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Reducing Computational Complexity of Tensor Contractions via Tensor-Train Networks
Ilya Kisil, Giuseppe G. Calvi, Kriton Konstantinidis +2
There is a significant expansion in both volume and range of applications along with the concomitant increase in the variety of data sources. These ever-expanding trends have highl…
Tensor Networks for Latent Variable Analysis: Higher Order Canonical Polyadic Decomposition
Anh-Huy Phan, Andrzej Cichocki, Ivan Oseledets +3
The Canonical Polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher-order tensors, it often exhibits high computational cost…
Rank Minimization on Tensor Ring: A New Paradigm in Scalable Tensor Decomposition and Completion
Longhao Yuan, Chao Li, Danilo Mandic +2
In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods,…
Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
A. Cichocki, A-H. Phan, Q. Zhao +4
Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-ord…
Simultaneous diagonalisation of the covariance and complementary covariance matrices in quaternion widely linear signal processing
Min Xiang, Shirin Enshaeifar, Alexander E. Stott +4
Recent developments in quaternion-valued widely linear processing have established that the exploitation of complete second-order statistics requires consideration of both the stan…
Tensor Networks for Latent Variable Analysis. Part I: Algorithms for Tensor Train Decomposition
Anh-Huy Phan, Andrzej Cichocki, Andre Uschmajew +3
Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general ten…
Low-Rank Tensor Networks for Dimensionality Reduction and Large-Scale Optimization Problems: Perspectives and Challenges PART 1
A. Cichocki, N. Lee, I. V. Oseledets +3
Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently…
Quaternion Gradient and Hessian
Dongpo Xu, Danilo P. Mandic
The optimization of real scalar functions of quaternion variables, such as the mean square error or array output power, underpins many practical applications. Solutions often requi…
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…