{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T13:05:43Z","timestamp":1765976743988,"version":"3.37.3"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2023,12,21]],"date-time":"2023-12-21T00:00:00Z","timestamp":1703116800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,12,21]],"date-time":"2023-12-21T00:00:00Z","timestamp":1703116800000},"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":["12171168, 12071159"],"award-info":[{"award-number":["12171168, 12071159"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005273","name":"Natural Science Foundation of Yunnan Province","doi-asserted-by":"publisher","award":["202101BA070001-047","12271187"],"award-info":[{"award-number":["202101BA070001-047","12271187"]}],"id":[{"id":"10.13039\/501100005273","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2024,4]]},"DOI":"10.1007\/s10589-023-00545-5","type":"journal-article","created":{"date-parts":[[2023,12,21]],"date-time":"2023-12-21T19:02:32Z","timestamp":1703185352000},"page":"1033-1057","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Internet traffic tensor completion with tensor nuclear norm"],"prefix":"10.1007","volume":"87","author":[{"given":"Can","family":"Li","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3121-3602","authenticated-orcid":false,"given":"Yannan","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Dong-Hui","family":"Li","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,12,21]]},"reference":[{"key":"545_CR1","doi-asserted-by":"crossref","unstructured":"Ouyang, Y., Xie, K., Wang, X., Wen, J., Zhang, G.: Lightweight trilinear pooling based tensor completion for network traffic monitoring. In: IEEE INFOCOM 2022\u2014IEEE Conference on Computer Communications, pp. 2128\u20132137 (2022)","DOI":"10.1109\/INFOCOM48880.2022.9796873"},{"issue":"3","key":"545_CR2","doi-asserted-by":"publisher","first-page":"662","DOI":"10.1109\/TNET.2011.2169424","volume":"20","author":"M Roughan","year":"2012","unstructured":"Roughan, M., Zhang, Y., Willinger, W., Qiu, L.: Spatio-temporal compressive sensing and internet traffic matrices (extended version). IEEE\/ACM Trans. Netw. 20(3), 662\u2013676 (2012)","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"545_CR3","doi-asserted-by":"crossref","unstructured":"Chen, Y. C., Qiu, L., Zhang, Y., Xue, G., Hu, Z.: Robust network compressive sensing. In: Proceedings of The 20th Annual International Conference on Mobile Computing and Networking, pp. 545\u2013556 (2014)","DOI":"10.1145\/2639108.2639129"},{"key":"545_CR4","doi-asserted-by":"crossref","unstructured":"G\u00fcrsun, G., Crovella, M.: On traffic matrix completion in the internet. In: Proceedings of The 2012 Internet Measurement Conference, pp. 399\u2013412 (2012)","DOI":"10.1145\/2398776.2398818"},{"key":"545_CR5","doi-asserted-by":"crossref","unstructured":"Kumar, A., Saradhi, V. V., Venkatesh, T.: Compressive sensing of internet traffic matrices using CUR decomposition. In: Proceedings of the 19th International Conference on Distributed Computing and Networking, pp. 1\u20137 (2018)","DOI":"10.1145\/3154273.3154315"},{"key":"545_CR6","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/j.comcom.2019.05.023","volume":"145","author":"D Li","year":"2019","unstructured":"Li, D., Xing, C., Zhang, G., Cao, H., Xu, B.: An online dynamic traffic matrix completion method in software defined networks. Comput. Commun. 145, 43\u201353 (2019)","journal-title":"Comput. Commun."},{"issue":"1","key":"545_CR7","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1145\/1012888.1005697","volume":"32","author":"A Lakhina","year":"2004","unstructured":"Lakhina, A., Papagiannaki, K., Crovella, M., Diot, C., Kolaczyk, E., Taft, N.: Structural analysis of network traffic flows. ACM Sigmetrics Perform. Eval. Rev. 32(1), 61\u201372 (2004)","journal-title":"ACM Sigmetrics Perform. Eval. Rev."