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Randomized Tensor Ring Decomposition and Its Application to Large-scale Data Reconstruction
Longhao Yuan, Chao Li, Jianting Cao +1
Dimensionality reduction is an essential technique for multi-way large-scale data, i.e., tensor. Tensor ring (TR) decomposition has become popular due to its high representation ab…
Higher-dimension Tensor Completion via Low-rank Tensor Ring Decomposition
Longhao Yuan, Jianting Cao, Qiang Wu +1
The problem of incomplete data is common in signal processing and machine learning. Tensor completion algorithms aim to recover the incomplete data from its partially observed entr…
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,…
High-dimension Tensor Completion via Gradient-based Optimization Under Tensor-train Format
Longhao Yuan, Qibin Zhao, Lihua Gui +1
Tensor train (TT) decomposition has drawn people's attention due to its powerful representation ability and performance stability in high-order tensors. In this paper, we propose a…
High-order Tensor Completion for Data Recovery via Sparse Tensor-train Optimization
Longhao Yuan, Qibin Zhao, Jianting Cao
In this paper, we aim at the problem of tensor data completion. Tensor-train decomposition is adopted because of its powerful representation ability and linear scalability to tenso…
Completion of High Order Tensor Data with Missing Entries via Tensor-train Decomposition
Longhao Yuan, Qibin Zhao, Jianting Cao
In this paper, we aim at the completion problem of high order tensor data with missing entries. The existing tensor factorization and completion methods suffer from the curse of di…
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…
Learning Efficient Tensor Representations with Ring Structure Networks
Qibin Zhao, Masashi Sugiyama, Andrzej Cichocki
Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However,…
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…
Tensor Ring Decomposition
Qibin Zhao, Guoxu Zhou, Shengli Xie +2
Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) de…
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…