The Expression of a Tensor or a Polyadic as a Sum of Products
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Tucker decomposition with a superdiagonal core tensor is equivalent to CP decomposition.
“It is interesting to note that the TuckER interpretation of the DistMult scoring function, given that matrices A and C are identical, can alternatively be interpreted as a special case of CP decomposition (Hitchcock, 1927), since Tucker decomposition with a superdiagonal core tensor is equivalent to CP decomposition.”
From TuckER: Tensor Factorization for Knowledge Graph Completion (2019) · cites this paper as Hitchcock, 1927
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Modeling Relational Data with Graph Convolutional Networks
Schlichtkrull, M., Kipf, T. N., Bloem, P., van den Berg, R., Titov, I., & Welling, M. (2018) · Lecture Notes in Computer Science · doi:10.1007/978-3-319-93417-4_38 · Cited by 5,570 · see citing works
Complex Embeddings for Simple Link Prediction
Trouillon, T., Welbl, J., Riedel, S., Gaussier, É., & Bouchard, G. (2016) · arXiv · doi:10.48550/arxiv.1606.06357 · Cited by 2,100 · see citing works
Multimodal Data Fusion: An Overview of Methods, Challenges, and Prospects
Lahat, D., Adali, T., & Jutten, C. (2015) · Proceedings of the IEEE · doi:10.1109/jproc.2015.2460697 · Cited by 1,296 · see citing works
TuckER: Tensor Factorization for Knowledge Graph Completion
Balazevic, I., Allen, C., & Hospedales, T. (2019) · Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP) · doi:10.18653/v1/d19-1522 · Cited by 696 · see citing works
Knowledge Graph Embedding for Link Prediction
Rossi, A., Barbosa, D., Firmani, D., Matinata, A., & Merialdo, P. (2021) · ACM Transactions on Knowledge Discovery from Data · doi:10.1145/3424672 · Cited by 601 · see citing works
“TuckER [6] relies on the Tucker decomposition [21], which factorizes a tensor into a set of vectors and a smaller shared coreW .”
MethodSimplE Embedding for Link Prediction in Knowledge Graphs
Kazemi, S. M., & Poole, D. (2018) · arXiv · doi:10.48550/arxiv.1802.04868 · Cited by 476 · see citing works
“In canonical Polyadic (CP) decomposition [15], the embedding for each entity e has two vectors he, te ∈ R, and for each relation r has a single vector vr ∈ R.”
BackgroundTensor Network Contractions: Methods and Applications to Quantum Many-Body Systems
Ran, S.-J., Tirrito, E., Peng, C., Chen, X., Tagliacozzo, L., Su, G., & Lewenstein, M. (2020) · Lecture Notes in Physics · doi:10.1007/978-3-030-34489-4 · Cited by 176 · see citing works
- Authors
- Hitchcock, F. L.
- Corresponding author
- Hitchcock, Frank L.
- Venue
- Journal of Mathematics and Physics
- Publisher
- Wiley
- Published
- 1927-04
- Volume
- 6
- Issue
- 1-4
- Pages
- 164-189
- ISSN
- 0022-2526 (ISSN-L)
- 0097-1421
- OpenAlex
- W2258054274
- Cited by
- 1,345
- References
- 0
- Citations by year
- 2026: 68 · 2025: 115 · 2024: 113 · 2023: 97 · 2022: 127 · 2021: 148 · 2020: 138 · 2019: 125 · 2018: 80 · 2017: 44 · 2016: 48 · 2015: 32 · 2014: 52 · 2013: 38 · 2012: 29
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Studies in Applied Mathematics (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Computational Mathematics › Tensor decomposition and applications
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Advanced Combinatorial Mathematics
- Keywords
- tensor decomposition, sums of products, tensor rank, multilinear algebra
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
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