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Orthogonal Tensor Decompositions
Abstract
We explore the orthogonal decomposition of tensors (also known as multidimensional arrays or n-way arrays) using two different definitions of orthogonality. We present numerous examples to illustrate the difficulties in understanding such decompositions. We conclude with a counterexample to a tensor extension of the Eckart--Young SVD approximation theorem by Leibovici and Sabatier [Linear Algebra Appl., 269 (1998), pp. 307--329].
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Cited by
Multilinear Analysis of Image Ensembles: TensorFaces
Vasilescu, M. A. O., & Terzopoulos, D. (2002) · Lecture Notes in Computer Science · doi:10.1007/3-540-47969-4_30 · Cited by 836
Deshpande, G., Rangaprakash, D., Oeding, L., Cichocki, A., & Hu, X. P. (2017) · Frontiers in Neuroscience · doi:10.3389/fnins.2017.00246 · Cited by 29
Metadata
- Authors
- Kolda, T. G.
- Venue
- SIAM Journal on Matrix Analysis and Applications
- Published
- 2001-01
- Volume
- 23
- Issue
- 1
- Pages
- 243-255
- ISSN
- 0895-4798 (ISSN-L)
- 1095-7162
- OpenAlex
- W1978376511
- Cited by
- 376
- References
- 0
- FWCI
- 2.91
- Type
- journal article
- Language
- en
- Open access
- closed
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