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Recently, there has been a trend to combine independent component analysis and canonical polyadic decomposition (ICA-CPD) for an enhanced robustness for the computation of CPD, and ICA-CPD could be further converted into CPD of a 5th-order…

Machine Learning · Statistics 2016-12-30 Xiao-Feng Gong , Cheng-Yuan Wang , Ya-Na Hao , Qiu-Hua Lin

CANDECOMP/PARAFAC (CPD) approximates multiway data by sum of rank-1 tensors. Our recent study has presented a method to rank-1 tensor deflation, i.e. sequential extraction of the rank-1 components. In this paper, we extend the method to…

Numerical Analysis · Computer Science 2015-06-17 Anh-Huy Phan , Petr Tichavsky , Andrzej Cichocki

Koopman mode decomposition and tensor component analysis (also known as CANDECOMP/PARAFAC or canonical polyadic decomposition) are two popular approaches of decomposing high dimensional data sets into low dimensional modes that capture the…

Numerical Analysis · Mathematics 2021-05-19 William T. Redman

Canonical Polyadic (CP) tensor decomposition is a workhorse algorithm for discovering underlying low-dimensional structure in tensor data. This is accomplished in conventional CP decomposition by fitting a low-rank tensor to data with…

Numerical Analysis · Mathematics 2026-01-12 Alex Mulrooney , David Hong

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

A new algorithm of the canonical polyadic decomposition (CPD) presented here. It features lower computational complexity and memory usage than the available state of the art implementations. We begin with some examples of CPD applications…

Numerical Analysis · Mathematics 2021-10-13 Felipe Bottega Diniz

Tensors decompositions are a class of tools for analysing datasets of high dimensionality and variety in a natural manner, with the Canonical Polyadic Decomposition (CPD) being a main pillar. While the notion of CPD is closely intertwined…

Signal Processing · Electrical Eng. & Systems 2019-11-15 Giuseppe G. Calvi , Bruno Scalzo Dees , Danilo P. Mandic

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

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

CANDECOMP/PARAFAC (CP) decomposition has been widely used to deal with multi-way data. For real-time or large-scale tensors, based on the ideas of randomized-sampling CP decomposition algorithm and online CP decomposition algorithm, a novel…

Machine Learning · Computer Science 2020-07-22 Congbo Ma , Xiaowei Yang , Hu Wang

The CANDECOMP/PARAFAC (or Canonical polyadic, CP) decomposition of tensors has numerous applications in various fields, such as chemometrics, signal processing, machine learning, etc. Tensor CP decomposition assumes the knowledge of the…

Numerical Analysis · Mathematics 2025-01-08 Zihao Wang , Minru Bai , Liang Chen , Xueying Zhao

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

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 this paper, the canonical polyadic (CP) decomposition of tensors that corresponds to matrix multiplications is studied. Finding the rank of these tensors and computing the decompositions is a fundamental problem of algebraic complexity…

Computational Complexity · Computer Science 2021-04-13 Petr Tichavsky

Recently, coupled tensor decomposition has been widely used in data fusion of a hyperspectral image (HSI) and a multispectral image (MSI) for hyperspectral super-resolution (HSR). However, exsiting works often ignore the inherent…

Signal Processing · Electrical Eng. & Systems 2025-01-28 Xi-Yuan Liu , Xiao-Feng Gong , Lei Wang , Wei Feng , Qiu-Hua Lin

Tensor decompositions have proven to be effective in analyzing the structure of multidimensional data. However, most of these methods require a key parameter: the number of desired components. In the case of the CANDECOMP/PARAFAC…

Machine Learning · Computer Science 2024-05-28 William Shiao , Evangelos E. Papalexakis

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

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

We investigate a novel approach to approximate tensor-network contraction via the exact, matrix-free decomposition of full tensor-networks. We study this method as a means to eliminate the propagation of error in the approximation of…

Chemical Physics · Physics 2025-06-23 Karl Pierce

Multi-way data analysis has become an essential tool for capturing underlying structures in higher-order datasets stored in tensor $\mathcal{X} \in \mathbb{R} ^{I_1 \times \dots \times I_N} $. $CANDECOMP/PARAFAC$ (CP) decomposition has been…

Machine Learning · Computer Science 2020-03-20 Ali Anaissi , Basem Suleiman , Seid Miad Zandavi