  A novel tensor decomposition framework, termed Tensor Star (TS)
decomposition, is proposed which represents a new type of tensor network
decomposition based on tensor contractions. This is achieved by connecting the
core tensors in a ring shape, whereby the core tensors act as skip connections
between the factor tensors and allow for direct correlation characterisation
between any two arbitrary dimensions. Uniquely, this makes it possible to
decompose an order-$N$ tensor into $N$ order-$3$ factor tensors
$\{\mathcal{G}_{k}\}_{k=1}^{N}$ and $N$ order-$4$ core tensors
$\{\mathcal{C}_{k}\}_{k=1}^{N}$, which are arranged in a star shape. Unlike the
class of Tensor Train (TT) decompositions, these factor tensors are not
directly connected to one another. The so obtained core tensors also enable
consecutive factor tensors to have different latent ranks. In this way, the TS
decomposition alleviates the "curse of dimensionality" and controls the "curse
of ranks", exhibiting a storage complexity which scales linearly with the
number of dimensions and as the fourth power of the ranks.
