{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T13:06:29Z","timestamp":1762175189009,"version":"3.37.3"},"reference-count":42,"publisher":"Elsevier BV","issue":"4","license":[{"start":{"date-parts":[[2000,4,1]],"date-time":"2000-04-01T00:00:00Z","timestamp":954547200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"funder":[{"DOI":"10.13039\/501100002347","name":"Bundesministerium f\u00fcr Bildung und Forschung","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002347","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Pattern Recognition"],"published-print":{"date-parts":[[2000,4]]},"DOI":"10.1016\/s0031-3203(99)00078-3","type":"journal-article","created":{"date-parts":[[2002,7,25]],"date-time":"2002-07-25T15:01:39Z","timestamp":1027609299000},"page":"651-669","source":"Crossref","is-referenced-by-count":33,"title":["Data visualization by multidimensional scaling: a deterministic annealing approach"],"prefix":"10.1016","volume":"33","author":[{"given":"Hansj\u00f6rg","family":"Klock","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joachim M.","family":"Buhmann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/S0031-3203(99)00078-3_BIB1","doi-asserted-by":"crossref","unstructured":"I. Borg, P. Groenen, Modern Multidimensional Scaling, Springer Series in Statistics, Springer, Berlin, 1997.","DOI":"10.1007\/978-1-4757-2711-1"},{"key":"10.1016\/S0031-3203(99)00078-3_BIB2","unstructured":"T.F. Cox, M.A.A. Cox, Multidimensional Scaling, Monographs on Statistics and Applied Probability, vol. 59, Chapman & Hall, London, 1994."},{"issue":"1","key":"10.1016\/S0031-3203(99)00078-3_BIB3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02289565","article-title":"Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis","volume":"29","author":"Kruskal","year":"1964","journal-title":"Psychometrika"},{"key":"10.1016\/S0031-3203(99)00078-3_BIB4","doi-asserted-by":"crossref","first-page":"1140","DOI":"10.1080\/01621459.1967.10500922","article-title":"Representations of similarity matrices by trees","volume":"62","author":"Hartigan","year":"1967","journal-title":"J. Am. Statist. Assoc."},{"key":"10.1016\/S0031-3203(99)00078-3_BIB5","doi-asserted-by":"crossref","unstructured":"H. Klock, J.M. Buhmann, Multidimensional scaling by deterministic annealing, in: M. Pellilo, E.R. Hancock (Eds.), Proc. EMMCVPR\u201997, Lecture Notes in Computer Science, vol. 1223, Springer, Berlin, 1997, pp. 245\u2013260.","DOI":"10.1007\/3-540-62909-2_84"},{"key":"10.1016\/S0031-3203(99)00078-3_BIB6","unstructured":"R.O. Duda, P.E. Hart, Pattern Classification and Scene Analysis, Wiley, New York, 1973."},{"issue":"1","key":"10.1016\/S0031-3203(99)00078-3_BIB7","doi-asserted-by":"crossref","first-page":"7, 67 ALSCAL","DOI":"10.1007\/BF02293745","article-title":"Nonmetric individual differences multidimensional scaling: an alternating least squares method with optimal scaling features","volume":"42","author":"Takane","year":"1977","journal-title":"Psychometrika"},{"issue":"5","key":"10.1016\/S0031-3203(99)00078-3_BIB8","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1109\/T-C.1969.222678","article-title":"A nonlinear mapping for data structure analysis","volume":"C-18","author":"Sammon","year":"1969","journal-title":"IEEE Trans. Comput."},{"key":"10.1016\/S0031-3203(99)00078-3_BIB9","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/BF02289630","article-title":"The analysis of proximities: multidimensional scaling with an unknown distance function I","volume":"27","author":"Shepard","year":"1962","journal-title":"Psychometrica"},{"issue":"2","key":"10.1016\/S0031-3203(99)00078-3_BIB10","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/BF02289694","article-title":"Nonmetric multidimensional scaling: a numerical method","volume":"29","author":"Kruskal","year":"1964","journal-title":"Psychometrika"},{"key":"10.1016\/S0031-3203(99)00078-3_BIB11","unstructured":"J. De Leeuw, Applications of convex analysis to multidimensional scaling, in: J.R. Barra, F. Brodeau, G. Romier, B. van Cutsen (Eds.), Recent Developments in Statistics, North-Holland, Amsterdam, 1977, pp. 133\u2013145."