{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:39:28Z","timestamp":1740123568559,"version":"3.37.3"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,8,22]],"date-time":"2022-08-22T00:00:00Z","timestamp":1661126400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,8,22]],"date-time":"2022-08-22T00:00:00Z","timestamp":1661126400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771099"],"award-info":[{"award-number":["11771099"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2022,10]]},"DOI":"10.1007\/s10915-022-01973-x","type":"journal-article","created":{"date-parts":[[2022,8,22]],"date-time":"2022-08-22T19:02:49Z","timestamp":1661194969000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The Abstract Laplacian Tensor of a Hypergraph with Applications in Clustering"],"prefix":"10.1007","volume":"93","author":[{"given":"Tianhang","family":"Liu","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6192-0546","authenticated-orcid":false,"given":"Yimin","family":"Wei","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,8,22]]},"reference":[{"key":"1973_CR1","volume-title":"Optimization Algorithms on Matrix Manifolds","author":"P-A Absil","year":"2009","unstructured":"Absil, P.-A., Mahony, R., Sepulchre, R.: Optimization Algorithms on Matrix Manifolds. Princeton University Press, Princeton, NJ (2009)"},{"key":"1973_CR2","first-page":"283","volume":"67","author":"S Amghibech","year":"2003","unstructured":"Amghibech, S.: Eigenvalues of the discrete p-Laplacian for graphs. Ars Combin. 67, 283\u2013302 (2003)","journal-title":"Ars Combin."},{"key":"1973_CR3","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1016\/j.tcs.2016.03.016","volume":"658","author":"G Ausiello","year":"2017","unstructured":"Ausiello, G., Laura, L.: Directed hypergraphs: introduction and fundamental algorithms - a survey. Theoret. Comput. Sci. 658, 293\u2013306 (2017)","journal-title":"Theoret. Comput. Sci."},{"key":"1973_CR4","doi-asserted-by":"crossref","unstructured":"Berge, C.: Hypergraphs: Combinatorics of Finite Sets, volume 45. Elsevier, North Holland (1984)","DOI":"10.1016\/S0304-0208(08)72921-9"},{"issue":"3","key":"1973_CR5","doi-asserted-by":"publisher","first-page":"1157","DOI":"10.1137\/19M1291601","volume":"13","author":"J Chang","year":"2020","unstructured":"Chang, J., Chen, Y., Qi, L., Yan, H.: Hypergraph clustering using a new Laplacian tensor with applications in image processing. SIAM J. Imag. Sci. 13(3), 1157\u20131178 (2020)","journal-title":"SIAM J. Imag. Sci."},{"issue":"1","key":"1973_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10915-017-0520-x","volume":"75","author":"J Chang","year":"2018","unstructured":"Chang, J., Ding, W., Qi, L., Yan, H.: Computing the p-spectral radii of uniform hypergraphs with applications. J. Sci. Comput. 75(1), 1\u201325 (2018)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"1973_CR7","doi-asserted-by":"publisher","first-page":"507","DOI":"10.4310\/CMS.2008.v6.n2.a12","volume":"6","author":"K-C Chang","year":"2008","unstructured":"Chang, K.-C., Pearson, K., Zhang, T.: Perron-frobenius theorem for nonnegative tensors. Commun. Math. Sci. 6(2), 507\u2013520 (2008)","journal-title":"Commun. Math. Sci."},{"issue":"1","key":"1973_CR8","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1016\/j.jmaa.2008.09.067","volume":"350","author":"K-C Chang","year":"2009","unstructured":"Chang, K.-C., Pearson, K., Zhang, T.: On eigenvalue problems of real symmetric tensors. J. Math. Anal. Appl. 350(1), 416\u2013422 (2009)","journal-title":"J. Math. Anal. Appl."},{"issue":"4","key":"1973_CR9","doi-asserted-by":"publisher","first-page":"2889","DOI":"10.1109\/TNSE.2020.3002963","volume":"7","author":"C Chen","year":"2020","unstructured":"Chen, C., Rajapakse, I.: Tensor entropy for uniform hypergraphs. IEEE Transactions on Network Science and Engineering 7(4), 2889\u20132900 (2020)","journal-title":"IEEE Transactions on Network Science and Engineering"},{"issue":"6","key":"1973_CR10","doi-asserted-by":"publisher","first-page":"A2508","DOI":"10.1137\/16M1094828","volume":"39","author":"Y Chen","year":"2017","unstructured":"Chen, Y., Qi, L., Zhang, X.: The Fiedler vector of a Laplacian tensor for hypergraph partitioning. SIAM J. Sci. Comput. 