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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

The CP tensor decomposition is a low-rank approximation of a tensor. We present a distributed-memory parallel algorithm and implementation of an alternating optimization method for computing a CP decomposition of dense tensor data that can…

Numerical Analysis · Computer Science 2018-06-22 Grey Ballard , Koby Hayashi , Ramakrishnan Kannan

Low-rank matrix completion (LRMC) has demonstrated remarkable success in a wide range of applications. To address the NP-hard nature of the rank minimization problem, the nuclear norm is commonly used as a convex and computationally…

Computer Vision and Pattern Recognition · Computer Science 2025-12-25 Zhijie Wang , Liangtian He , Qinghua Zhang , Jifei Miao , Liang-Jian Deng , Jun Liu

The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization…

Optimization and Control · Mathematics 2013-06-04 B. Mishra , G. Meyer , F. Bach , R. Sepulchre

We propose a symmetric graph convolutional autoencoder which produces a low-dimensional latent representation from a graph. In contrast to the existing graph autoencoders with asymmetric decoder parts, the proposed autoencoder has a newly…

Machine Learning · Computer Science 2019-08-08 Jiwoong Park , Minsik Lee , Hyung Jin Chang , Kyuewang Lee , Jin Young Choi

Existing methods of vector autoregressive model for multivariate time series analysis make use of low-rank matrix approximation or Tucker decomposition to reduce the dimension of the over-parameterization issue. In this paper, we propose a…

Statistics Theory · Mathematics 2026-01-05 Sijia Xia , Michael K. Ng , Xiongjun Zhang

This paper introduces an algorithm for the nonnegative matrix factorization-and-completion problem, which aims to find nonnegative low-rank matrices X and Y so that the product XY approximates a nonnegative data matrix M whose elements are…

Information Theory · Computer Science 2015-11-23 Yangyang Xu , Wotao Yin , Zaiwen Wen , Yin Zhang

Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…

Numerical Analysis · Mathematics 2025-12-22 Kingsley Yeon , Mihai Anitescu

The robust tensor completion (RTC) problem, which aims to reconstruct a low-rank tensor from partially observed tensor contaminated by a sparse tensor, has received increasing attention. In this paper, by leveraging the superior expression…

Computer Vision and Pattern Recognition · Computer Science 2021-10-19 Yun-Yang Liu , Xi-Le Zhao , Guang-Jing Song , Yu-Bang Zheng , Ting-Zhu Huang

In this paper, we discuss the acceleration of the regularized alternating least square (RALS) algorithm for tensor approximation. We propose a fast iterative method using a Aitken-Stefensen like updates for the regularized algorithm.…

Numerical Analysis · Mathematics 2017-07-25 Xiaofei Wang , Carmeliza Navasca , Stefan Kindermann

Tensor factorization has become an increasingly popular approach to knowledge graph completion(KGC), which is the task of automatically predicting missing facts in a knowledge graph. However, even with a simple model like…

Machine Learning · Computer Science 2019-02-11 Koki Kishimoto , Katsuhiko Hayashi , Genki Akai , Masashi Shimbo , Kazunori Komatani

This paper introduces a randomized variation of the alternating least squares (ALS) algorithm for rank reduction of canonical tensor formats. The aim is to address the potential numerical ill-conditioning of least squares matrices at each…

Numerical Analysis · Mathematics 2015-10-07 Matthew Reynolds , Alireza Doostan , Gregory Beylkin

In the low-rank matrix completion (LRMC) problem, the low-rank assumption means that the columns (or rows) of the matrix to be completed are points on a low-dimensional linear algebraic variety. This paper extends this thinking to cases…

Machine Learning · Statistics 2020-09-08 Greg Ongie , Daniel Pimentel-Alarcón , Laura Balzano , Rebecca Willett , Robert D. Nowak

The linear complementarity problem is a continuous optimization problem that generalizes convex quadratic programming, Nash equilibria of bimatrix games and several such problems. This paper presents a continuous optimization formulation…

Discrete Mathematics · Computer Science 2018-10-19 Parthe Pandit , Ankur A. Kulkarni

The canonical polyadic (CP) decomposition is one of the most widely used tensor decomposition techniques. The conventional CP decomposition algorithm combines alternating least squares (ALS) with the normal equation. However, the normal…

Numerical Analysis · Mathematics 2025-10-28 Wenchao Xie , Jiawei Xu , Zheng Peng , Qingsong Wang

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

Tensor decomposition is a fundamental technique widely applied in signal processing, machine learning, and various other fields. However, traditional tensor decomposition methods encounter limitations when jointly analyzing multi-block…

Machine Learning · Computer Science 2024-06-27 Xiulin Wang , Jing Liu , Fengyu Cong

We present a parallel version of the cut-pursuit algorithm for minimizing functionals involving the graph total variation. We show that the decomposition of the iterate into constant connected components, which is at the center of this…

Data Structures and Algorithms · Computer Science 2019-05-08 Hugo Raguet , Loic Landrieu

Higher-order low-rank tensor arises in many data processing applications and has attracted great interests. Inspired by low-rank approximation theory, researchers have proposed a series of effective tensor completion methods. However, most…

Computer Vision and Pattern Recognition · Computer Science 2020-06-23 Haijin Zeng , Xiaozhen Xie , Jifeng Ning

Tensor ring (TR) decomposition has been widely applied as an effective approach in a variety of applications to discover the hidden low-rank patterns in multidimensional data. A well-known method for TR decomposition is the alternating…

Numerical Analysis · Mathematics 2022-10-21 Yajie Yu , Hanyu Li