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On identifiability of 3-tensors of multilinear rank (1; Lr; Lr)

1. Department of Computer Science Southern Illinois University-Carbondale Carbondale, IL 62901, USA;
2. Department of Computer Science Southern Illinois University-Carbondale Carbondale, IL 62901, USA;
3. Department of Mathematics Lamar University Beaumont, TX 77710, USA;
4. Department of Mathematics Southern Illinois University-Carbondale Carbondale, IL 62901, USA

In this paper, we study a specific big data model via multilinear rank tensor decompositions. The model approximates to a given tensor by the sum of multilinear rank (1; Lr; Lr) terms. And we characterize the identifiability property of this model from a geometric point of view. Our main results consists of exact identifiability and generic identifiability. The arguments of generic identifiability relies on the exact identifiability, which is in particular closely related to the well-known "trisecant lemma" in the context of algebraic geometry (see Proposition 2.6 in[1]). This connection discussed in this paper demonstrates a clear geometric picture of this model.
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Keywords Multilinear algebra; tensor rank; generically unique; multilinear rank; big data; algebraic geometry

Citation: Ming Yang, Dunren Che, Wen Liu, Zhao Kang, Chong Peng, Mingqing Xiao, Qiang Cheng. On identifiability of 3-tensors of multilinear rank (1; Lr; Lr). Big Data and Information Analytics, 2016, 1(4): 391-401. doi: 10.3934/bdia.2016017

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Copyright Info: 2016, Mingqing Xiao, Qiang Cheng, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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