{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T22:05:15Z","timestamp":1780524315355,"version":"3.54.1"},"reference-count":22,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2003,7,31]],"date-time":"2003-07-31T00:00:00Z","timestamp":1059609600000},"content-version":"vor","delay-in-days":152,"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2003,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The magnification behavior of a generalized family of self\u2010organizing feature maps, the winner relaxing and winner enhancing Kohonen algorithms is analyzed by the magnification law in the one\u2010dimensional case, which can be obtained analytically. The winner\u2010enhancing case allows to achieve a magnification exponent of one and therefore provides optimal mapping in the sense of information theory. A numerical verification of the magnification law is included, and the ordering behavior is analyzed. Compared to the original self\u2010organizing map and some other approaches, the generalized winner enforcing algorithm requires minimal extra computations per learning step and is conveniently easy to implement. \u00a9 2003 Wiley Periodicals, Inc.<\/jats:p>","DOI":"10.1002\/cplx.10084","type":"journal-article","created":{"date-parts":[[2003,8,1]],"date-time":"2003-08-01T10:15:55Z","timestamp":1059732955000},"page":"15-22","source":"Crossref","is-referenced-by-count":5,"title":["Winner\u2010relaxing and winner\u2010enhancing Kohonen maps: Maximal mutual information from enhancing the winner"],"prefix":"10.1002","volume":"8","author":[{"given":"Jens Christian","family":"Claussen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2003,7,31]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00337288"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1038\/326689a0"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1989.1.3.402"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00205972"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.45.7568"},{"key":"e_1_2_1_7_2","volume-title":"Artificial Neural Networks","author":"Kohonen T.","year":"1991"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00320480"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","unstructured":"Claussen J.C.;Schuster H.G.Asymptotic level density of the elastic net self\u2010organizing map; Dorronsoro J.R. Ed. Proc ICANN 2002; pp939\u2013944.","DOI":"10.1007\/3-540-46084-5_152"},{"key":"e_1_2_1_10_2","volume-title":"Neuronale Netze","author":"Ritter H.","year":"1992"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.220.4598.671"},{"key":"e_1_2_1_12_2","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/BF00339943","article-title":"Neural computation of decisions in optimization problems","volume":"52","author":"Hopfield J.J.","year":"1985","journal-title":"Biol Cybernet"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1088\/0954-898X\/1\/1\/007"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1088\/0954-898X\/10\/1\/003"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1109\/72.80310"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1109\/72.363433"},{"key":"e_1_2_1_17_2","unstructured":"Claussen (born Gruel) J.C.1992.Selbstorganisation Neuronaler Karten. Diploma thesis Kiel Germany; J.C. Claussen and H.G. Schuster preprint 1994."},{"key":"e_1_2_1_18_2","first-page":"75","article-title":"Optimal magnification factors in self\u2010organizing maps","author":"Hermann M.","year":"1995","journal-title":"Proc ICANN"},{"key":"e_1_2_1_19_2","first-page":"191","article-title":"Magnification control in neural maps","author":"Villmann T.","year":"1998","journal-title":"Proc ESANN"},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.56.3876"},{"key":"e_1_2_1_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/B978-044450270-4\/50024-3"},{"key":"e_1_2_1_22_2","unstructured":"Claussen J.C.Generalized winner relaxing Kohonen feature maps e\u2010print cond\u2010mat\/0208414;2002."},{"key":"e_1_2_1_23_2","first-page":"93","volume-title":"Magnification control in winner relaxing neural gas","author":"Claussen J.C.","year":"2003"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fcplx.10084","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/cplx.10084","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T05:08:41Z","timestamp":1694495321000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/10.1002\/cplx.10084"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,3]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2003,3]]}},"alternative-id":["10.1002\/cplx.10084"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1002\/cplx.10084","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"value":"1076-2787","type":"print"},{"value":"1099-0526","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,3]]}}}