Canonical Polyadic Tensor Decomposition With Low-Rank Factor Matrices

This paper proposes a constrained canonical polyadic (CP) tensor decomposition method with low-rank factor matrices. In this way, we allow the CP decomposition with high rank while keeping the number of the model parameters small. First, we propose an algorithm to decompose the tensors into factor matrices of given ranks. Second, we propose an algorithm which can determine the ranks of the factor matrices automatically, such that the fitting error is bounded by a user-selected constant. The algorithms are verified on the decomposition of a tensor of the MNIST hand-written image dataset.