Learning Unbalanced and Sparse Low-Order Tensors

Efficient techniques are developed for completing unbalanced and sparse low-order tensors, which cannot be effectively completed by popular matrix-rank optimization based such as compressed sensing and/or the $\ell _{q}$ -matrix-metric. We use our previously 2D-index encoding technique tensor augmentation in order to represent these incomplete tensors high-order but low-dimensional with their modes building up a coarse-grained hierachy of correlations among entries. The concept tensor-trains is then exploited decomposing augmented into trains balanced matrices efficient completion. More explicitly, we develop powerful algorithms exhibiting an excellent performance vs. complexity trade-off, supported numerical examples relying on matrix data third-order derived from color image pixels.