{"title":"Rank-revealing fully-connected tensor network decomposition and its application to tensor completion","authors":"Yun-Yang Liu , Xi-Le Zhao , Gemine Vivone","doi":"10.1016/j.patcog.2025.111610","DOIUrl":null,"url":null,"abstract":"<div><div>Fully-connected tensor network (FCTN) decomposition has become a powerful tool for handling high-dimensional data. However, for a given <span><math><mi>N</mi></math></span>th-order data, <span><math><mrow><mi>N</mi><mrow><mo>(</mo><mi>N</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mo>/</mo><mn>2</mn></mrow></math></span> tuning parameters (i.e., FCTN rank) in FCTN decomposition is a tricky challenge, which hinders its wide deployments. Although many recent works have emerged to adaptively search for a (near)-optimal FCTN rank, these methods suffer from expensive computational costs since they require too many search and evaluation processes, significantly limiting their applications to high-dimensional data. To tackle the above challenges, we develop a rank-revealing FCTN (revealFCTN) decomposition, whose FCTN rank is adaptively and efficiently inferred. More specifically, by analyzing the sizes of the sub-network tensors in the FCTN decomposition, we establish the equivalent relationships between the FCTN rank and the ranks of single-mode and double-mode unfolding matrices of the given data. The FCTN rank can be directly revealed through the ranks of these unfolding matrices, which does not require any search and evaluation process, making the computational cost almost negligible compared to the search-based methods. To evaluate the performance of the developed revealFCTN decomposition, we test its performance on a representative task: tensor completion (TC). Comprehensive experimental results demonstrate that our method outperforms several state-of-the-art methods, achieving a MPSNR gain of around 1 dB in most cases compared to the original FCTN decomposition.</div></div>","PeriodicalId":49713,"journal":{"name":"Pattern Recognition","volume":"165 ","pages":"Article 111610"},"PeriodicalIF":7.5000,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pattern Recognition","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0031320325002705","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
Fully-connected tensor network (FCTN) decomposition has become a powerful tool for handling high-dimensional data. However, for a given th-order data, tuning parameters (i.e., FCTN rank) in FCTN decomposition is a tricky challenge, which hinders its wide deployments. Although many recent works have emerged to adaptively search for a (near)-optimal FCTN rank, these methods suffer from expensive computational costs since they require too many search and evaluation processes, significantly limiting their applications to high-dimensional data. To tackle the above challenges, we develop a rank-revealing FCTN (revealFCTN) decomposition, whose FCTN rank is adaptively and efficiently inferred. More specifically, by analyzing the sizes of the sub-network tensors in the FCTN decomposition, we establish the equivalent relationships between the FCTN rank and the ranks of single-mode and double-mode unfolding matrices of the given data. The FCTN rank can be directly revealed through the ranks of these unfolding matrices, which does not require any search and evaluation process, making the computational cost almost negligible compared to the search-based methods. To evaluate the performance of the developed revealFCTN decomposition, we test its performance on a representative task: tensor completion (TC). Comprehensive experimental results demonstrate that our method outperforms several state-of-the-art methods, achieving a MPSNR gain of around 1 dB in most cases compared to the original FCTN decomposition.
期刊介绍:
The field of Pattern Recognition is both mature and rapidly evolving, playing a crucial role in various related fields such as computer vision, image processing, text analysis, and neural networks. It closely intersects with machine learning and is being applied in emerging areas like biometrics, bioinformatics, multimedia data analysis, and data science. The journal Pattern Recognition, established half a century ago during the early days of computer science, has since grown significantly in scope and influence.