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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

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

This work considers the problem of computing the canonical polyadic decomposition (CPD) of large tensors. Prior works mostly leverage data sparsity to handle this problem, which is not suitable for handling dense tensors that often arise in…

Signal Processing · Electrical Eng. & Systems 2020-03-26 Xiao Fu , Shahana Ibrahim , Hoi-To Wai , Cheng Gao , Kejun Huang

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

We investigate the efficient combination of the canonical polyadic decomposition (CPD) and tensor hyper-contraction (THC) approaches. We first present a novel low-cost CPD solver which leverages a precomputed THC factorization of an…

Chemical Physics · Physics 2025-05-28 Karl Pierce , Miguel Morales

The canonical polyadic decomposition (CPD) is a compact decomposition which expresses a tensor as a sum of its rank-1 components. A common step in the computation of a CPD is computing a generalized eigenvalue decomposition (GEVD) of the…

Numerical Analysis · Mathematics 2021-12-16 Eric Evert , Michiel Vandecappelle , Lieven De Lathauwer

We consider the problem of constructing a canonical polyadic (CP) decomposition for a tensor network, rather than a single tensor. We illustrate how it is possible to reduce the complexity of constructing an approximate CP representation of…

Chemical Physics · Physics 2024-07-30 Karl Pierce , Edward F Valeev

Canonical Polyadic Decomposition (CPD) represents a third-order tensor as the minimal sum of rank-1 terms. Because of its uniqueness properties the CPD has found many concrete applications in telecommunication, array processing, machine…

Spectral Theory · Mathematics 2019-12-06 Ignat Domanov , Lieven De Lathauwer

We consider the problem of factorizing a structured 3-way tensor into its constituent Canonical Polyadic (CP) factors. This decomposition, which can be viewed as a generalization of singular value decomposition (SVD) for tensors, reveals…

Machine Learning · Computer Science 2020-07-01 Sirisha Rambhatla , Xingguo Li , Jarvis Haupt

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 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

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 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

Convolutional Neural Networks (CNNs) has shown a great success in many areas including complex image classification tasks. However, they need a lot of memory and computational cost, which hinders them from running in relatively low-end…

Machine Learning · Computer Science 2017-01-26 Marcella Astrid , Seung-Ik Lee

Tensor decomposition of convolutional and fully-connected layers is an effective way to reduce parameters and FLOP in neural networks. Due to memory and power consumption limitations of mobile or embedded devices, the quantization step is…

Machine Learning · Computer Science 2023-08-10 Daria Cherniuk , Stanislav Abukhovich , Anh-Huy Phan , Ivan Oseledets , Andrzej Cichocki , Julia Gusak

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

Tensors are ubiquitous in science and engineering and tensor factorization approaches have become important tools for the characterization of higher order structure. Factorizations includes the outer-product rank Canonical Polyadic…

Machine Learning · Statistics 2023-10-05 Jesper Løve Hinrich , Morten Mørup

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

Coupled decompositions are a widely used tool for data fusion. As the volume of data increases, so does the dimensionality of matrices and tensors, highlighting the need for more efficient coupled decomposition algorithms. This paper…

Numerical Analysis · Mathematics 2026-04-22 Erna Begovic , Anita Carevic , Ivana Sain Glibic