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Tensors or multiarray data are generalizations of matrices. Tensor clustering has become a very important research topic due to the intrinsically rich structures in real-world multiarray datasets. Subspace clustering based on vectorizing…

Computer Vision and Pattern Recognition · Computer Science 2015-04-30 Yanfeng Sun , Junbin Gao , Xia Hong , Bamdev Mishra , Baocai Yin

Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due…

Machine Learning · Computer Science 2021-05-21 Chenjian Pan , Chen Ling , Hongjin He , Liqun Qi , Yanwei Xu

This paper derives the CUR-type factorization for tensors in the Tucker format based on a new variant of the discrete empirical interpolation method known as L-DEIM. This novel sampling technique allows us to construct an efficient…

Numerical Analysis · Mathematics 2023-04-12 Zhengbang Cao , Yimin Wei , Pengpeng Xie

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…

Signal Processing · Electrical Eng. & Systems 2023-07-19 Xiao Fu , Nico Vervliet , Lieven De Lathauwer , Kejun Huang , Nicolas Gillis

Big data analysis has become a crucial part of new emerging technologies such as the internet of things, cyber-physical analysis, deep learning, anomaly detection, etc. Among many other techniques, dimensionality reduction plays a key role…

The Tucker decomposition expresses a given tensor as the product of a small core tensor and a set of factor matrices. Apart from providing data compression, the construction is useful in performing analysis such as principal component…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-07-19 Venkatesan T Chakaravarthy , Jee W Choi , Douglas J Joseph , Xing Liu , Prakash Murali , Yogish Sabharwal , Dheeraj Sreedhar

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 ability and flexibility. However, the traditional TR…

Numerical Analysis · Mathematics 2024-12-20 Longhao Yuan , Chao Li , Jianting Cao , Qibin Zhao

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 tensor model which represents data as an ordered network of…

Numerical Analysis · Computer Science 2016-09-30 Anh-Huy Phan , Andrzej Cichocki , Andre Uschmajew , Petr Tichavsky , George Luta , Danilo Mandic

Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…

Numerical Analysis · Computer Science 2017-09-12 A. Cichocki , N. Lee , I. V. Oseledets , A. -H. Phan , Q. Zhao , D. Mandic

We propose a strategy to compress and store large volumes of scientific data represented on unstructured grids. Approaches utilizing tensor decompositions for data compression have already been proposed. Here, data on a structured grid is…

Numerical Analysis · Mathematics 2024-09-23 Prashant Rai , Hemanth Kolla , Lewis Cannada , Alex Gorodetsky

Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging…

Machine Learning · Computer Science 2015-05-12 Qibin Zhao , Liqing Zhang , Andrzej Cichocki

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 towards more versatile data analysis tools. We show that…

Numerical Analysis · Computer Science 2015-06-19 A. Cichocki , D. Mandic , A-H. Phan , C. Caiafa , G. Zhou , Q. Zhao , L. De Lathauwer

The tensor-train (TT) decomposition expresses a tensor in a data-sparse format used in molecular simulations, high-order correlation functions, and optimization. In this paper, we propose four parallelizable algorithms that compute the TT…

Numerical Analysis · Mathematics 2021-11-23 Tianyi Shi , Maximilian Ruth , Alex Townsend

In structure from motion, quadrifocal tensors capture more information than their pairwise counterparts (essential matrices), yet they have often been thought of as impractical and only of theoretical interest. In this work, we challenge…

Computer Vision and Pattern Recognition · Computer Science 2026-04-21 Daniel Miao , Gilad Lerman , Joe Kileel

High-dimensional data in the form of tensors are challenging for kernel classification methods. To both reduce the computational complexity and extract informative features, kernels based on low-rank tensor decompositions have been…

Machine Learning · Statistics 2023-02-17 Kirandeep Kour , Sergey Dolgov , Peter Benner , Martin Stoll , Max Pfeffer

Tensors naturally model many real world processes which generate multi-aspect data. Such processes appear in many different research disciplines, e.g, chemometrics, computer vision, psychometrics and neuroimaging analysis. Tensor…

Data Structures and Algorithms · Computer Science 2009-09-29 Charalampos E. Tsourakakis

We study the problems arising from modeling high-dimensional tensor-valued time series under a Tucker decomposition-based factor model with multiple structural change points. First, we propose an algorithm for detecting the multiple change…

Statistics Theory · Mathematics 2026-04-14 Yuqi Zhang , Zetai Cen , Haeran Cho

In this paper, we propose a novel model to recover a low-rank tensor by simultaneously performing double nuclear norm regularized low-rank matrix factorizations to the all-mode matricizations of the underlying tensor. An block successive…

Computer Vision and Pattern Recognition · Computer Science 2020-05-07 Haijin Zeng , Xiaozhen Xie , Jifeng Ning

The paper introduces a hybrid approach to the CUR-type decomposition of tensors in the Tucker format. The idea of the hybrid algorithm is to write a tensor $\mathcal{X}$ as a product of a core tensor $\mathcal{S}$, a matrix $C$ obtained by…

Numerical Analysis · Mathematics 2024-03-20 Erna Begovic

Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…

Methodology · Statistics 2021-10-29 Jiaxin Hu , Chanwoo Lee , Miaoyan Wang