},{"key":"10.1016\/S0031-3203(99)00078-3_BIB12","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/BF01897162","article-title":"Convergence of the majorization method for multidimensional scaling","volume":"5","author":"De Leeuw","year":"1988","journal-title":"J. Classification"},{"key":"10.1016\/S0031-3203(99)00078-3_BIB13","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1007\/BF02294582","article-title":"A generalized majorization method for least squares multidimensional scaling of pseudodistances that may be negative","volume":"38","author":"Heiser","year":"1991","journal-title":"Psychometrika"},{"issue":"12","key":"10.1016\/S0031-3203(99)00078-3_BIB14","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/BF01202265","article-title":"The majorization approach to multidimensional scaling","volume":"12","author":"Groenen","year":"1995","journal-title":"J. Classification"},{"key":"10.1016\/S0031-3203(99)00078-3_BIB15","unstructured":"P.J.F. Groenen, The majorization approach to multidimensional scaling: some problems and extensions, PhD thesis, Leiden University, 1993."},{"issue":"2","key":"10.1016\/S0031-3203(99)00078-3_BIB16","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/0031-3203(89)90067-8","article-title":"Experiments in projection and clustering by simulated annealing","volume":"22","author":"Klein","year":"1989","journal-title":"Pattern Recognition"},{"key":"10.1016\/S0031-3203(99)00078-3_BIB17","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/BF01100693","article-title":"A class of test functions for global optimization","volume":"5","author":"Mathar","year":"1994","journal-title":"J. Global Optim."},{"issue":"2","key":"10.1016\/S0031-3203(99)00078-3_BIB18","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1109\/72.363467","article-title":"Artificial neural networks for feature extraction and multivariate data projection","volume":"6","author":"Mao","year":"1995","journal-title":"IEEE Trans. Neural Networks"},{"key":"10.1016\/S0031-3203(99)00078-3_BIB19","unstructured":"M.E. Tipping, Topographic mappings and feed-forward neural networks, PhD thesis, University of Aston in Birmingham, 1996."},{"key":"10.1016\/S0031-3203(99)00078-3_BIB20","unstructured":"D. Lowe, Novel \u2018topographic\u2019 nonlinear feature extraction using radial basis functions for concentration coding in the \u2018artifical nose\u2019, in: Proc. 3rd IEE Int. Conf. on Artificial Neural Networks, IEE, London, 1993."},{"issue":"5","key":"10.1016\/S0031-3203(99)00078-3_BIB21","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1016\/0031-3203(94)00135-9","article-title":"Multidimensional scaling by iterative majorization using radial basis functions","volume":"28","author":"Webb","year":"1995","journal-title":"Pattern Recognition"},{"key":"10.1016\/S0031-3203(99)00078-3_BIB22","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1126\/science.220.4598.671","article-title":"Optimization by simulated annealing","volume":"220","author":"Kirkpatrick","year":"1983","journal-title":"Science"},{"key":"10.1016\/S0031-3203(99)00078-3_BIB23","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1103\/PhysRev.106.620","article-title":"Information theory and statistical mechanics","volume":"106","author":"Jaynes","year":"1957","journal-title":"Phys. Rev."},{"key":"10.1016\/S0031-3203(99)00078-3_BIB24","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1109\/TPAMI.1984.4767596","article-title":"Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images","volume":"6","author":"Geman","year":"1984","journal-title":"IEEE Trans. Pattern Anal. Machine Intell."},{"issue":"8","key":"10.1016\/S0031-3203(99)00078-3_BIB25","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1103\/PhysRevLett.65.945","article-title":"Statistical mechanics and phase transitions in clustering","volume":"65","author":"Rose","year":"1990","journal-title":"Phys. Rev. Lett."},{"issue":"4","key":"10.1016\/S0031-3203(99)00078-3_BIB26","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.1109\/18.243432","article-title":"Vector quantization with complexity costs","volume":"39","author":"Buhmann","year":"1993","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"1","key":"10.1016\/S0031-3203(99)00078-3_BIB27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/34.566806","article-title":"Pairwise data clustering by deterministic annealing","volume":"19","author":"Hofmann","year":"1997","journal-title":"IEEE Trans. Pattern Anal. Machine Intell."},{"issue":"4","key":"10.1016\/S0031-3203(99)00078-3_BIB28","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1109\/34.491619","article-title":"A graduated assignment algorithm for graph matching","volume":"18","author":"Gold","year":"1996","journal-title":"IEEE Trans. Pattern Anal. Machine Intell."