scholarly journals High-order tensor estimation via trains of coupled third-order CP and Tucker decompositions

2020 ◽  
Vol 588 ◽  
pp. 304-337 ◽  
Author(s):  
Yassine Zniyed ◽  
Rémy Boyer ◽  
André L.F. de Almeida ◽  
Gérard Favier
Keyword(s):  
High Order ◽  
Third Order ◽  
Order Tensor

A Novel Regularized Model for Third-Order Tensor Completion

2021 ◽  
pp. 1-1
Author(s):  
Yi Yang ◽  
Lixin Han ◽  
Yuanzhen Liu ◽  
Jun Zhu ◽  
Hong Yan
Keyword(s):  
Tensor Completion ◽  
Third Order ◽  
Order Tensor ◽  
Regularized Model

scholarly journals Bipartite Consensus of High-Order Edge Dynamics on Coopetition Multiagent Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Yilong Yang ◽  
Zhijian Ji ◽  
Lei Tian ◽  
Huizi Ma ◽  
Qingyuan Qi
Keyword(s):  
Multiagent Systems ◽  
Line Graph ◽  
Sufficient Conditions ◽  
High Order ◽  
Third Order ◽  
Positive Weight ◽  
The Third ◽  
Initial Graph ◽  
Strongly Connected ◽  
Bipartite Consensus

The bipartite consensus of high-order edge dynamics is investigated for coopetition multiagent systems, in which the cooperative and competitive relationships among agents are characterized by positive weight and negative weight, respectively. By mapping the initial graph to a line graph, the distributed control protocol is proposed for the strongly connected, digon sign-symmetric structurally balanced line graph; and then we give sufficient conditions for the third-order multi-gent system to achieve both the bipartite consensus of edge dynamics and the final value of bipartite consensus. By transforming the coefficients of characteristic polynomial from complex domain to real number domain, the sufficient conditions for the bipartite consensus of high-order edge dynamics are also proposed, and the final values of the high-order edge dynamics on multiagent systems are obtained.

scholarly journals Robust Low-Tubal-Rank Tensor Completion via Convex Optimization

2019 ◽  
Author(s):  
Qiang Jiang ◽  
Michael Ng
Keyword(s):  
Degrees Of Freedom ◽  
L1 Norm ◽  
Third Order ◽  
Order Tensor ◽  
Rank Tensor ◽  
Real World Applications ◽  
Algebraic Framework ◽  
Tensor Nuclear Norm ◽  
Theoretical Results ◽  
Weighted Combination

This paper considers the problem of recovering multidimensional array, in particular third-order tensor, from a random subset of its arbitrarily corrupted entries. Our study is based on a recently proposed algebraic framework in which the tensor-SVD is introduced to capture the low-tubal-rank structure in tensor. We analyze the performance of a convex program, which minimizes a weighted combination of the tensor nuclear norm, a convex surrogate for the tensor tubal rank, and the tensor l1 norm. We prove that under certain incoherence conditions, this program can recover the tensor exactly with overwhelming probability, provided that its tubal rank is not too large and that the corruptions are reasonably sparse. The number of required observations is order optimal (up to a logarithm factor) when comparing with the degrees of freedom of the low-tubal-rank tensor. Numerical experiments verify our theoretical results and real-world applications demonstrate the effectiveness of our algorithm.

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