},{"key":"545_CR8","doi-asserted-by":"crossref","unstructured":"Xie, K., Wang, L., Wang, X., Xie, G., Wen, J., Zhang, G.: Accurate recovery of internet traffic data: a tensor completion approach. In: IEEE INFOCOM 2016\u2014The 35th Annual IEEE International Conference on Computer Communications, pp. 1\u20139 (2016)","DOI":"10.1109\/INFOCOM.2016.7524463"},{"issue":"1","key":"545_CR9","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1109\/TPAMI.2012.39","volume":"35","author":"J Liu","year":"2013","unstructured":"Liu, J., Musialski, P., Wonka, P., Ye, J.: Tensor completion for estimating missing values in visual data. IEEE Trans. Pattern Anal. Mach. Intell. 35(1), 208\u2013220 (2013)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"545_CR10","first-page":"2017","volume":"1347\u20131352","author":"Y Zhang","year":"2017","unstructured":"Zhang, Y., Silva, C.D., Kumar, R., Herrmann, F.J.: Massive 3D seismic data compression and inversion with hierarchical Tucker. SEG Tech. Program Expand. Abstr. 1347\u20131352, 2017 (2017)","journal-title":"SEG Tech. Program Expand. Abstr."},{"issue":"1","key":"545_CR11","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1002\/widm.1","volume":"1","author":"M M\u00f8rup","year":"2011","unstructured":"M\u00f8rup, M.: Applications of tensor (multiway array) factorizations and decompositions in data mining. Wiley Interdiscip. Rev. Data Min. Knowl. Discov. 1(1), 24\u201340 (2011)","journal-title":"Wiley Interdiscip. Rev. Data Min. Knowl. Discov."},{"key":"545_CR12","doi-asserted-by":"crossref","unstructured":"Karatzoglou, A., Amatriain, X., Baltrunas, L., Oliver, N.: Multiverse recommendation: n-dimensional tensor factorization for context-aware collaborative filtering. In: Proceedings of The Fourth ACM Conference on Recommender Systems, pp. 79\u201386 (2010)","DOI":"10.1145\/1864708.1864727"},{"key":"545_CR13","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1007\/s10589-016-9872-7","volume":"66","author":"Z Huang","year":"2017","unstructured":"Huang, Z., Qi, L.: Formulating an $$n$$-person noncooperative game as a tensor complementarity problem. Comput. Optim. Appl. 66, 557\u2013576 (2017)","journal-title":"Comput. Optim. Appl."},{"key":"545_CR14","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1007\/BF02310791","volume":"35","author":"JD Carroll","year":"1970","unstructured":"Carroll, J.D., Chang, J.J.: Analysis of individual differences in multidimensional scaling via an N-way generalization of \u201cEckart-Young\u2019\u2019 decomposition. Psychometrika 35, 283\u2013319 (1970)","journal-title":"Psychometrika"},{"issue":"3","key":"545_CR15","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1137\/07070111X","volume":"51","author":"TG Kolda","year":"2009","unstructured":"Kolda, T.G., Bader, B.W.: Tensor decompositions and applications. SIAM Rev. 51(3), 455\u2013500 (2009)","journal-title":"SIAM Rev."},{"issue":"1","key":"545_CR16","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1016\/j.chemolab.2010.08.004","volume":"106","author":"E Acar","year":"2011","unstructured":"Acar, E., Dunlavy, D.M., Kolda, T.G., M\u00f8rup, M.: Scalable tensor factorizations for incomplete data. Chemom. Intell. Lab. Syst. 106(1), 41\u201356 (2011)","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"545_CR17","doi-asserted-by":"crossref","unstructured":"Zhou, H., Zhang, D., Xie, K., Chen, Y.: Spatio-temporal tensor completion for imputing missing internet traffic data. In: 2015 IEEE 34th International Performance Computing and Communications Conference, pp. 1\u20137 (2015)","DOI":"10.1109\/PCCC.2015.7410315"},{"issue":"3","key":"545_CR18","doi-asserted-by":"publisher","first-page":"1137","DOI":"10.1109\/TNET.2018.2819504","volume":"26","author":"K Xie","year":"2018","unstructured":"Xie, K., Peng, C., Wang, X., Xie, G., Wen, J., Cao, J., Zhang, D., Qin, Z.: