English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Tensors decompositions are a class of tools for analysing datasets of highdimensionality and variety in a natural manner, with the Canonical PolyadicDecomposition (CPD) being a main pillar. While the notion of CPD is closelyintertwined with that of the tensor rank, $R$, unlike the matrix rank, thecomputation of the tensor rank is an NP-hard problem, owing to the associatedcomputational burden of evaluating the CPD. To address this issue, weinvestigate tight lower bounds on $R$ with the aim to provide a reduced searchspace, and hence to lessen the computational costs of the CPD evaluation. Thisis achieved by establishing a link between the maximum attainable lower boundon $R$ and the dimensions of the matrix unfolding of the tensor with aspectratio closest to unity (maximally square). Moreover, we demonstrate that, for ageneric tensor, such lower bound can be attained under very mild conditions,whereby the tensor rank becomes detectable. Numerical examples demonstrate thebenefits of this result.

Tight Lower Bound on the Tensor Rank based on the Maximally Square Unfolding