Canonical Polyadic Decomposition of Incomplete Tensors: an Algebraic Study

We discuss a new approach to find the CPD of a tensor that is not fully available. While standard techniques for tensor completion rely on random sampling of entries or on sampling full columns, rows as well as fibers (e.g. cross approximation), we follow a way in between --- we sample fibers in one mode and one mode only. We explain that under mild conditions this type of sampling allows us to reduce the computation of the CPD to rank-1 matrix completion. The reduction relies on linear algebra only. We also present generalizations, for fiber-sampled incomplete tensors, of algebraic conditions for CPD uniqueness.

This is joint work with Mikael Sorensen (University of Virginia, VA).