Matrix and tensor completion using tensor ring decomposition with sparse representation

Asante-Mensah, Maame G.; Ahmadi‐Asl, Salman; Cichocki, Andrzej

doi:10.1088/2632-2153/abcb4f

Cited by 5 publications

(6 citation statements)

References 87 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the case of organized missing components, such as missing rows and columns or blocks or patches, the work of finishing a data tensor is made more difficult since these components are not dispersed randomly. Such circumstances are not handled by many of the available tensor completion techniques [Ahmadi et al [ 10 ]]. a. Solver of Tensor Train …”

Section: Introductionmentioning

confidence: 99%

Tensor Multi-Clustering Parallel Intelligent Computing Method Based on Tensor Chain Decomposition

Zhang

Fan

et al. 2022

Computational Intelligence and Neuroscience

View full text Add to dashboard Cite

Adaptable methods for representing higher-order data with various features and high dimensionality have been demanded by the increasing usage of multi-sensor technologies and the emergence of large data sets. Arrays of multi-dimensional data, known as tensors, can be found in a variety of applications. Standard data that depicts things from a single point of view lacks the semantic richness, utility, and complexity of multi-dimensional data. Research into multi-clustering has taken off since traditional clustering methods are unable to handle large datasets. There are three main kinds of multi-clustering algorithms: Self-weighted Multiview Clustering (SwMC), Latent Multi-view Subspace Clustering (LMSC), and Multi-view Subspace Clustering with Intactness-Aware Similarity (MSC IAS) that are explored in this paper. To evaluate their performance, we do in-depth tests on seven real-world datasets. The three most important metrics Accuracy (ACC), normalized mutual information (NMI), and purity are grouped. Furthermore, traditional Principal Component Analysis (PCA) cannot uncover hidden components within multi-dimensional data. For this purpose, tensor decomposition algorithms have been presented that are flexible in terms of constraint selection and extract more broad latent components. In this examination, we also go through the various tensor decomposition methods, with an emphasis on the issues that classical PCA is designed to solve. Various tensor models are also tested for dimensionality reduction and supervised learning applications in the experiments presented here.

show abstract

Section: Introductionmentioning

confidence: 99%

Tensor Multi-Clustering Parallel Intelligent Computing Method Based on Tensor Chain Decomposition

Zhang

Fan

et al. 2022

Computational Intelligence and Neuroscience

View full text Add to dashboard Cite

show abstract

“…The process of recovering (reconstructing) an incomplete data tensor from its partially observed data tensor is called tensor completion. In the past few decades, many algorithms have been developed to solve this problem [5,6,7] due to its importance in several applications such as in recommender systems [8], computer vision [9], chemometrics [10], link prediction [11], etc. Tensor completion algorithms are generally categorized into 1) rank minimization and 2) tensor decomposition techniques in which the concepts of tensor rank and tensor decomposition play key roles in the analysis.…”

Section: Introductionmentioning

confidence: 99%

Cross Tensor Approximation for Image and Video Completion

Ahmadi‐Asl¹,

Asante-Mensah²,

Cichocki³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

This paper proposes a general framework to use the cross tensor approximation or tensor CUR approximation for reconstructing incomplete images and videos. The new algorithms are simple and easy to be implemented with low computational complexity. For the case of data tensors with 1) structural missing components or 2) a high missing rate, we propose an efficient smooth tensor CUR algorithms which first make the sampled fibers smooth and then apply the proposed CUR algorithms. The main contribution of this paper is to develop/investigate improved multistage CUR algorithms with filtering (smoothing ) preprocessing for tensor completion. The second contribution is a detailed comparison of the performance of image recovery for four different CUR strategies via extensive computer simulations. Our simulations clearly indicated that the proposed algorithms are much faster than most of the existing state-of-the-art algorithms developed for tensor completion, while performance is comparable and often even better.Furthermore, we will provide in GitHub developed software in MATLAB which can be used for various applications. Moreover, to our best knowledge, the CUR (cross approximation) algorithms have not been investigated nor compared till now for image and video completion.

show abstract

“…Sparse signal representation (SSR) is used in many applications, such as image and tensor denoising, tensor compression, tensor completion, face and audio signal recognition, blind source separation, inverse synthetic aperture radar (ISAR) image formation and classification, and so on [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. This area of signal processing consists of two fundamental principles, proper selection of basis signals (called atoms) which is known as Dictionary Learning (DL), and introducing efficient methods for computing the sparse representation of the signals over the set of obtained atoms (dictionary) called Sparse Coding (SC).…”

Section: Introductionmentioning

confidence: 99%

3D inverse synthetic aperture radar image quality improvement using sparse signal representation

Mehrpooya

Karbasi

Nazari

et al. 2022

IET Radar Sonar & Navi

View full text Add to dashboard Cite

Generalisation of one‐dimensional dictionary learning (1DDL) algorithms to Multidimensional (MD) mode and its utilisation in MD data applications, increases the speed and reduces the computational complexity. An example of such an application is 3D inverse synthetic aperture radar (ISAR) image reconstruction and noise reduction. In this study, in addition to MD mode generalisation, the formulation structure of the multidimensional dictionary learning (MDDL) problem is discussed followed by two novel algorithms to solve it. The first one is based on the K‐singular value decomposition algorithm for 1DDL, which uses alternating minimisation and singular value decomposition. The second algorithm is the extension of the sequential generalisation of K‐means 1DDL algorithm to the MD mode. Moreover, the MD tensor denoising method based on the MDDL algorithm (MDDL‐ALG) is proposed. As an application, the proposed method is used to denoise the 3D ISAR image. The numerical simulations reveal that the proposed methods, in addition to reducing the memory consumption and the computational complexity, also enjoy higher convergence rate in comparison to 1D algorithms. Specifically, convergence speed of MD algorithms, depending on the training data size, is up to at least 10 times faster than the equivalent 1D counterparts. As revealed through the simulations, the amount of signal to noise ratio recovered by the proposed methods is almost 2 dB higher than the case using a pre‐designed dictionary for denoising. Moreover, it outperforms about 10 dB over the case with the conventional 3D‐IFFT method for image construction.

show abstract

Matrix and tensor completion using tensor ring decomposition with sparse representation

Cited by 5 publications

References 87 publications

Tensor Multi-Clustering Parallel Intelligent Computing Method Based on Tensor Chain Decomposition

Tensor Multi-Clustering Parallel Intelligent Computing Method Based on Tensor Chain Decomposition

Cross Tensor Approximation for Image and Video Completion

3D inverse synthetic aperture radar image quality improvement using sparse signal representation

Contact Info

Product

Resources

About