higher than one, a scenario
encountered in numerous and diverse applications. Its uniqueness and
approximation have thus been thoroughly studied. The challenging problem of
estimating the BTD model structure, namely the number of block terms (rank) and
their individual (block) ranks, is of crucial importance in practice and has
only recently started to attract significant attention. In data-streaming
scenarios and/or big data applications, where the tensor dimension in one of
its modes grows in time or can only be processed incrementally, it is essential
to be able to perform model selection and computation in a recursive
(incremental/online) manner. To date there is only one such work in the
literature concerning the (general rank-) BTD model, which proposes an
incremental method, however with the BTD rank and block ranks assumed to be
a-priori known and time invariant. In this preprint, a novel approach to
rank- BTD model selection and tracking is proposed, based on the
idea of imposing column sparsity jointly on the factors and estimating the
ranks as the numbers of factor columns of nonnegligible magnitude. An online
method of the alternating iteratively reweighted least squares (IRLS) type is
developed and shown to be computationally efficient and fast converging, also
allowing the model ranks to change in time. Its time and memory efficiency are
evaluated and favorably compared with those of the batch approach. Simulation
results are reported that demonstrate the effectiveness of the proposed scheme
in both selecting and tracking the correct BTD model