The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Decompositions of a Higher-Order Tensor in Block Terms—Part II: Definitions and Uniqueness
Abstract
In this paper we introduce a new class of tensor decompositions. Intuitively, we decompose a given tensor block into blocks of smaller size, where the size is characterized by a set of mode-n ranks. We study different types of such decompositions. For each type we derive conditions under which essential uniqueness is guaranteed. The parallel factor decomposition and Tucker's decomposition can be considered as special cases in the new framework. The paper sheds new light on fundamental aspects of tensor algebra.
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Cites
The Expression of a Tensor or a Polyadic as a Sum of Products
Hitchcock, F. L. (1927) · Journal of Mathematics and Physics · doi:10.1002/sapm192761164 · Cited by 1,345
Cited by
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
Multimodal intelligence: Representation learning, information fusion, and applications
Zhang, C., Yang, Z., He, X., & Deng, L. (2020) · IEEE Journal of Selected Topics in Signal Processing · doi:10.1109/jstsp.2020.2987728 · Cited by 511
Metadata
- Authors
- De Lathauwer, L.
- Venue
- SIAM Journal on Matrix Analysis and Applications
- Published
- 2008-01
- Volume
- 30
- Issue
- 3
- Pages
- 1033-1066
- ISSN
- 0895-4798 (ISSN-L)
- 1095-7162
- OpenAlex
- W2000045479
- Cited by
- 479
- References
- 1
- FWCI
- 3.79
- Type
- journal article
- Language
- en
- Open access
- closed
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- De Lathauwer, L. (2008). Decompositions of a Higher-Order Tensor in Block Terms—Part II: Definitions and Uniqueness. SIAM Journal on Matrix Analysis and Applications. https://doi.org/10.1137/070690729
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
