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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 higher-order orthogonal iteration (HOOI) and the alternating subspace iteration (ASI) are two popular numerical methods for computing the Tucker decomposition of a multiple-mode tensor. Xu [Linear and Multilinear Algebra,…

Numerical Analysis · Mathematics 2026-05-19 Ren-Cang Li , Li Wang , Mei Yang

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

Tensor decomposition is a powerful tool for extracting physically meaningful latent factors from multi-dimensional nonnegative data, and has been an increasing interest in a variety of fields such as image processing, machine learning, and…

Machine Learning · Computer Science 2024-12-03 Xiongjun Zhang , Michael K. Ng

High-dimensional tensors or multi-way data are becoming prevalent in areas such as biomedical imaging, chemometrics, networking and bibliometrics. Traditional approaches to finding lower dimensional representations of tensor data include…

Machine Learning · Statistics 2012-02-14 Genevera I. Allen

This paper introduces matrix product state (MPS) decomposition as a computational tool for extracting features of multidimensional data represented by higher-order tensors. Regardless of tensor order, MPS extracts its relevant features to…

Computer Vision and Pattern Recognition · Computer Science 2016-01-22 Johann A. Bengua , Ho N. Phien , Hoang D. Tuan , Minh N. Do

We address the computational barrier of deploying advanced deep learning segmentation models in clinical settings by studying the efficacy of network compression through tensor decomposition. We propose a post-training Tucker factorization…

Image and Video Processing · Electrical Eng. & Systems 2024-04-19 Tobias Weber , Jakob Dexl , David Rügamer , Michael Ingrisch

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…

Numerical Analysis · Mathematics 2014-11-04 Holger Rauhut , Reinhold Schneider , Zeljka Stojanac

Tucker decomposition is a popular technique for many data analysis and machine learning applications. Finding a Tucker decomposition is a nonconvex optimization problem. As the scale of the problems increases, local search algorithms such…

Machine Learning · Computer Science 2020-07-01 Abraham Frandsen , Rong Ge

Tensor decomposition methodologies are proposed to reduce the memory requirement of translation operator tensors arising in the fast multipole method-fast Fourier transform (FMM-FFT)-accelerated surface integral equation (SIE) simulators.…

Signal Processing · Electrical Eng. & Systems 2020-11-25 Cheng Qian , Abdulkadir C. Yucel

By representing documents as mixtures of topics, topic modeling has allowed the successful analysis of datasets across a wide spectrum of applications ranging from ecology to genetics. An important body of recent work has demonstrated the…

Statistics Theory · Mathematics 2025-01-03 Yating Liu , Claire Donnat

As tensors become widespread in modern data analysis, Tucker low-rank Principal Component Analysis (PCA) has become essential for dimensionality reduction and structural discovery in tensor datasets. Motivated by the common scenario where…

Methodology · Statistics 2025-04-08 Elynn Chen , Xi Chen , Wenbo Jing , Yichen Zhang

This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its…

Data Structures and Algorithms · Computer Science 2024-06-19 Mehrdad Ghadiri , Matthew Fahrbach , Gang Fu , Vahab Mirrokni

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

In this work, we develop an optimization framework for problems whose solutions are well-approximated by Hierarchical Tucker (HT) tensors, an efficient structured tensor format based on recursive subspace factorizations. By exploiting the…

Numerical Analysis · Mathematics 2014-05-12 Curt Da Silva , Felix J. Herrmann

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…

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

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

Low-rank tensor recovery problems have been widely studied in many applications of signal processing and machine learning. Tucker decomposition is known as one of the most popular decompositions in the tensor framework. In recent years,…

Numerical Analysis · Mathematics 2020-07-17 Rachel Grotheer , Shuang Li , Anna Ma , Deanna Needell , Jing Qin

Deep neural networks (DNNs) have enabled impressive breakthroughs in various artificial intelligence (AI) applications recently due to its capability of learning high-level features from big data. However, the current demand of DNNs for…

Computer Vision and Pattern Recognition · Computer Science 2020-09-22 Bijiao Wu , Dingheng Wang , Guangshe Zhao , Lei Deng , Guoqi Li