{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,28]],"date-time":"2026-07-28T11:33:19Z","timestamp":1785238399187,"version":"3.55.0"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2018,10,22]],"date-time":"2018-10-22T00:00:00Z","timestamp":1540166400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"LABEX MILYON","award":["ANR-10-LABX-0070"],"award-info":[{"award-number":["ANR-10-LABX-0070"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Algorithmica"],"published-print":{"date-parts":[[2019,5]]},"DOI":"10.1007\/s00453-018-0525-3","type":"journal-article","created":{"date-parts":[[2018,10,22]],"date-time":"2018-10-22T01:44:15Z","timestamp":1540172655000},"page":"2092-2121","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Computing Dense Tensor Decompositions with Optimal Dimension Trees"],"prefix":"10.1007","volume":"81","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4444-1516","authenticated-orcid":false,"given":"Oguz","family":"Kaya","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yves","family":"Robert","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2018,10,22]]},"reference":[{"issue":"2","key":"525_CR1","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1002\/cem.1335","volume":"25","author":"E Acar","year":"2011","unstructured":"Acar, E., Dunlavy, D.M., Kolda, T.G.: A scalable optimization approach for fitting canonical tensor decompositions. J. Chemom. 25(2), 67\u201386 (2011)","journal-title":"J. Chemom."},{"issue":"1","key":"525_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0169-7439(00)00071-X","volume":"52","author":"CA Andersson","year":"2000","unstructured":"Andersson, C.A., Bro, R.: The N-way toolbox for MATLAB. Chemom. Intell. Lab. Syst. 52(1), 1\u20134 (2000)","journal-title":"Chemom. Intell. Lab. Syst."},{"issue":"1","key":"525_CR3","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1137\/060676489","volume":"30","author":"BW Bader","year":"2007","unstructured":"Bader, B.W., Kolda, T.G.: Efficient MATLAB computations with sparse and factored tensors. SIAM J. Sci. Comput. 30(1), 205\u2013231 (2007)","journal-title":"SIAM J. Sci. Comput."},{"key":"525_CR4","unstructured":"Bader, B.W., Kolda, T.G., et\u00a0al.: Matlab tensor toolbox version 2.6. Available online (2015)"},{"key":"525_CR5","doi-asserted-by":"publisher","unstructured":"Baskaran, M., Meister, B., Vasilache, N., Lethin, R.: Efficient and scalable computations with sparse tensors. In: Proceedings of the IEEE Conference on High Performance Extreme Computing, HPEC 2012, pp. 1\u20136 (2012). https:\/\/doi.org\/10.1109\/HPEC.2012.6408676","DOI":"10.1109\/HPEC.2012.6408676"},{"key":"525_CR6","unstructured":"Carlson, A., Betteridge, J., Kisiel, B., Settles, B., Jr., E.R.H., Mitchell, T.M.: Toward an architecture for never-ending language learning. In: Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence, AAAI \u201910, pp. 1306\u20131313. AAAI Press (2010). http:\/\/dl.acm.org\/citation.cfm?id=2898607.2898816"},{"issue":"3","key":"525_CR7","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1007\/BF02310791","volume":"35","author":"DJ Carroll","year":"1970","unstructured":"Carroll, D.J., Chang, J.: Analysis of individual differences in multidimensional scaling via an N-way generalization of \u201cEckart-Young\u201d decomposition. Psychometrika 35(3), 283\u2013319 (1970)","journal-title":"Psychometrika"},{"key":"525_CR8","doi-asserted-by":"crossref","unstructured":"Chakaravarthy, V.T., Choi, J., Joseph, D.J., Liu, X., Murali, P., Sabharwal, Y., Sreedhar, D.: On optimizing distributed tucker decomposition for dense tensors. In: Proceedings of the IEEE International Symposium on Parallel and Distributed Processing, IPDPS \u201917, Orlando, FL, USA (2017)","DOI":"10.1109\/IPDPS.2017.86"},{"key":"525_CR9","unstructured":"Choi, J.H., Vishwanathan, S.V.N.: DFacTo: distributed factorization of tensors. In: 27th Advances in Neural Information Processing Systems, Montreal, Quebec, Canada, pp. 1296\u20131304 (2014)"},{"issue":"4","key":"525_CR10","doi-asserted-by":"publisher","first-page":"2029","DOI":"10.1137\/090764189","volume":"31","author":"L Grasedyck","year":"2010","unstructured":"Grasedyck, L.: Hierarchical singular value decomposition of tensors. SIAM J. Matrix Anal. Appl. 31(4), 2029\u20132054 (2010)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"525_CR11","unstructured":"Harshman, R.A.: Foundations of the PARAFAC procedure: models and conditions for an \u201cexplanatory\u201d multi-modal factor analysis. UCLA Working Papers in Phonetics 16, 1\u201384 (1970)"},{"issue":"4","key":"525_CR12","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"},{"key":"525_CR13","doi-asserted-by":"crossref","unstructured":"Kang, U., Papalexakis, E., Harpale, A., Faloutsos, C.: GigaTensor: Scaling tensor analysis up by 100 times\u2014algorithms and discoveries. In: Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD \u201912, pp. 316\u2013324. ACM, New York (2012)","DOI":"10.1145\/2339530.2339583"},{"key":"525_CR14","doi-asserted-by":"crossref","unstructured":"Kaya, O., U\u00e7ar, B.: High-performance parallel algorithms for the Tucker decomposition of higher order sparse tensors. Technical Report RR-8801, Inria, Grenoble\u2013Rh\u00f4ne-Alpes (2015)","DOI":"10.1109\/ICPP.2016.19"},{"key":"525_CR15","doi-asserted-by":"crossref","unstructured":"Kaya, O., U\u00e7ar, B.: Scalable sparse tensor decompositions in distributed memory systems. Technical Report RR-8722, Inria, Grenoble\u2013Rh\u00f4ne-Alpes (2015)","DOI":"10.1145\/2807591.2807624"},{"key":"525_CR16","doi-asserted-by":"publisher","unstructured":"Kaya, O., U\u00e7ar, B.: Scalable sparse tensor decompositions in distributed memory systems. In: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, SC \u201915, pp. 77:1\u201377:11. ACM, New York (2015). https:\/\/doi.org\/10.1145\/2807591.2807624","DOI":"10.1145\/2807591.2807624"},{"key":"525_CR17","doi-asserted-by":"publisher","unstructured":"Kaya, O., U\u00e7ar, B.: High performance parallel algorithms for the Tucker decomposition of sparse tensors. In: Proceedings of the 45th International Conference on Parallel Processing, ICPP \u201916, pp. 103\u2013112 (2016). https:\/\/doi.org\/10.1109\/ICPP.2016.19","DOI":"10.1109\/ICPP.2016.19"},{"key":"525_CR18","unstructured":"Kaya, O., U\u00e7ar, B.: Parallel CP decomposition of sparse tensors using dimension trees. Research Report RR-8976, Inria - Research Centre Grenoble\u2013Rh\u00f4ne-Alpes (2016)"},{"key":"525_CR19","unstructured":"Kolda, T.G., Bader, B.: The TOPHITS model for higher-order web link analysis. In: Proceedings of Link Analysis, Counterterrorism and Security, pp. 26\u201329 (2006)"},{"issue":"3","key":"525_CR20","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1137\/07070111X","volume":"51","author":"TG Kolda","year":"2009","unstructured":"Kolda, T.G., Bader, B.: Tensor decompositions and applications. SIAM Rev. 51(3), 455\u2013500 (2009)","journal-title":"SIAM Rev."},{"key":"525_CR21","unstructured":"Lathauwer, L.D., Moor, B.D.: From matrix to tensor: Multilinear algebra and signal processing. In: Proceedings of the Institute of Mathematics and Its Applications Conference Series, vol. 67, pp. 1\u201316 (1998)"},{"issue":"4","key":"525_CR22","doi-asserted-by":"publisher","first-page":"1253","DOI":"10.1137\/S0895479896305696","volume":"21","author":"LD Lathauwer","year":"2000","unstructured":"Lathauwer, L.D., Moor, B.D., Vandewalle, J.: A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl. 21(4), 1253\u20131278 (2000)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"525_CR23","doi-asserted-by":"crossref","unstructured":"Li, J., Choi, J., Perros, I., Sun, J., Vuduc, R.: Model-driven sparse CP decomposition for higher-order tensors. In: Proceedings of the IEEE International Symposium on Parallel and Distributed Processing, IPDPS \u201917, Orlando, FL, USA, pp. 1048\u20131057 (2017)","DOI":"10.1109\/IPDPS.2017.80"},{"issue":"2","key":"525_CR24","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1016\/j.ejor.2010.05.034","volume":"207","author":"C Ng","year":"2010","unstructured":"Ng, C., Barketau, M., Cheng, T., Kovalyov, M.Y.: Product partition and related problems of scheduling and systems reliability: computational complexity and approximation. Eur. J. Oper. Res. 207(2), 601\u2013604 (2010). https:\/\/doi.org\/10.1016\/j.ejor.2010.05.034","journal-title":"Eur. J. Oper. Res."},{"issue":"6","key":"525_CR25","doi-asserted-by":"publisher","first-page":"1193","DOI":"10.1109\/TASL.2009.2031694","volume":"18","author":"D Nion","year":"2010","unstructured":"Nion, D., Mokios, K.N., Sidiropoulos, N.D., Potamianos, A.: Batch and adaptive PARAFAC-based blind separation of convolutive speech mixtures. IEEE Trans. Audio Speech Lang. Process. 18(6), 1193\u20131207 (2010). https:\/\/doi.org\/10.1109\/TASL.2009.2031694","journal-title":"IEEE Trans. Audio Speech Lang. Process."},{"issue":"11","key":"525_CR26","doi-asserted-by":"publisher","first-page":"5693","DOI":"10.1109\/TSP.2010.2058802","volume":"58","author":"D Nion","year":"2010","unstructured":"Nion, D., Sidiropoulos, N.D.: Tensor algebra and multidimensional harmonic retrieval in signal processing for mimo radar. IEEE Trans. Signal Process. 