{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T21:00:50Z","timestamp":1740171650242,"version":"3.37.3"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,10,9]],"date-time":"2022-10-09T00:00:00Z","timestamp":1665273600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,10,9]],"date-time":"2022-10-09T00:00:00Z","timestamp":1665273600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62171063"],"award-info":[{"award-number":["62171063"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Manufacturing High Quality Development Fund Project in China","award":["TC210H03D"],"award-info":[{"award-number":["TC210H03D"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["EURASIP J. Adv. Signal Process."],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Tensor decomposition is widely used to exploit the internal correlation in multi-way data analysis and process for communications and radar systems. As one of the main tensor decomposition methods, CANDECOMP\/PARAFAC decomposition has advantages of uniqueness and interpretation properties which are significant in practical applications. However, traditional decomposition method is sensitive to both predefined rank and noise that results in inaccurate tensor decomposition. In this paper, we propose a improved algorithm called the Element-wise Average Alternating Direction Method of Multipliers by minimizing the sum of all factors\u2019 trace norm and the noise variance. Our algorithm could overcome the dependence on predefined rank in traditional decomposition algorithms and alleviate the impact of noise. Moreover, this algorithm can be transferred to solve the problem of tensor completion conveniently. The simulation results show that our proposed algorithm could decompose the noisy tensor to the factors with above 90% similarity in various SNR and also interpolate the incomplete tensor with higher similar coefficient and lower relative reconstruction error when the missing rate is less than 0.5.<\/jats:p>","DOI":"10.1186\/s13634-022-00928-6","type":"journal-article","created":{"date-parts":[[2022,10,9]],"date-time":"2022-10-09T22:02:30Z","timestamp":1665352950000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["EA-ADMM: noisy tensor PARAFAC decomposition based on element-wise average ADMM"],"prefix":"10.1186","volume":"2022","author":[{"given":"Gang","family":"Yue","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3333-722X","authenticated-orcid":false,"given":"Zhuo","family":"Sun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,10,9]]},"reference":[{"key":"928_CR1","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1016\/j.inffus.2021.09.007","volume":"78","author":"L Wan","year":"2022","unstructured":"L. Wan, R. Liu, L. Sun, H. Nie, X. Wang, Uav swarm based radar signal sorting via multi-source data fusion: A deep transfer learning framework. Inf. Fusion 78, 90\u2013101 (2022). https:\/\/doi.org\/10.1016\/j.inffus.2021.09.007","journal-title":"Inf. Fusion"},{"issue":"7","key":"928_CR2","doi-asserted-by":"publisher","first-page":"1524","DOI":"10.1109\/JSAC.2017.2699338","volume":"35","author":"Z Zhou","year":"2017","unstructured":"Z. Zhou, J. Fang, L. Yang, H. Li, Z. Chen, R.S. Blum, Low-rank tensor decomposition-aided channel estimation for millimeter wave mimo-ofdm systems. IEEE J. Sel. Areas Commun. 35(7), 1524\u20131538 (2017). https:\/\/doi.org\/10.1109\/JSAC.2017.2699338","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"928_CR3","doi-asserted-by":"publisher","first-page":"69839","DOI":"10.1109\/ACCESS.2022.3187112","volume":"10","author":"G Yue","year":"2022","unstructured":"G. Yue, Z. Sun, J. Fan, Ag-lrtr: An adaptive and generic low-rank tensor-based recovery for iiot network traffic factors denoising. IEEE Access 10, 69839\u201369850 (2022). https:\/\/doi.org\/10.1109\/ACCESS.2022.3187112","journal-title":"IEEE Access"},{"issue":"20","key":"928_CR4","doi-asserted-by":"publisher","first-page":"5450","DOI":"10.1109\/TSP.2015.2454476","volume":"63","author":"AP Liavas","year":"2015","unstructured":"A.P. Liavas, N.D. Sidiropoulos, Parallel algorithms for constrained tensor factorization via alternating direction method of multipliers. IEEE Trans. Signal Process. 63(20), 5450\u20135463 (2015). https:\/\/doi.org\/10.1109\/TSP.2015.2454476","journal-title":"IEEE Trans. Signal Process."