Accurate recovery of internet traffic data under variable rate measurements. IEEE\/ACM Trans. Netw. 26(3), 1137\u20131150 (2018)","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"545_CR19","doi-asserted-by":"publisher","first-page":"532","DOI":"10.1109\/ACCESS.2017.2770146","volume":"6","author":"L Wang","year":"2017","unstructured":"Wang, L., Xie, K., Semong, T., Zhou, H.: Missing data recovery based on tensor-CUR decomposition. IEEE Access 6, 532\u2013544 (2017)","journal-title":"IEEE Access"},{"issue":"1","key":"545_CR20","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1137\/20M1323266","volume":"42","author":"L Qi","year":"2021","unstructured":"Qi, L., Chen, Y., Bakshi, M., Zhang, X.: Triple decomposition and tensor recovery of third order tensors. SIAM J. Matrix Anal. Appl. 42(1), 299\u2013329 (2021)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"545_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10915-021-01574-0","volume":"88","author":"Y Chen","year":"2021","unstructured":"Chen, Y., Zhang, X., Qi, L., Xu, Y.: A Barzilai\u2013Borwein gradient algorithm for spatio-temporal internet traffic data completion via tensor triple decomposition. J. Sci. Comput. 88, 1\u201324 (2021)","journal-title":"J. Sci. Comput."},{"key":"545_CR22","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-021-04147-4","author":"Z Zhang","year":"2021","unstructured":"Zhang, Z., Ling, C., He, H., Qi, L.: A tensor train approach for internet traffic data completion. Ann. Oper. Res. (2021). https:\/\/doi.org\/10.1007\/s10479-021-04147-4","journal-title":"Ann. Oper. Res."},{"issue":"5","key":"545_CR23","doi-asserted-by":"publisher","first-page":"2295","DOI":"10.1137\/090752286","volume":"33","author":"IV Oseledets","year":"2011","unstructured":"Oseledets, I.V.: Tensor-train decomposition. SIAM J. Sci. Comput. 33(5), 2295\u20132317 (2011)","journal-title":"SIAM J. Sci. Comput."},{"issue":"3","key":"545_CR24","doi-asserted-by":"publisher","first-page":"1152","DOI":"10.1109\/TIP.2017.2762595","volume":"27","author":"P Zhou","year":"2017","unstructured":"Zhou, P., Lu, C., Lin, Z., Zhang, C.: Tensor factorization for low-rank tensor completion. IEEE Trans. Image Process. 27(3), 1152\u20131163 (2017)","journal-title":"IEEE Trans. Image Process."},{"issue":"3","key":"545_CR25","doi-asserted-by":"publisher","first-page":"883","DOI":"10.1007\/s10589-021-00315-1","volume":"80","author":"C Ling","year":"2021","unstructured":"Ling, C., Yu, G., Qi, L., Xu, Y.: T-product factorization method for internet traffic data completion with spatio-temporal regularization. Comput. Optim. Appl. 80(3), 883\u2013913 (2021)","journal-title":"Comput. Optim. Appl."},{"issue":"3","key":"545_CR26","first-page":"486","volume":"17","author":"G Yu","year":"2021","unstructured":"Yu, G., Wang, L., Wan, S., Qi, L., Xu, Y.: Tensor factorization with total variation for internet traffic data imputation. Pac. J. Optim. 17(3), 486\u2013505 (2021)","journal-title":"Pac. J. Optim."},{"key":"545_CR27","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/s10915-022-02006-3","volume":"93","author":"H He","year":"2022","unstructured":"He, H., Ling, C., Xie, W.: Tensor completion via a generalized transformed tensor T-product decomposition without t-SVD. J. Sci. Comput. 93, 47 (2022)","journal-title":"J. Sci. Comput."},{"issue":"4","key":"545_CR28","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1016\/0196-6774(90)90014-6","volume":"11","author":"J H\u00e5stad","year":"1990","unstructured":"H\u00e5stad, J.: Tensor rank is NP-complete. J. Algorithms 11(4), 644\u2013654 (1990)","journal-title":"J. Algorithms"},{"issue":"1","key":"545_CR29","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1109\/TPAMI.2012.39","volume":"35","author":"J Liu","year":"2013","unstructured":"Liu, J., Musialski, P., Wonka, P., Ye, J.: Tensor completion for estimating missing values in visual data. IEEE Trans. Pattern Anal. Mach. Intell. 