{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,25]],"date-time":"2026-07-25T07:11:43Z","timestamp":1784963503084,"version":"3.55.0"},"reference-count":15,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2006,12,1]],"date-time":"2006-12-01T00:00:00Z","timestamp":1164931200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[2006,12]]},"abstract":"<jats:p>\n            Tensors (also known as multidimensional arrays or\n            <jats:italic>N<\/jats:italic>\n            -way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as tensor multiplication. The tensor_as_matrix class supports the \u201cmatricization\u201d of a tensor, that is, the conversion of a tensor to a matrix (and vice versa), a commonly used operation in many algorithms. Two additional classes represent tensors stored in decomposed formats: cp_tensor and tucker_tensor. We describe all of these classes and then demonstrate their use by showing how to implement several tensor algorithms that have appeared in the literature.\n          <\/jats:p>","DOI":"10.1145\/1186785.1186794","type":"journal-article","created":{"date-parts":[[2007,1,16]],"date-time":"2007-01-16T19:38:29Z","timestamp":1168976309000},"page":"635-653","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":351,"title":["Algorithm 862"],"prefix":"10.1145","volume":"32","author":[{"given":"Brett W.","family":"Bader","sequence":"first","affiliation":[{"name":"Sandia National Laboratories, Livermore, CA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tamara G.","family":"Kolda","sequence":"additional","affiliation":[{"name":"Sandia National Laboratories, Livermore, CA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2006,12]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0169-7439(00)00071-X"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02310791"},{"key":"e_1_2_2_3_1","first-page":"487","article-title":"Blind identification of convolutive mim systems with 3 sources and 2 sensors","volume":"5","author":"Chen B.","year":"2002","unstructured":"Chen , B. , Petropolu , A. , and De Lathauwer , L. 2002 . Blind identification of convolutive mim systems with 3 sources and 2 sensors . Appl. Signal Processing 5 , 487 -- 496 . Chen, B., Petropolu, A., and De Lathauwer, L. 2002. Blind identification of convolutive mim systems with 3 sources and 2 sensors. Appl. Signal Processing 5, 487--496.","journal-title":"Appl. Signal Processing"},{"key":"e_1_2_2_4_1","volume-title":"Mathematics in Signal Processing V","author":"Comon P.","unstructured":"Comon , P. 2001. Tensor decompositions . In Mathematics in Signal Processing V , J. G. McWhirter and I. K. Proudler, Eds. Oxford University Press , Oxford, UK , 1--24. Comon, P. 2001. Tensor decompositions. In Mathematics in Signal Processing V, J. G. McWhirter and I. K. Proudler, Eds. Oxford University Press, Oxford, UK, 1--24."},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479896305696"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479898346995"},{"key":"e_1_2_2_7_1","first-page":"1","article-title":"Foundations of the PARAFAC procedure: Models and conditions for an \u201cexplanatory\u201d multi-modal factor analysis","volume":"16","author":"Harshman R. A.","year":"1970","unstructured":"Harshman , R. A. 1970 . Foundations of the PARAFAC procedure: Models and conditions for an \u201cexplanatory\u201d multi-modal factor analysis . UCLA Working Papers in Phonetics 16 , 1 -- 84 . Harshman, R. A. 1970. Foundations of the PARAFAC procedure: Models and conditions for an \u201cexplanatory\u201d multi-modal factor analysis. UCLA Working Papers in Phonetics 16, 1--84.","journal-title":"UCLA Working Papers in Phonetics"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1002\/cem.665"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/1099-128X(200005\/06)14:3<105::AID-CEM582>3.0.CO;2-I"},{"key":"e_1_2_2_10_1","volume-title":"CA, July 19--23","author":"Kroonenberg P.","year":"2004","unstructured":"Kroonenberg , P. 2004. Applications of three-mode techniques: Overview, problems, and prospects. Presentation at the AIM Tensor Decompositions Workshop (Palo Alto , CA, July 19--23 , 2004 . http:\/\/csmr.ca.sandia.gov\/~tgkolda\/tdw2004\/Kroonenberg%20-%20Talk.pdf. Kroonenberg, P. 2004. Applications of three-mode techniques: Overview, problems, and prospects. Presentation at the AIM Tensor Decompositions Workshop (Palo Alto, CA, July 19--23, 2004. http:\/\/csmr.ca.sandia.gov\/~tgkolda\/tdw2004\/Kroonenberg%20-%20Talk.pdf."},{"key":"e_1_2_2_11_1","doi-asserted-by":"crossref","unstructured":"Smilde A. Bro R. and Geladi P. 2004. Multi-Way Analysis: Applications in the Chemical Sciences. Wiley.  Smilde A. Bro R. and Geladi P. 2004. Multi-Way Analysis: Applications in the Chemical Sciences. Wiley.","DOI":"10.1002\/0470012110"},{"key":"e_1_2_2_12_1","volume-title":"Documentation: MATLAB: Programming: Classes and objects","author":"The MathWorks","year":"2004","unstructured":"The MathWorks , Inc . 2004 a. Documentation: MATLAB: Programming: Classes and objects . http:\/\/www.mathworks.com\/access\/helpdesk_r13\/help\/techdoc\/matlab_prog\/ch14_oop.html. The MathWorks, Inc. 2004a. Documentation: MATLAB: Programming: Classes and objects. http:\/\/www.mathworks.com\/access\/helpdesk_r13\/help\/techdoc\/matlab_prog\/ch14_oop.html."},{"key":"e_1_2_2_13_1","volume-title":"Documentation: MATLAB: Programming: Multidimensional arrays","author":"The MathWorks","year":"2004","unstructured":"The MathWorks , Inc . 2004 b. Documentation: MATLAB: Programming: Multidimensional arrays . http:\/\/www.mathworks.com\/access\/helpdesk_r13\/help\/techdoc\/matlab_prog\/ch12_ndf.html. The MathWorks, Inc. 2004b. Documentation: MATLAB: Programming: Multidimensional arrays. http:\/\/www.mathworks.com\/access\/helpdesk_r13\/help\/techdoc\/matlab_prog\/ch12_ndf.html."},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02289464"},{"key":"e_1_2_2_15_1","volume-title":"Proceedings of the 7th European Conference on Computer Vision (ECCV'02)","volume":"2350","author":"Vasilescu M. A. O.","unstructured":"Vasilescu , M. A. O. and Terzopoulos , D . 2002. Multilinear analysis of image ensembles: Tensorfaces . In Proceedings of the 7th European Conference on Computer Vision (ECCV'02) . Copenhagen, Denmark, May. Lecture Notes in Computer Science vol. 2350 . Springer Verlag, 447--460. Vasilescu, M. A. O. and Terzopoulos, D. 2002. Multilinear analysis of image ensembles: Tensorfaces. In Proceedings of the 7th European Conference on Computer Vision (ECCV'02). Copenhagen, Denmark, May. Lecture Notes in Computer Science vol. 2350. Springer Verlag, 447--460."}],"container-title":["ACM Transactions on Mathematical Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1186785.1186794","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1186785.1186794","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T14:47:52Z","timestamp":1750258072000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1186785.1186794"}},"subtitle":["MATLAB tensor classes for fast algorithm prototyping"],"short-title":[],"issued":{"date-parts":[[2006,12]]},"references-count":15,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2006,12]]}},"alternative-id":["10.1145\/1186785.1186794"],"URL":"https:\/\/doi.org\/10.1145\/1186785.1186794","relation":{},"ISSN":["0098-3500","1557-7295"],"issn-type":[{"value":"0098-3500","type":"print"},{"value":"1557-7295","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,12]]},"assertion":[{"value":"2006-12-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}