},{"key":"928_CR5","doi-asserted-by":"publisher","unstructured":"M. Roald, C. Schenker, J.E. Cohen, E. Acar, PARAFAC2 AO-ADMM: Constraints in all modes. arXiv (2021). https:\/\/doi.org\/10.48550\/ARXIV.2102.02087. https:\/\/arxiv.org\/abs\/2102.02087","DOI":"10.48550\/ARXIV.2102.02087"},{"key":"928_CR6","unstructured":"R.A. Harshman, Foundations of the parafac procedure : Models and conditions for an \u201cexplanatory\u201d multimodal factor analysis. Ucla Working Papers in Phonetics 16 (1970)"},{"key":"928_CR7","doi-asserted-by":"publisher","first-page":"108503","DOI":"10.1016\/j.comnet.2021.108503","volume":"200","author":"A Streit","year":"2021","unstructured":"A. Streit, G. H. A. Santos, R. M. M. Le\u00e3o, E. de Souza e Silva, D. Menasch\u00e9, D. Towsley, Network anomaly detection based on tensor decomposition. Comput. Netw. 200, 108503 (2021). https:\/\/doi.org\/10.1016\/j.comnet.2021.108503","journal-title":"Comput. Netw."},{"issue":"13","key":"928_CR8","doi-asserted-by":"publisher","first-page":"3551","DOI":"10.1109\/TSP.2017.2690524","volume":"65","author":"ND Sidiropoulos","year":"2017","unstructured":"N.D. Sidiropoulos, L. De Lathauwer, X. Fu, K. Huang, E.E. Papalexakis, C. Faloutsos, Tensor decomposition for signal processing and machine learning. IEEE Trans. Signal Process. 65(13), 3551\u20133582 (2017). https:\/\/doi.org\/10.1109\/TSP.2017.2690524","journal-title":"IEEE Trans. Signal Process."},{"issue":"11","key":"928_CR9","doi-asserted-by":"publisher","first-page":"2178","DOI":"10.1109\/TKDE.2018.2873391","volume":"31","author":"V Ranjbar","year":"2019","unstructured":"V. Ranjbar, M. Salehi, P. Jandaghi, M. Jalili, Qanet: Tensor decomposition approach for query-based anomaly detection in heterogeneous information networks. IEEE Trans. Knowl. Data Eng. 31(11), 2178\u20132189 (2019). https:\/\/doi.org\/10.1109\/TKDE.2018.2873391","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"928_CR10","doi-asserted-by":"publisher","unstructured":"Y. Ouyang, K. Xie, X. Wang, J. Wen, G. Zhang, Lightweight trilinear pooling based tensor completion for network traffic monitoring. in IEEE INFOCOM 2022-IEEE Conference on Computer Communications, pp. 2128\u20132137 (2022). https:\/\/doi.org\/10.1109\/INFOCOM48880.2022.9796873","DOI":"10.1109\/INFOCOM48880.2022.9796873"},{"issue":"1","key":"928_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1348\/000711000159132","volume":"53","author":"ME Timmerman","year":"2011","unstructured":"M.E. Timmerman, H. Kiers, Three-mode principal components analysis: Choosing the numbers of components and sensitivity to local optima. Br. J. Math. Stat. Psychol. 53(1), 1\u201316 (2011)","journal-title":"Br. J. Math. Stat. Psychol."},{"issue":"1","key":"928_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TFUZZ.2018.2851575","volume":"27","author":"Y Yu","year":"2019","unstructured":"Y. Yu, Z. Li, X. Liu, K. Hirota, X. Chen, T. Fernando, H.H.C. Iu, A nested tensor product model transformation. IEEE Trans. Fuzzy Syst. 27(1), 1\u201315 (2019). https:\/\/doi.org\/10.1109\/TFUZZ.2018.2851575","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"928_CR13","doi-asserted-by":"publisher","unstructured":"G. Tsitsikas, E.E. Papalexakis, The core consistency of a compressed tensor. in 2019 IEEE Data Science Workshop (DSW) (2019), pp. 1\u20135 . https:\/\/doi.org\/10.1109\/DSW.2019.8755593","DOI":"10.1109\/DSW.2019.8755593"},{"issue":"1","key":"928_CR14","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1109\/TIE.2018.2815997","volume":"66","author":"J Zhao","year":"2019","unstructured":"J. Zhao, L. Chen, W. Pedrycz, W. Wang, Variational inference-based automatic relevance determination kernel for embedded feature selection of noisy industrial data. IEEE Trans. Ind. Electron. 66(1), 416\u2013428 (2019). https:\/\/doi.org\/10.1109\/TIE.2018.2815997","journal-title":"IEEE Trans. Ind. Electron."},{"issue":"C","key":"928_CR15","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1016\/j.dsp.2015.08.014","volume":"48","author":"S Pouryazdian","year":"2016","unstructured":"S. Pouryazdian, S. Beheshti, S. Krishnan, Candecomp\/parafac model order selection based on reconstruction error in the presence of kronecker structured colored noise. Digit. Signal Process. 48(C), 12\u201326 (2016)","journal-title":"Digit. Signal Process."},{"issue":"11","key":"928_CR16","doi-asserted-by":"publisher","first-page":"2437","DOI":"10.1109\/TCYB.2014.2374695","volume":"45","author":"Y Liu","year":"2015","unstructured":"Y. Liu, F. Shang, L. Jiao, J. Cheng, H. Cheng, Trace norm regularized candecomp\/parafac decomposition with missing data. IEEE Trans. Cybern. 45(11), 2437\u20132448 (2015). https:\/\/doi.org\/10.1109\/TCYB.2014.2374695","journal-title":"IEEE Trans. Cybern."