Canonical Polyadic Decomposition of a Tensor That Has Missing Fibers: A Monomial Factorization Approach
Mikael Sørensen, Nicholas D. Sidiropoulos, Lieven De Lathauwer
Abstract
The Canonical Polyadic Decomposition (CPD) is one of the most basic tensor models used in signal processing and machine learning. Despite its wide applicability, identifiability conditions and algorithms for CPD in cases where the tensor is incomplete are lagging behind its practical use. We first present a tensor-based framework for bilinear factorizations subject to monomial constraints, called monomial factorizations. Next, we explain that the CPD of a tensor that has missing fibers can be interpreted as a monomial factorization problem. Finally, using the monomial factorization interpretation, we show that CPD recovery conditions can be obtained that only rely on the observed fibers of the tensor.
BibTeX
@inproceedings{icassp2019_canonicalpolyadi,
title = {Canonical Polyadic Decomposition of a Tensor That Has Missing Fibers: A Monomial Factorization Approach},
author = {Mikael Sørensen and Nicholas D. Sidiropoulos and Lieven De Lathauwer},
booktitle = {ICASSP 2019},
year = {2019}
}