58(11), 5693\u20135705 (2010). https:\/\/doi.org\/10.1109\/TSP.2010.2058802","journal-title":"IEEE Trans. Signal Process."},{"key":"525_CR27","doi-asserted-by":"crossref","unstructured":"Perros, I., Chen, R., Vuduc, R., Sun, J.: Sparse hierarchical Tucker factorization and its application to healthcare. In: Proceedings of the 2015 IEEE International Conference on Data Mining, ICDM 2015, pp. 943\u2013948 (2015)","DOI":"10.1109\/ICDM.2015.29"},{"issue":"19","key":"525_CR28","doi-asserted-by":"publisher","first-page":"4834","DOI":"10.1109\/TSP.2013.2269903","volume":"61","author":"AH Phan","year":"2013","unstructured":"Phan, A.H., Tichavsk\u00fd, P., Cichocki, A.: Fast alternating LS algorithms for high order CANDECOMP\/PARAFAC tensor factorizations. IEEE Trans. Signal Process. 61(19), 4834\u20134846 (2013). https:\/\/doi.org\/10.1109\/TSP.2013.2269903","journal-title":"IEEE Trans. Signal Process."},{"key":"525_CR29","doi-asserted-by":"publisher","unstructured":"Rendle, S., Lars, T.S.: Pairwise interaction tensor factorization for personalized tag recommendation. In: Proceedings of the Third ACM International Conference on Web Search and Data Mining, WSDM \u201910, pp. 81\u201390. ACM, New York (2010). https:\/\/doi.org\/10.1145\/1718487.1718498","DOI":"10.1145\/1718487.1718498"},{"key":"525_CR30","doi-asserted-by":"publisher","unstructured":"Rendle, S., Leandro, B.M., Nanopoulos, A., Schmidt-Thieme, L.: Learning optimal ranking with tensor factorization for tag recommendation. In: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD \u201909, pp. 727\u2013736. ACM, New York (2009). https:\/\/doi.org\/10.1145\/1557019.1557100","DOI":"10.1145\/1557019.1557100"},{"issue":"8","key":"525_CR31","doi-asserted-by":"publisher","first-page":"2377","DOI":"10.1109\/78.852018","volume":"48","author":"ND Sidiropoulos","year":"2000","unstructured":"Sidiropoulos, N.D., Bro, R., Giannakis, G.B.: Parallel factor analysis in sensor array processing. IEEE Trans. Signal Process. 48(8), 2377\u20132388 (2000). https:\/\/doi.org\/10.1109\/78.852018","journal-title":"IEEE Trans. Signal Process."},{"key":"525_CR32","doi-asserted-by":"crossref","unstructured":"Smith, S., Karypis, G.: A medium-grained algorithm for sparse tensor factorization. In: 2016 IEEE International Parallel and Distributed Processing Symposium, IPDPS 2016, Chicago, IL, USA, May 23\u201327, 2016, pp. 902\u2013911 (2016)","DOI":"10.1109\/IPDPS.2016.113"},{"key":"525_CR33","doi-asserted-by":"crossref","unstructured":"Smith, S., Ravindran, N., Sidiropoulos, N.D., Karypis, G.: SPLATT: Efficient and parallel sparse tensor\u2013matrix multiplication. In: Proceedings of the 29th IEEE International Parallel and Distributed Processing Symposium, IPDPS \u201915, pp. 61\u201370. IEEE Computer Society, Hyderabad (2015)","DOI":"10.1109\/IPDPS.2015.27"},{"key":"525_CR34","doi-asserted-by":"publisher","unstructured":"Symeonidis, P., Nanopoulos, A., Manolopoulos, Y.: Tag recommendations based on tensor dimensionality reduction. In: Proceedings of the 2008 ACM Conference on Recommender Systems, RecSys \u201908, pp. 43\u201350. ACM, New York (2008). https:\/\/doi.org\/10.1145\/1454008.1454017","DOI":"10.1145\/1454008.1454017"},{"key":"525_CR35","doi-asserted-by":"crossref","unstructured":"Vasilescu, M.A.O., Terzopoulos, D.: Multilinear analysis of image ensembles: TensorFaces. In: Computer Vision\u2014ECCV 2002, pp. 447\u2013460. Springer, Berlin (2002)","DOI":"10.1007\/3-540-47969-4_30"}],"container-title":["Algorithmica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00453-018-0525-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00453-018-0525-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00453-018-0525-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,27]],"date-time":"2019-10-27T06:57:43Z","timestamp":1572159463000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00453-018-0525-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,22]]},"references-count":35,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2019,5]]}},"alternative-id":["525"],"URL":"https:\/\/doi.org\/10.1007\/s00453-018-0525-3","relation":{},"ISSN":["0178-4617","1432-0541"],"issn-type":[{"value":"0178-4617","type":"print"},{"value":"1432-0541","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,22]]},"assertion":[{"value":"22 December 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 October 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 October 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}