39(6), A2508\u2013A2537 (2017)","journal-title":"SIAM J. Sci. Comput."},{"key":"1973_CR11","unstructured":"Chowdhury, S., Needham, T., Semrad, E., Wang, B., Zhou, Y.: Hypergraph co-optimal transport: Metric and categorical properties. arXiv:2112.03904v2, (2021)"},{"key":"1973_CR12","unstructured":"Chung, F.R., Graham, F.C.: Spectral Graph Theory. Number\u00a092. American Mathematical Society, Providence, RI (1997)"},{"issue":"9","key":"1973_CR13","doi-asserted-by":"publisher","first-page":"3268","DOI":"10.1016\/j.laa.2011.11.018","volume":"436","author":"J Cooper","year":"2012","unstructured":"Cooper, J., Dutle, A.: Spectra of uniform hypergraphs. Linear Algebra Appl. 436(9), 3268\u20133292 (2012)","journal-title":"Linear Algebra Appl."},{"issue":"3","key":"1973_CR14","doi-asserted-by":"publisher","first-page":"1073","DOI":"10.1137\/140975656","volume":"36","author":"W Ding","year":"2015","unstructured":"Ding, W., Wei, Y.: Generalized tensor eigenvalue problems. SIAM J. Matrix Anal. Appl. 36(3), 1073\u20131099 (2015)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"2","key":"1973_CR15","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1007\/s10107-014-0816-7","volume":"153","author":"B Jiang","year":"2015","unstructured":"Jiang, B., Dai, Y.-H.: A framework of constraint preserving update schemes for optimization on Stiefel manifold. Math. Program. 153(2), 535\u2013575 (2015)","journal-title":"Math. Program."},{"key":"1973_CR16","unstructured":"Lim, L.-H.: Singular values and eigenvalues of tensors: a variational approach. In 1st IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, 2005., pages 129\u2013132. IEEE, (2005)"},{"key":"1973_CR17","unstructured":"Ly, I.: The first eigenvalue for the p-Laplacian operator. Journal of Inequalities in Pure and Applied Mathematics, 6, Article 91, (2005)"},{"issue":"6","key":"1973_CR18","doi-asserted-by":"publisher","first-page":"1302","DOI":"10.1016\/j.jsc.2005.05.007","volume":"40","author":"L Qi","year":"2005","unstructured":"Qi, L.: Eigenvalues of a real supersymmetric tensor. J. Symb. Comput. 40(6), 1302\u20131324 (2005)","journal-title":"J. Symb. Comput."},{"issue":"6","key":"1973_CR19","doi-asserted-by":"publisher","first-page":"1045","DOI":"10.4310\/CMS.2014.v12.n6.a3","volume":"12","author":"L Qi","year":"2014","unstructured":"Qi, L.: $${H}^+$$-eigenvalues of Laplacian and signless Laplacian tensors. Commun. Math. Sci. 12(6), 1045\u20131064 (2014)","journal-title":"Commun. Math. Sci."},{"key":"1973_CR20","doi-asserted-by":"crossref","unstructured":"Qi, L., Luo, Z.: Tensor Analysis: Spectral Theory and Special Tensors, volume 151. SIAM, (2017)","DOI":"10.1137\/1.9781611974751"},{"key":"1973_CR21","doi-asserted-by":"crossref","unstructured":"Veldt, N., Benson, A.R., Kleinberg, J.: Minimizing localized ratio cut objectives in hypergraphs. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pages 1708\u20131718, (2020)","DOI":"10.1145\/3394486.3403222"},{"key":"1973_CR22","first-page":"1601","volume":"19","author":"D Zhou","year":"2006","unstructured":"Zhou, D., Huang, J., Sch\u00f6lkopf, B.: Learning with hypergraphs: Clustering, classification, and embedding. Adv. Neural. Inf. Process. Syst. 19, 1601\u20131608 (2006)","journal-title":"Adv. Neural. Inf. Process. Syst."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-022-01973-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-022-01973-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-022-01973-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,31]],"date-time":"2022-10-31T23:54:52Z","timestamp":1667260492000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-022-01973-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,22]]},"references-count":22,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,10]]}},"alternative-id":["1973"],"URL":"https:\/\/doi.org\/10.1007\/s10915-022-01973-x","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2022,8,22]]},"assertion":[{"value":"18 December 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 July 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 August 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 August 2022","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 have not disclosed any competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"7"}}