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Most state of the art deep neural networks are overparameterized and exhibit a high computational cost. A straightforward approach to this problem is to replace convolutional kernels with its low-rank tensor approximations, whereas the…

Computer Vision and Pattern Recognition · Computer Science 2020-08-13 Anh-Huy Phan , Konstantin Sobolev , Konstantin Sozykin , Dmitry Ermilov , Julia Gusak , Petr Tichavsky , Valeriy Glukhov , Ivan Oseledets , Andrzej Cichocki

We propose and evaluate new techniques for compressing and speeding up dense matrix multiplications as found in the fully connected and recurrent layers of neural networks for embedded large vocabulary continuous speech recognition (LVCSR).…

Machine Learning · Computer Science 2018-02-07 Markus Kliegl , Siddharth Goyal , Kexin Zhao , Kavya Srinet , Mohammad Shoeybi

Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…

Machine Learning · Statistics 2017-08-03 Masaaki Imaizumi , Takanori Maehara , Kohei Hayashi

Modern decision-making scenarios often involve data that is both high-dimensional and rich in higher-order contextual information, where existing bandits algorithms fail to generate effective policies. In response, we propose in this paper…

Machine Learning · Computer Science 2025-01-24 Jiannan Li , Yiyang Yang , Yao Wang , Shaojie Tang

In this paper, we study the problem of low-rank tensor learning, where only a few of training samples are observed and the underlying tensor has a low-rank structure. The existing methods are based on the sum of nuclear norms of unfolding…

Machine Learning · Computer Science 2024-10-25 Sijia Xia , Michael K. Ng , Xiongjun Zhang

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

With the availability of extraordinarily huge data sets, solving the problems of distributed statistical methodology and computing for such data sets has become increasingly crucial in the big data area. In this paper, we focus on the…

Machine Learning · Statistics 2023-10-24 Yue Chao , Lei Huang , Xuejun Ma

Tensor clustering has become an important topic, specifically in spatio-temporal modeling, due to its ability to cluster spatial modes (e.g., stations or road segments) and temporal modes (e.g., time of the day or day of the week). Our…

Methodology · Statistics 2024-04-09 Jiuyun Hu , Ziyue Li , Chen Zhang , Fugee Tsung , Hao Yan

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

In this paper we consider from two different aspects the proximal alternating direction method of multipliers (ADMM) in Hilbert spaces. We first consider the application of the proximal ADMM to solve well-posed linearly constrained…

Optimization and Control · Mathematics 2023-10-11 Qinian Jin

Aiming at solving large-scale learning problems, this paper studies distributed optimization methods based on the alternating direction method of multipliers (ADMM). By formulating the learning problem as a consensus problem, the ADMM can…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-05-04 Tsung-Hui Chang , Mingyi Hong , Wei-Cheng Liao , Xiangfeng Wang

Linearized alternating direction method of multipliers (ADMM) as an extension of ADMM has been widely used to solve linearly constrained problems in signal processing, machine leaning, communications, and many other fields. Despite its…

Optimization and Control · Mathematics 2017-11-02 Qinghua Liu , Xinyue Shen , Yuantao Gu

We propose a set of convex low rank inducing norms for a coupled matrices and tensors (hereafter coupled tensors), which shares information between matrices and tensors through common modes. More specifically, we propose a mixture of the…

Machine Learning · Statistics 2018-06-15 Kishan Wimalawarne , Makoto Yamada , Hiroshi Mamitsuka

Sparse tensors are prevalent in real-world applications, often characterized by their large-scale, high-order, and high-dimensional nature. Directly handling raw tensors is impractical due to the significant memory and computational…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-05-24 Zixuan Li , Mingxing Duan , Huizhang Luo , Wangdong Yang , Kenli Li , Keqin Li

Modern technological advances have enabled an unprecedented amount of structured data with complex temporal dependence, urging the need for new methods to efficiently model and forecast high-dimensional tensor-valued time series. This paper…

Methodology · Statistics 2023-09-28 Di Wang , Yao Zheng , Guodong Li

In this paper we develop two new Tensor Alternating Steepest Descent algorithms for tensor completion in the low-rank $\star_{M}$-product format, whereby we aim to reconstruct an entire low-rank tensor from a small number of measurements…

Numerical Analysis · Mathematics 2025-06-13 Oliver Townsend , Sergey Dolgov , Silvia Gazzola , Misha Kilmer

Tensor completion can estimate missing values of a high-order data from its partially observed entries. Recent works show that low rank tensor ring approximation is one of the most powerful tools to solve tensor completion problem. However,…

Numerical Analysis · Mathematics 2021-01-03 Abdul Ahad , Zhen Long , Ce Zhu , Yipeng Liu

We propose a new numerical algorithm for computing the tensor rank decomposition or canonical polyadic decomposition of higher-order tensors subject to a rank and genericity constraint. Reformulating this computational problem as a system…

Numerical Analysis · Mathematics 2024-07-02 Simon Telen , Nick Vannieuwenhoven

We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…

Numerical Analysis · Mathematics 2019-05-24 Omri Azencot , Wotao Yin , Andrea Bertozzi

Tensor factorization with hard and/or soft constraints has played an important role in signal processing and data analysis. However, existing algorithms for constrained tensor factorization have two drawbacks: (i) they require…

Numerical Analysis · Mathematics 2024-07-01 Shunsuke Ono , Takuma Kasai