35(1), 208\u2013220 (2013)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"545_CR30","unstructured":"Romera-Paredes, B., Pontil, M.: A new convex relaxation for tensor completion. In: Proceeding of the 26th International Conference on Neutral Information Processing Systems, pp. 2967\u20132975 (2013)"},{"issue":"3","key":"545_CR31","doi-asserted-by":"publisher","first-page":"641","DOI":"10.1016\/j.laa.2010.09.020","volume":"435","author":"ME Kilmer","year":"2011","unstructured":"Kilmer, M.E., Martin, C.D.: Factorization strategies for third-order tensors. Linear Algebra Appl. 435(3), 641\u2013658 (2011)","journal-title":"Linear Algebra Appl."},{"key":"545_CR32","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Ely, G., Aeron, S., Hao, N., Kilmer, M.: Novel methods for multilinear data completion and de-noising based on tensor-SVD. In: Proceedings of The IEEE Conference on Computer Vision and Pattern Recognition, pp. 3842\u20133849 (2014)","DOI":"10.1109\/CVPR.2014.485"},{"issue":"7","key":"545_CR33","doi-asserted-by":"publisher","first-page":"1867","DOI":"10.1007\/s10994-021-05987-8","volume":"110","author":"H Kong","year":"2021","unstructured":"Kong, H., Lu, C., Lin, Z.: Tensor Q-rank: new data dependent definition of tensor rank. Mach. Learn. 110(7), 1867\u20131900 (2021)","journal-title":"Mach. Learn."},{"issue":"3","key":"545_CR34","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1109\/TPAMI.2017.2689021","volume":"40","author":"C Lu","year":"2018","unstructured":"Lu, C., Feng, J., Yan, S., Lin, Z.: A unified alternating direction method of multipliers by majorization minimization. IEEE Trans. Pattern Anal. Mach. Intell. 40(3), 527\u2013541 (2018)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"4","key":"545_CR35","doi-asserted-by":"publisher","first-page":"925","DOI":"10.1109\/TPAMI.2019.2891760","volume":"42","author":"C Lu","year":"2020","unstructured":"Lu, C., Feng, J., Chen, Y., Lin, Z., Yan, S.: Tensor robust principal component analysis with a new tensor nuclear norm. IEEE Trans. Pattern Anal. Mach. Intell. 42(4), 925\u2013938 (2020)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"4","key":"545_CR36","doi-asserted-by":"publisher","first-page":"1678","DOI":"10.1109\/TIP.2014.2305840","volume":"23","author":"O Semerci","year":"2014","unstructured":"Semerci, O., Hao, N., Kilmer, M.E., Mille, E.L.: Tensor-based formulation and nuclear norm regularization for multienergy computed tomography. IEEE Trans. Image Process. 23(4), 1678\u20131693 (2014)","journal-title":"IEEE Trans. Image Process."},{"key":"545_CR37","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton, NJ (1970)"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-023-00545-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10589-023-00545-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-023-00545-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,6]],"date-time":"2024-11-06T17:08:59Z","timestamp":1730912939000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10589-023-00545-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,21]]},"references-count":37,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,4]]}},"alternative-id":["545"],"URL":"https:\/\/doi.org\/10.1007\/s10589-023-00545-5","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"type":"print","value":"0926-6003"},{"type":"electronic","value":"1573-2894"}],"subject":[],"published":{"date-parts":[[2023,12,21]]},"assertion":[{"value":"6 July 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 December 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 December 2023","order":3,"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 conflicts of interest to this work.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}