Improved Uniqueness Conditions for Canonical Tensor Decompositions with Linearly Dependent Loadings
| Autor: | Tam T. T. Lam, Alwin Stegeman |
|---|---|
| Přispěvatelé: | Heymans Institute for Psychological Research |
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
Low-rank approximation
CANDECOMP/PARAFAC MODEL tensor decomposition DS-CDMA SIGNALS SYSTEMS Tensor (intrinsic definition) Tensor decomposition Applied mathematics Uniqueness ORDER TENSOR BLOCK TERMS X-2 ARRAYS Mathematics INDEPENDENT COMPONENT ANALYSIS Mathematical analysis CONFAC Outer product uniqueness 3-WAY ARRAYS Independent component analysis Constraint (information theory) PARALIND LOW-RANK APPROXIMATION DIVERGING COMPONENTS parafac Linear independence candecomp Analysis |
| Zdroj: | SIAM Journal on Matrix Analysis and Applications, 33(4), 1250-1271 |
| ISSN: | 0895-4798 1250-1271 |
| DOI: | 10.1137/110847275 |
| Popis: | In this paper, we derive improved uniqueness conditions for a constrained version of the canonical order-3 tensor decomposition, also known as Candecomp/Parafac (CP). CP decomposes a three-way array into a prespecified number of outer product arrays. The constraint is that some vectors forming the outer product arrays are linearly dependent according to a prespecified pattern. This is known as the PARALIND family of decompositions. We provide both uniqueness conditions and partial uniqueness conditions for PARALIND, and show that these are improved and more precise variants of existing conditions. Our results are illustrated by means of examples. |
| Databáze: | OpenAIRE |
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