},{"key":"10.1016\/S0031-3203(99)00078-3_BIB29","unstructured":"J.M. Buhmann, T. Hofmann, Central and pairwise data clustering by competitive neural networks, in: Advances in Neural Information Processing Systems, vol. 6, Morgan Kaufmann, Los Altos, CA, 1994, pp. 104\u2013111."},{"key":"10.1016\/S0031-3203(99)00078-3_BIB30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","article-title":"Maximum likelihood from incomplete data via the EM algorithm","volume":"39","author":"Dempster","year":"1977","journal-title":"J. Royal Statist. Soc. Ser. B (methodological)"},{"key":"10.1016\/S0031-3203(99)00078-3_BIB31","doi-asserted-by":"crossref","unstructured":"R.M. Neal, G.E. Hinton, A new view of the EM algorithm that justifies incremental and other variants, in: M.I. Jordan (Ed.), Learning In Graphical Models, NATO ASI Series D, Kluwer Academic Publishers, Dortrecht, 1998, pp. 355\u2013368.","DOI":"10.1007\/978-94-011-5014-9_12"},{"key":"10.1016\/S0031-3203(99)00078-3_BIB32","unstructured":"W. Press, S. Teukolsky, W. Vetterling, B. Flannery, Numerical Recipes in C, 2nd ed., Cambridge University Press, Cambridge, 1992."},{"key":"10.1016\/S0031-3203(99)00078-3_BIB33","unstructured":"A.K. Jain, R.C. Dubes, Algorithms for Clustering Data, Prentice-Hall, Englewood Cliffs, NJ 07632, 1988."},{"key":"10.1016\/S0031-3203(99)00078-3_BIB34","doi-asserted-by":"crossref","unstructured":"B.D Ripley, Pattern Recognition and Neural Networks, Cambridge University Press, Cambridge, 1996.","DOI":"10.1017\/CBO9780511812651"},{"key":"10.1016\/S0031-3203(99)00078-3_BIB35","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1109\/TC.1979.1675303","article-title":"A fast converging algorithm for nonlinear mapping of high-dimensional data to a plane","volume":"C-28","author":"Niemann","year":"1979","journal-title":"IEEE Trans. Comput."},{"key":"10.1016\/S0031-3203(99)00078-3_BIB36","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1016\/0893-6080(90)90055-P","article-title":"Algebraic transformations of objective functions","volume":"3","author":"Mjolsness","year":"1990","journal-title":"Neural Networks"},{"issue":"6","key":"10.1016\/S0031-3203(99)00078-3_BIB37","doi-asserted-by":"crossref","first-page":"1365","DOI":"10.1109\/72.548165","article-title":"A Lagrangian relaxation network for graph matching","volume":"7","author":"Rangarajan","year":"1996","journal-title":"IEEE Trans. Neural Networks"},{"key":"10.1016\/S0031-3203(99)00078-3_BIB38","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.1162\/neco.1995.7.5.1079","article-title":"Convex potentials and their conjugates in analog mean-field optimization","volume":"7","author":"Elfadel","year":"1995","journal-title":"Neural Computation"},{"key":"10.1016\/S0031-3203(99)00078-3_BIB39","doi-asserted-by":"crossref","unstructured":"G. Strang, Introduction to Applied Mathematics, Wellesley, Cambridge, MA, 1986.","DOI":"10.1115\/1.3171799"},{"key":"10.1016\/S0031-3203(99)00078-3_BIB40","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1111\/j.1469-1809.1936.tb02137.x","article-title":"The use of multiple measurements on taxonomic problems","volume":"7","author":"Fisher","year":"1936","journal-title":"Ann. Eugenics"},{"key":"10.1016\/S0031-3203(99)00078-3_BIB41","unstructured":"T. Kohonen, H. Hynninen, J. Kangas, H. Laaksonen, K. Torkkola, LVQ-PAK: The learning vector quantization program package, Technical Report A30, Helsinki University of Technology, Laboratory of Computer and Information Science, FIN-02150 Espoo, Finland, 1996."},{"key":"10.1016\/S0031-3203(99)00078-3_BIB42","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1109\/12.210173","article-title":"Distortion invariant object recognition in the dynamic link architecture","volume":"42","author":"Lades","year":"1993","journal-title":"IEEE Trans. Comput."}],"container-title":["Pattern Recognition"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0031320399000783?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0031320399000783?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2024,12,4]],"date-time":"2024-12-04T05:24:47Z","timestamp":1733289887000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0031320399000783"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,4]]},"references-count":42,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2000,4]]}},"alternative-id":["S0031320399000783"],"URL":"https:\/\/doi.org\/10.1016\/s0031-3203(99)00078-3","relation":{},"ISSN":["0031-3203"],"issn-type":[{"type":"print","value":"0031-3203"}],"subject":[],"published":{"date-parts":[[2000,4]]}}}