# American Institute of Mathematical Sciences

October  2016, 1(4): 391-401. doi: 10.3934/bdia.2016017

## On identifiability of 3-tensors of multilinear rank $(1,\ L_{r},\ L_{r})$

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

* Corresponding author: Qiang Cheng, Mingqing Xiao. This research is supported in part by NSF-DMS 1419028 and NSF-IIS 1218712 of United States

Revised  May 2017 Published  May 2017

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 $(1, \ L_{r}, \ L_{r})$ 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.

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