Canonical Polyadic Decomposition of a Tensor That Has Missing Fibers: A Monomial Factorization Approach

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 p...

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Bibliographic Details
Published inProceedings of the ... IEEE International Conference on Acoustics, Speech and Signal Processing (1998) pp. 7490 - 7494
Main Authors Sorensen, Mikael, Sidiropoulos, Nicholas D., De Lathauwer, Lieven
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.05.2019
Subjects
Bipartite graph
canonical polyadic decomposition
Europe
missing data
monomial
Null space
Signal processing
Signal processing algorithms
Stacking
subsampling
Tensor
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ISSN2379-190X
DOI10.1109/ICASSP.2019.8682416

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Summary: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.
ISSN:2379-190X
DOI:10.1109/ICASSP.2019.8682416