{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T12:25:12Z","timestamp":1768911912137,"version":"3.49.0"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,12,3]],"date-time":"2024-12-03T00:00:00Z","timestamp":1733184000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,12,3]],"date-time":"2024-12-03T00:00:00Z","timestamp":1733184000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12471349"],"award-info":[{"award-number":["12471349"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012669","name":"Natural Science Foundation Project of Chongqing, Chongqing Science and Technology Commission","doi-asserted-by":"publisher","award":["cstc2019jcyj-msxmX0267"],"award-info":[{"award-number":["cstc2019jcyj-msxmX0267"]}],"id":[{"id":"10.13039\/501100012669","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2025,3]]},"DOI":"10.1007\/s40314-024-03019-4","type":"journal-article","created":{"date-parts":[[2024,12,3]],"date-time":"2024-12-03T03:55:54Z","timestamp":1733198154000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Tracking tensor ring decompositions of streaming tensors"],"prefix":"10.1007","volume":"44","author":[{"given":"Yajie","family":"Yu","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5033-578X","authenticated-orcid":false,"given":"Hanyu","family":"Li","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,12,3]]},"reference":[{"issue":"1","key":"3019_CR1","doi-asserted-by":"publisher","DOI":"10.1088\/2632-2153\/abad87","volume":"2","author":"S Ahmadi-Asl","year":"2020","unstructured":"Ahmadi-Asl S, Cichocki A, Phan AH, Asante-Mensah MG, Ghazani MM, Tanaka T, Oseledets IV (2020) Randomized algorithms for fast computation of low rank tensor ring model. Mach Learn Sci Technol 2(1):011001. https:\/\/doi.org\/10.1088\/2632-2153\/abad87","journal-title":"Mach Learn Sci Technol"},{"key":"3019_CR2","doi-asserted-by":"publisher","first-page":"150809","DOI":"10.1109\/ACCESS.2021.3125069","volume":"9","author":"S Ahmadi-Asl","year":"2021","unstructured":"Ahmadi-Asl S, Caiafa CF, Cichocki A, Phan AH, Tanaka T, Oseledets I, Wang J (2021) Cross tensor approximation methods for compression and dimensionality reduction. IEEE Access 9:150809\u2013150838. https:\/\/doi.org\/10.1109\/ACCESS.2021.3125069","journal-title":"IEEE Access"},{"key":"3019_CR3","unstructured":"Bader BW, Kolda TG, et al (2021) Tensor Toolbox for MATLAB. Version 3.2.1. https:\/\/www.tensortoolbox.org Accessed 2021\/04\/05"},{"issue":"2","key":"3019_CR4","doi-asserted-by":"publisher","first-page":"876","DOI":"10.1137\/17M1112303","volume":"39","author":"C Battaglino","year":"2018","unstructured":"Battaglino C, Ballard G, Kolda TG (2018) A practical randomized CP tensor decomposition. SIAM J Matrix Anal Appl 39(2):876\u2013901. https:\/\/doi.org\/10.1137\/17M1112303","journal-title":"SIAM J Matrix Anal Appl"},{"key":"3019_CR5","doi-asserted-by":"publisher","unstructured":"Chachlakis DG, Dhanaraj M, Prater-Bennette A, Markopoulos PP (2021) Dynamic l1-norm Tucker tensor decomposition. IEEE J Sel Topics Signal Process 15(3):587\u2013602. https:\/\/doi.org\/10.1109\/JSTSP.2021.3058846","DOI":"10.1109\/JSTSP.2021.3058846"},{"key":"3019_CR6","doi-asserted-by":"publisher","unstructured":"Drineas P, Kannan R, Mahoney MW (2006) Fast Monte Carlo algorithms for matrices i: Approximating matrix multiplication. SIAM J Comput 36(1):132\u2013157. https:\/\/doi.org\/10.1137\/S0097539704442684","DOI":"10.1137\/S0097539704442684"},{"issue":"2","key":"3019_CR7","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/s00211-010-0331-6","volume":"117","author":"P Drineas","year":"2011","unstructured":"Drineas P, Mahoney