Tensor Learning for Signal Processing

As a generalization of array with three or more indices, a higher-order tensor has a series of new notations and operations for computation, such as matricization, tensor inner product, tensor outer product, mode-n product of tensor, tensor product, etc. Based on these tensor operations, the main tensor decompositions, as the higher-order extensions of the matrix singular value decomposition, are presented, such as CANDECOMP/PARAFAC (CP) decomposition, Tucker decomposition, block term decomposition, tensor singular value decomposition (t-SVD), tensor train, tensor tree, tensor ring, etc. we will compare these decompositions, and discuss both their advantages and disadvantages.