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We propose a novel algorithm for the computation of canonical polyadic decomposition (CPD) of large-scale tensors. The proposed algorithm generalizes the random projection (RAP) technique, which is often used to compute large-scale…

Machine Learning · Computer Science 2021-05-11 Lu-Ming Wang , Ya-Nan Wang , Xiao-Feng Gong , Qiu-Hua Lin , Fei Xiang

Canonical Polyadic (CP) tensor decomposition is a fundamental technique for analyzing high-dimensional tensor data. While the Alternating Least Squares (ALS) algorithm is widely used for computing CP decomposition due to its simplicity and…

Methodology · Statistics 2025-05-30 Runshi Tang , Julien Chhor , Olga Klopp , Anru R. Zhang

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

This paper introduces a novel collaborative neurodynamic model for computing nonnegative Canonical Polyadic Decomposition (CPD). The model relies on a system of recurrent neural networks to solve the underlying nonconvex optimization…

Numerical Analysis · Mathematics 2025-01-03 Salman Ahmadi-Asl , Valentin Leplat , Anh-Huy Phan , Andrzej Cichocki

The tensor rank decomposition, also known as canonical polyadic(CP) or simply tensor decomposition, has a long history in multilinear algebra. However, computing a rank decomposition becomes particularly challenging when the rank lies…

Optimization and Control · Mathematics 2025-11-11 Zequn Zheng , Hongchao Zhang , Guangming Zhou

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

Because of the attractiveness of the canonical polyadic (CP) tensor decomposition in various applications, several algorithms have been designed to compute it, but efficient ones are still lacking. Iterative deflation algorithms based on…

Numerical Analysis · Computer Science 2015-08-24 Alex Pereira da Silva , Pierre Comon , Andre Lima Ferrer de Almeida

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

Tensor decomposition is a fundamental unsupervised machine learning method in data science, with applications including network analysis and sensor data processing. This work develops a generalized canonical polyadic (GCP) low-rank tensor…

Numerical Analysis · Mathematics 2020-07-09 David Hong , Tamara G. Kolda , Jed A. Duersch

Tensor Networks (TNs) have recently been used to speed up kernel machines by constraining the model weights, yielding exponential computational and storage savings. In this paper we prove that the outputs of Canonical Polyadic Decomposition…

Machine Learning · Computer Science 2024-03-29 Frederiek Wesel , Kim Batselier

Neural Network designs are quite diverse, from VGG-style to ResNet-style, and from Convolutional Neural Networks to Transformers. Towards the design of efficient accelerators, many works have adopted a dataflow-based, inter-layer pipelined…

Machine Learning · Computer Science 2023-06-23 Zhewen Yu , Christos-Savvas Bouganis

In the present work, a method is proposed in order to compute a Canonical Polyadic (CP) approximation of a given tensor. It is based on a greedy method and an adaptation of the TT-SVD method. The proposed approach can be straightforwardly…

Numerical Analysis · Mathematics 2020-11-20 Virginie Ehrlacher , Maria Fuente Ruiz , Damiano Lombardi

Tensor decompositions are powerful tools for large data analytics as they jointly model multiple aspects of data into one framework and enable the discovery of the latent structures and higher-order correlations within the data. One of the…

Machine Learning · Computer Science 2018-07-05 Ekta Gujral , Ravdeep Pasricha , Tianxiong Yang , Evangelos E. Papalexakis

A rising problem in the compression of Deep Neural Networks is how to reduce the number of parameters in convolutional kernels and the complexity of these layers by low-rank tensor approximation. Canonical polyadic tensor decomposition…

Machine Learning · Computer Science 2022-03-08 Anh-Huy Phan , Konstantin Sobolev , Dmitry Ermilov , Igor Vorona , Nikolay Kozyrskiy , Petr Tichavsky , Andrzej Cichocki

This paper proposes fast randomized algorithms for computing the Kronecker Tensor Decomposition (KTD). The proposed algorithms can decompose a given tensor into the KTD format much faster than the existing state-of-the-art algorithms. Our…

Numerical Analysis · Mathematics 2025-05-22 Salman Ahmadi-Asl , Naeim Rezaeian , Andre L. F. de Almeida , Yipeng Liu

Tensor decomposition has been widely used in machine learning and high-volume data analysis. However, large-scale tensor factorization often consumes huge memory and computing cost. Meanwhile, modernized computing hardware such as tensor…

Optimization and Control · Mathematics 2022-09-12 Zi Yang , Junnan Shan , Zheng Zhang

Physiological signals are often organized in the form of multiple dimensions (e.g., channel, time, task, and 3D voxel), so it is better to preserve original organization structure when processing. Unlike vector-based methods that destroy…

Computer Vision and Pattern Recognition · Computer Science 2019-07-31 Junhua Li , Chao Li , Andrzej Cichocki

Efficient modelling of feature interactions underpins supervised learning for non-sequential tasks, characterized by a lack of inherent ordering of features (variables). The brute force approach of learning a parameter for each interaction…

Machine Learning · Computer Science 2021-03-31 Alexandros Haliassos , Kriton Konstantinidis , Danilo P. Mandic

Tensor decomposition methods are widely used for model compression and fast inference in convolutional neural networks (CNNs). Although many decompositions are conceivable, only CP decomposition and a few others have been applied in…

Machine Learning · Computer Science 2019-11-28 Kohei Hayashi , Taiki Yamaguchi , Yohei Sugawara , Shin-ichi Maeda

To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new…

Machine Learning · Statistics 2018-03-13 Jérémy E. Cohen , Nicolas Gillis