MW, Muthukrishnan S, Sarl\u00f3s T (2011) Faster least squares approximation. Numer Math 117(2):219\u2013249. https:\/\/doi.org\/10.1007\/s00211-010-0331-6","journal-title":"Numer Math"},{"issue":"1","key":"3019_CR8","first-page":"3475","volume":"13","author":"P Drineas","year":"2012","unstructured":"Drineas P, Magdon-Ismail M, Mahoney MW, Woodruff DP (2012) Fast approximation of matrix coherence and statistical leverage. J Mach Learn Res 13(1):3475\u20133506","journal-title":"J Mach Learn Res"},{"key":"3019_CR9","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1007\/s00791-014-0218-7","volume":"15","author":"M Espig","year":"2012","unstructured":"Espig M, Naraparaju KK, Schneider J (2012) A note on tensor chain approximation. Comput Visual Sci 15:331\u2013344. https:\/\/doi.org\/10.1007\/s00791-014-0218-7","journal-title":"Comput Visual Sci"},{"issue":"12","key":"3019_CR10","doi-asserted-by":"publisher","first-page":"8312","DOI":"10.1109\/TCSVT.2022.3190818","volume":"32","author":"Y He","year":"2022","unstructured":"He Y, Atia GK (2022) Patch tracking-based streaming tensor ring completion for visual data recovery. IEEE Trans Circuits Syst Video Technol 32(12):8312\u20138326. https:\/\/doi.org\/10.1109\/TCSVT.2022.3190818","journal-title":"IEEE Trans Circuits Syst Video Technol"},{"key":"3019_CR11","doi-asserted-by":"publisher","first-page":"2657","DOI":"10.1109\/LSP.2022.3231469","volume":"29","author":"Z Huang","year":"2022","unstructured":"Huang Z, Qiu Y, Yu J, Zhou G (2022) Multi-aspect streaming tensor ring completion for dynamic incremental data. IEEE Signal Process Lett 29:2657\u20132661. https:\/\/doi.org\/10.1109\/LSP.2022.3231469","journal-title":"IEEE Signal Process Lett"},{"issue":"4","key":"3019_CR12","doi-asserted-by":"publisher","first-page":"1533","DOI":"10.1093\/imaiai\/iaaa028","volume":"10","author":"R Jin","year":"2021","unstructured":"Jin R, Kolda TG, Ward R (2021) Faster Johnson-Lindenstrauss transforms via Kronecker products. Inf Inference 10(4):1533\u20131562. https:\/\/doi.org\/10.1093\/imaiai\/iaaa028","journal-title":"Inf Inference"},{"issue":"3","key":"3019_CR13","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1137\/07070111X","volume":"51","author":"TG Kolda","year":"2009","unstructured":"Kolda TG, Bader BW (2009) Tensor decompositions and applications. SIAM Rev 51(3):455\u2013500. https:\/\/doi.org\/10.1137\/07070111X","journal-title":"SIAM Rev"},{"issue":"5","key":"3019_CR14","doi-asserted-by":"publisher","first-page":"2610","DOI":"10.1137\/22M1515045","volume":"45","author":"D Kressner","year":"2023","unstructured":"Kressner D, Vandereycken B, Voorhaar R (2023) Streaming tensor train approximation. SIAM J Sci Comput 45(5):2610\u20132631. https:\/\/doi.org\/10.1137\/22M1515045","journal-title":"SIAM J Sci Comput"},{"issue":"2","key":"3019_CR15","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1109\/TBDATA.2018.2867485","volume":"7","author":"H Liu","year":"2021","unstructured":"Liu H, Yang LT, Guo Y, Xie X, Ma J (2021) An incremental tensor-train decomposition for cyber-physical-social big data. IEEE Trans Big Data 7(2):341\u2013354. https:\/\/doi.org\/10.1109\/TBDATA.2018.2867485","journal-title":"IEEE Trans Big Data"},{"key":"3019_CR16","unstructured":"Malik OA (2022) More efficient sampling for tensor decomposition with worst-case guarantees. In: Proceedings of the 39th international conference on machine learning, vol 162, pp 14887\u201314917. PMLR, Virtual Event"},{"key":"3019_CR17","unstructured":"Malik OA, Becker S (2021) A sampling-based method for tensor ring decomposition. In: Proceedings of the 38th international conference on