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Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA),…

Numerical Analysis · Computer Science 2013-05-03 Andrzej Cichocki

This paper proposes a channel estimation method for Multiple-Input Multiple-Output (MIMO) systems based on Canonical Polyadic (CP) decomposition applied to a mode-factorized tensor representation of the channel. The proposed approach…

Information Theory · Computer Science 2026-05-20 Alexander Blagodarnyi , Alexander Sherstobitov , Vladimir Lyashev

Large CNNs have delivered impressive performance in various computer vision applications. But the storage and computation requirements make it problematic for deploying these models on mobile devices. Recently, tensor decompositions have…

Machine Learning · Computer Science 2016-02-16 Cheng Tai , Tong Xiao , Yi Zhang , Xiaogang Wang , Weinan E

We introduce and analyze the new range-separated (RS) canonical/Tucker tensor format which aims for numerical modeling of the 3D long-range interaction potentials in multi-particle systems. The main idea of the RS tensor format is the…

Numerical Analysis · Mathematics 2016-10-11 Peter Benner , Venera Khoromskaia , Boris N. Khoromskij

Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…

Numerical Analysis · Mathematics 2020-02-11 Oscar Mickelin , Sertac Karaman

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 internal structures and correlations of data. Unfortunately most…

Numerical Analysis · Computer Science 2014-12-30 Guoxu Zhou , Andrzej Cichocki , Shengli Xie

The canonical polyadic decomposition (CPD) is a fundamental tensor decomposition which expresses a tensor as a sum of rank one tensors. In stark contrast to the matrix case, with light assumptions, the CPD of a low rank tensor is…

Numerical Analysis · Mathematics 2022-02-24 Eric Evert , Michiel Vandecappelle , Lieven De Lathauwer

We discuss how recently discovered techniques and tools from compressed sensing can be used in tensor decompositions, with a view towards modeling signals from multiple arrays of multiple sensors. We show that with appropriate bounds on a…

Numerical Analysis · Mathematics 2015-05-18 Lek-Heng Lim , Pierre Comon

This paper explores a new version of the Levenberg-Marquardt algorithm used for Tensor Canonical Polyadic (CP) decomposition with an emphasis on image compression and reconstruction. Tensor computation, especially CP decomposition, holds…

Numerical Analysis · Mathematics 2024-07-26 Ramin Goudarzi Karim , Dipak Dulal , Carmeliza Navasca

Coupled tensor decomposition reveals the joint data structure by incorporating priori knowledge that come from the latent coupled factors. The tensor ring (TR) decomposition is invariant under the permutation of tensors with different mode…

Machine Learning · Computer Science 2020-11-10 Huyan Huang , Yipeng Liu , Ce Zhu

Downsampling images and labels, often necessitated by limited resources or to expedite network training, leads to the loss of small objects and thin boundaries. This undermines the segmentation network's capacity to interpret images…

Image and Video Processing · Electrical Eng. & Systems 2024-10-27 Shahzad Ali , Yu Rim Lee , Soo Young Park , Won Young Tak , Soon Ki Jung

The low-tubal-rank tensor model has been recently proposed for real-world multidimensional data. In this paper, we study the low-tubal-rank tensor completion problem, i.e., to recover a third-order tensor by observing a subset of its…

Machine Learning · Computer Science 2016-10-12 Xiao-Yang Liu , Shuchin Aeron , Vaneet Aggarwal , Xiaodong Wang

Tensors with unit Frobenius norm are fundamental objects in many fields, including scientific computing and quantum physics, which are able to represent normalized eigenvectors and pure quantum states. While the tensor train decomposition…

Numerical Analysis · Mathematics 2025-11-07 Renfeng Peng , Chengkai Zhu , Bin Gao , Xin Wang , Ya-xiang Yuan

One of the main issues in computing a tensor decomposition is how to choose the number of rank-one components, since there is no finite algorithms for determining the rank of a tensor. A commonly used approach for this purpose is to find a…

Computer Vision and Pattern Recognition · Computer Science 2023-09-15 Claudio Turchetti

CP tensor decomposition with alternating least squares (ALS) is dominated in cost by the matricized-tensor times Khatri-Rao product (MTTKRP) kernel that is necessary to set up the quadratic optimization subproblems. State-of-art parallel…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-10-26 Linjian Ma , Edgar Solomonik

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…

Data Structures and Algorithms · Computer Science 2014-01-21 Aditya Bhaskara , Moses Charikar , Ankur Moitra , Aravindan Vijayaraghavan

The alternating least squares algorithm for CP and Tucker decomposition is dominated in cost by the tensor contractions necessary to set up the quadratic optimization subproblems. We introduce a novel family of algorithms that uses…

Numerical Analysis · Mathematics 2021-04-15 Linjian Ma , Edgar Solomonik

In general, algorithms for order-3 CANDECOMP/-PARAFAC (CP), also coined canonical polyadic decomposition (CPD), are easily to implement and can be extended to higher order CPD. Unfortunately, the algorithms become computationally demanding,…

Numerical Analysis · Mathematics 2017-04-26 Anh Huy Phan , Petr Tichavsky , Andrzej Cichocki

The recently established Convolution Nuclear Norm Minimization (CNNM) addresses the problem of \textit{tensor completion with arbitrary sampling} (TCAS), which involves restoring a tensor from a subset of its entries sampled in an arbitrary…

Computer Vision and Pattern Recognition · Computer Science 2026-04-21 Wei Li , Yuyang Li , Kaile Du , Yi Yu , Guangcan Liu

In intelligent transportation systems, traffic data imputation, estimating the missing value from partially observed data is an inevitable and challenging task. Previous studies have not fully considered traffic data's multidimensionality…

Machine Learning · Statistics 2023-11-01 Wenwu Gong , Zhejun Huang , Lili Yang