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Decomposition of Big Tensors With Low Multilinear Rank
Guoxu Zhou, Andrzej Cichocki, Shengli Xie
Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex intern…
Very Large-Scale Singular Value Decomposition Using Tensor Train Networks
Namgil Lee, Andrzej Cichocki
We propose new algorithms for singular value decomposition (SVD) of very large-scale matrices based on a low-rank tensor approximation technique called the tensor train (TT) format…
Tensor Networks for Big Data Analytics and Large-Scale Optimization Problems
Andrzej Cichocki
In this paper we review basic and emerging models and associated algorithms for large-scale tensor networks, especially Tensor Train (TT) decompositions using novel mathematical an…
Fundamental Tensor Operations for Large-Scale Data Analysis in Tensor Train Formats
Namgil Lee, Andrzej Cichocki
We discuss extended definitions of linear and multilinear operations such as Kronecker, Hadamard, and contracted products, and establish links between them for tensor calculus. The…
Tensor Decompositions for Signal Processing Applications From Two-way to Multiway Component Analysis
A. Cichocki, D. Mandic, A-H. Phan +4
The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move toward…
Non-Orthogonal Tensor Diagonalization
Petr Tichavsky, Anh Huy Phan, Andrzej Cichocki
Tensor diagonalization means transforming a given tensor to an exactly or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices along selected d…