machine learning, vol 139, pp 7400\u20137411. PMLR, Virtual Event"},{"key":"3019_CR18","doi-asserted-by":"crossref","unstructured":"Ma C, Yang X, Wang H (2018) Randomized online CP decomposition. In: 2018 tenth international conference on advanced computational intelligence (ICACI), pp 414\u2013419. IEEE, Xiamen, China","DOI":"10.1109\/ICACI.2018.8377495"},{"issue":"3","key":"3019_CR19","doi-asserted-by":"publisher","first-page":"2289","DOI":"10.1002\/nla.2289","volume":"27","author":"O Mickelin","year":"2020","unstructured":"Mickelin O, Karaman S (2020) On algorithms for and computing with the tensor ring decomposition. Numer Linear Algebra Appl 27(3):2289. https:\/\/doi.org\/10.1002\/nla.2289","journal-title":"Numer Linear Algebra Appl"},{"issue":"5","key":"3019_CR20","doi-asserted-by":"publisher","first-page":"2295","DOI":"10.1137\/090752286","volume":"33","author":"IV Oseledets","year":"2011","unstructured":"Oseledets IV (2011) Tensor-train decomposition. SIAM J Sci Comput 33(5):2295\u20132317. https:\/\/doi.org\/10.1137\/090752286","journal-title":"SIAM J Sci Comput"},{"key":"3019_CR21","doi-asserted-by":"publisher","unstructured":"Sun J, Tao D, Papadimitriou S, Yu PS, Faloutsos C (2008) Incremental tensor analysis: Theory and applications. ACM Trans Knowl Discov Data 2(3):1556\u20134681. https:\/\/doi.org\/10.1145\/1409620.1409621","DOI":"10.1145\/1409620.1409621"},{"key":"3019_CR22","doi-asserted-by":"publisher","unstructured":"Sun Y, Guo Y, Luo C, Tropp J, Udell M (2020) Low-rank Tucker approximation of a tensor from streaming data. SIAM J Math Data Sci 2(4):1123\u20131150. https:\/\/doi.org\/10.1137\/19M1257718","DOI":"10.1137\/19M1257718"},{"key":"3019_CR23","doi-asserted-by":"crossref","unstructured":"Sun J, Tao D, Faloutsos C (2006) Beyond streams and graphs: Dynamic tensor analysis. In: Proceedings of the 12th ACM SIGKDD international conference on knowledge discovery and data mining, vol KDD \u201906, pp 374\u2013383. Association for Computing Machinery, New York, NY, USA","DOI":"10.1145\/1150402.1150445"},{"key":"3019_CR24","doi-asserted-by":"crossref","unstructured":"Thanh LT, Abed-Meraim K, Trung NL, Boyer R (2021) Adaptive algorithms for tracking tensor-train decomposition of streaming tensors. In: 2020 28th European signal processing conference (EUSIPCO), pp 995\u2013999. IEEE, Amsterdam, Netherlands","DOI":"10.23919\/Eusipco47968.2020.9287780"},{"key":"3019_CR25","doi-asserted-by":"publisher","unstructured":"Thanh LT, Abed-Meraim K, Trung NL, Hafiane A (2022) A contemporary and comprehensive survey on streaming tensor decomposition. IEEE Trans Knowl Data Eng 35(11):10897\u201310921. https:\/\/doi.org\/10.1109\/TKDE.2022.3230874","DOI":"10.1109\/TKDE.2022.3230874"},{"issue":"1\u20132","key":"3019_CR26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/0400000060","volume":"10","author":"DP Woodruff","year":"2014","unstructured":"Woodruff DP (2014) Sketching as a tool for numerical linear algebra. Found Trends Theor Comput Sci 10(1\u20132):1\u2013157. https:\/\/doi.org\/10.1561\/0400000060","journal-title":"Found Trends Theor Comput Sci"},{"key":"3019_CR27","doi-asserted-by":"crossref","unstructured":"Xiao H, Wang F, Ma F, Gao J (2018) eOTD: An efficient online Tucker decomposition for higher order tensors. In: 2018 IEEE international conference on data mining (ICDM), pp 1326\u20131331","DOI":"10.1109\/ICDM.2018.00180"},{"key":"3019_CR28","doi-asserted-by":"publisher","unstructured":"Yu Y, Li H (2024a) Practical sketching-based randomized tensor ring decomposition. Numer Linear Algebra Appl 31(4): 