Coupled matrix-tensor factorizations — The case of partially shared factors

Abstract

Coupled matrix-tensor factorizations have proved to be a powerful tool for data fusion problems in a variety of applications. Uniqueness conditions for such coupled decompositions have only recently been reported, demonstrating that coupling through a common factor can ensure uniqueness beyond what is possible when considering separate decompositions. In view of the increasing interest in application scenarios involving more general notions of coupling, we revisit in this paper the uniqueness question for the important case where the factors common to the tensor and the matrix only share some of their columns. Related computational aspects and numerical examples are also discussed.