Tensor decomposition

Summary

A tensor decomposition writes a multi-way array as a combination of simpler pieces. It plays the role that a matrix factorization plays for matrices. The canonical polyadic (CP) decomposition writes the tensor as a sum of simple tensors. The Tucker decomposition combines a small core tensor with one factor matrix per mode. The shortest CP decomposition has length equal to the tensor rank. Tensor decompositions are used to compress data and to find hidden structure in signal processing, statistics and chemistry.