},{"issue":"3","key":"928_CR17","doi-asserted-by":"publisher","first-page":"1758","DOI":"10.1137\/120887795","volume":"6","author":"Y Xu","year":"2015","unstructured":"Y. Xu, W. Yin, A block coordinate descent method for regularized multiconvex optimization with applications to nonnegative tensor factorization and completion. SIAM J. Imaging Ences 6(3), 1758\u20131789 (2015)","journal-title":"SIAM J. Imaging Ences"},{"issue":"3","key":"928_CR18","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1007\/BF02289464","volume":"31","author":"L Tucker","year":"1966","unstructured":"L. Tucker, Some mathematical notes on three-mode factor analysis. Psychometrika 31(3), 279\u2013311 (1966)","journal-title":"Psychometrika"},{"issue":"2","key":"928_CR19","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/0024-3795(77)90069-6","volume":"18","author":"JB Kruskal","year":"1977","unstructured":"J.B. Kruskal, Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics. Linear Algebra Appl. 18(2), 95\u2013138 (1977)","journal-title":"Linear Algebra Appl."},{"key":"928_CR20","unstructured":"M. Fazel, matrix rank minimization with applications. PhD thesis, Dissertation Abstracts International, vol. 63-04, Section: B. (Adviser: Stephen P. Boy, 2002). pp. 1981"},{"issue":"1","key":"928_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/2200000016","volume":"3","author":"S Boyd","year":"2010","unstructured":"S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Ec.Kstein, Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1\u2013122 (2010)","journal-title":"Found. Trends Mach. Learn."},{"key":"928_CR22","doi-asserted-by":"publisher","unstructured":"L. Wan, K. Liu, W. Zhang, Deep learning-aided off-grid channel estimation for millimeter wave cellular systems. in IEEE Transactions on Wireless Communications, vol. 1 (2021). https:\/\/doi.org\/10.1109\/TWC.2021.3120926","DOI":"10.1109\/TWC.2021.3120926"},{"issue":"21","key":"928_CR23","doi-asserted-by":"publisher","first-page":"3445","DOI":"10.4236\/am.2014.521322","volume":"5","author":"W Li","year":"2014","unstructured":"W. Li, J. Hu, C. Chen, On accelerated singular value thresholding algorithm for matrix completion. Appl. Math. 5(21), 3445\u20133451 (2014)","journal-title":"Appl. Math."},{"key":"928_CR24","doi-asserted-by":"publisher","DOI":"10.1145\/3278607","author":"Q Song","year":"2019","unstructured":"Q. Song, H. Ge, J. Caverlee, X. Hu, Tensor completion algorithms in big data analytics. ACM Trans. Knowl. Discov. Data. (2019). https:\/\/doi.org\/10.1145\/3278607","journal-title":"ACM Trans. Knowl. Discov. Data."},{"key":"928_CR25","doi-asserted-by":"publisher","unstructured":"T.G. Kolda, J. Sun, Scalable tensor decompositions for multi-aspect data mining, in 2008 Eighth IEEE International Conference on Data Mining (2008), pp. 363\u2013372. https:\/\/doi.org\/10.1109\/ICDM.2008.89","DOI":"10.1109\/ICDM.2008.89"},{"key":"928_CR26","doi-asserted-by":"publisher","unstructured":"P. Comon, X. Luciani, A.L.F. de Almeida, Tensor decompositions, alternating least squares and other tales. J. Chemom. 23(7\u20138), 393\u2013405 (2009)https:\/\/doi.org\/10.1002\/cem.1236. analyticalsciencejournals.onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/cem.1236","DOI":"10.1002\/cem.1236"},{"issue":"2","key":"928_CR27","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1027\/1614-2241.2.2.57","volume":"2","author":"U Lorenzo-Seva","year":"2006","unstructured":"U. Lorenzo-Seva, J.M. Ten Berge, Tucker\u2019s congruence coefficient as a meaningful index of factor similarity. Methodology 2(2), 57\u201364 (2006)","journal-title":"Methodology"},{"key":"928_CR28","doi-asserted-by":"publisher","unstructured":"B. Alexeev, M.A. Forbes, J. Tsimerman, Tensor rank: Some lower and upper bounds. in 2011 IEEE 26th Annual Conference on Computational Complexity (2011). https:\/\/doi.org\/10.1109\/ccc.2011.28","DOI":"10.1109\/ccc.2011.28"}],"container-title":["EURASIP Journal on Advances in Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s13634-022-00928-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s13634-022-00928-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s13634-022-00928-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,9]],"date-time":"2022-10-09T22:05:04Z","timestamp":1665353104000},"score":1,"resource":{"primary":{"URL":"https:\/\/asp-eurasipjournals.springeropen.com\/articles\/10.1186\/s13634-022-00928-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,9]]},"references-count":28,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["928"],"URL":"https:\/\/doi.org\/10.1186\/s13634-022-00928-6","relation":{},"ISSN":["1687-6180"],"issn-type":[{"type":"electronic","value":"1687-6180"}],"subject":[],"published":{"date-parts":[[2022,10,9]]},"assertion":[{"value":"19 March 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 September 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 October 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"We agree to the publication of the paper.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"The authors declare that they have no competing interests.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"95"}}