2548. https:\/\/doi.org\/10.1002\/nla.2548","DOI":"10.1002\/nla.2548"},{"issue":"3","key":"3019_CR29","doi-asserted-by":"publisher","first-page":"2542","DOI":"10.1002\/nla.2542","volume":"31","author":"Y Yu","year":"2024","unstructured":"Yu Y, Li H (2024) Practical alternating least squares for tensor ring decomposition. Numer Linear Algebra Appl 31(3):2542. https:\/\/doi.org\/10.1002\/nla.2542","journal-title":"Numer Linear Algebra Appl"},{"key":"3019_CR30","doi-asserted-by":"publisher","first-page":"314","DOI":"10.1016\/j.neunet.2022.05.023","volume":"153","author":"J Yu","year":"2022","unstructured":"Yu J, Zou T, Zhou G (2022) Online subspace learning and imputation by tensor-ring decomposition. Neural Netw 153:314\u2013324. https:\/\/doi.org\/10.1016\/j.neunet.2022.05.023","journal-title":"Neural Netw"},{"key":"3019_CR31","doi-asserted-by":"crossref","unstructured":"Yuan L, Cao J, Zhao X, Wu Q, Zhao Q (2018) Higher-dimension tensor completion via low-rank tensor ring decomposition. In: 2018 Asia-pacific signal and information processing association annual summit and conference (APSIPA ASC), pp 1071\u20131076. IEEE, Honolulu, HI, USA","DOI":"10.23919\/APSIPA.2018.8659708"},{"key":"3019_CR32","doi-asserted-by":"crossref","unstructured":"Yuan L, Li C, Cao J, Zhao Q (2019) Randomized tensor ring decomposition and its application to large-scale data reconstruction. In: ICASSP 2019 - 2019 IEEE international conference on acoustics, speech and signal processing (ICASSP), pp 2127\u20132131. IEEE, Brighton Conference Centre Brighton, U.K","DOI":"10.1109\/ICASSP.2019.8682197"},{"issue":"2","key":"3019_CR33","doi-asserted-by":"publisher","first-page":"832","DOI":"10.1137\/20M1319097","volume":"42","author":"C Zeng","year":"2021","unstructured":"Zeng C, Ng MK (2021) Incremental CP tensor decomposition by alternating minimization method. SIAM J Matrix Anal Appl 42(2):832\u2013858. https:\/\/doi.org\/10.1137\/20M1319097","journal-title":"SIAM J Matrix Anal Appl"},{"key":"3019_CR34","doi-asserted-by":"publisher","unstructured":"Zeng C, Ng MK, Jiang TX (2024) Incremental algorithms for truncated higher-order singular value decompositions. BIT Numer Math 64(1):4. https:\/\/doi.org\/10.1007\/s10543-023-01004-7","DOI":"10.1007\/s10543-023-01004-7"},{"key":"3019_CR35","unstructured":"Zhao Q, Zhou G, Xie S, Zhang L, Cichocki A (2016) Tensor ring decomposition. arXiv preprint arXiv:1606.05535"},{"key":"3019_CR36","doi-asserted-by":"crossref","unstructured":"Zhou S, Vinh NX, Bailey J, Jia Y, Davidson I (2016) Accelerating online CP decompositions for higher order tensors. In: Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining, vol KDD \u201916, pp 1375\u20131384. Association for Computing Machinery, New York, NY, USA","DOI":"10.1145\/2939672.2939763"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-024-03019-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-024-03019-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-024-03019-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,8]],"date-time":"2025-03-08T07:57:40Z","timestamp":1741420660000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-024-03019-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,3]]},"references-count":36,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,3]]}},"alternative-id":["3019"],"URL":"https:\/\/doi.org\/10.1007\/s40314-024-03019-4","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,3]]},"assertion":[{"value":"20 June 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 October 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 November 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 December 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"60"}}