Computing the unique CANDECOMP/PARAFAC decomposition of unbalanced tensors by homotopy method
Provides theoretical and algorithmic advances for CP decomposition of unbalanced tensors, which are common in practice but less studied.
The paper derives a new upper bound on tensor rank guaranteeing generic uniqueness of CP decomposition for unbalanced tensors, and develops a homotopy continuation algorithm to compute it. The bound depends only on tensor dimensions.
The Candecomp/Parafac (CP) decomposition of the tensor whose maximal dimension is greater than its rank is considered. We derive the upper bound of rank under which the generic uniqueness of CP decomposition is guaranteed. The bound only depends on the dimension of the tensor and the proof is constructive. Under these conditions, an algorithm applying homotopy continuation method is developed for computing the CP decomposition of tensors.