{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T22:38:17Z","timestamp":1767911897760,"version":"3.49.0"},"reference-count":32,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Neur. Syst."],"published-print":{"date-parts":[[2010,6]]},"abstract":"<jats:p> We present several applications of non-linear data modeling, using principal manifolds and principal graphs constructed using the metaphor of elasticity (elastic principal graph approach). These approaches are generalizations of the Kohonen's self-organizing maps, a class of artificial neural networks. On several examples we show advantages of using non-linear objects for data approximation in comparison to the linear ones. We propose four numerical criteria for comparing linear and non-linear mappings of datasets into the spaces of lower dimension. The examples are taken from comparative political science, from analysis of high-throughput data in molecular biology, from analysis of dynamical systems. <\/jats:p>","DOI":"10.1142\/s0129065710002383","type":"journal-article","created":{"date-parts":[[2010,6,16]],"date-time":"2010-06-16T11:27:25Z","timestamp":1276687645000},"page":"219-232","source":"Crossref","is-referenced-by-count":103,"title":["PRINCIPAL MANIFOLDS AND GRAPHS IN PRACTICE: FROM MOLECULAR BIOLOGY TO DYNAMICAL SYSTEMS"],"prefix":"10.1142","volume":"20","author":[{"given":"ALEXANDER N.","family":"GORBAN","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ANDREI","family":"ZINOVYEV","sequence":"additional","affiliation":[{"name":"Institut Curie, U900 INSERM\/Curie\/Mines Paritech, rue d'Ulm 26, Paris, 75005, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,4,30]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00337288"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0129065707001044"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1142\/S0129065708001579"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S0129065708001749"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/BF00201801"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1989.10478797"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1995.7.6.1165"},{"key":"rf8","volume-title":"Neural Computation and Self-Organizing Maps: An Introduction","author":"Ritter H.","year":"1992"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1109\/34.982884"},{"key":"rf10","first-page":"825","volume":"38","author":"Gorban A. N.","journal-title":"Journal of Computer and System Sciences International"},{"key":"rf11","unstructured":"A.\u00a0Zinovyev, Visualization of Multidimensional Data (Krasnoyarsk State University Press Publ., 2000)\u00a0p. 168."},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/s00607-005-0122-6"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2006.04.022"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-73750-6"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-73750-6_4"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-73750-6_4"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.4018\/978-1-60566-766-9.ch002"},{"key":"rf18","first-page":"363","volume":"11","author":"Gorban A. N.","journal-title":"Smart Engineering System Design"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(93)90068-5"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1007\/BF02241984"},{"key":"rf22","volume":"5","author":"Melville A. Yu.","journal-title":"Polis"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1016\/j.tig.2003.09.015"},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1142\/S012906570800135X"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1016\/S0140-6736(05)70933-8"},{"key":"rf27","doi-asserted-by":"publisher","DOI":"10.1038\/ng1061"},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.1186\/gb-2005-6-3-r22"},{"key":"rf29","doi-asserted-by":"publisher","DOI":"10.1007\/b98103"},{"key":"rf30","doi-asserted-by":"publisher","DOI":"10.1186\/1752-0509-2-86"},{"key":"rf32","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2003.10.043"},{"key":"rf33","first-page":"3","volume":"37","author":"Karhunen K.","journal-title":"Ann. Acad. Sci. Fennicae, Series A1, Math. Phys."},{"key":"rf34","volume-title":"Probability Theory","author":"Lo\u00e8ve M. M.","year":"1955"},{"key":"rf36","doi-asserted-by":"publisher","DOI":"10.1109\/72.238311"}],"container-title":["International Journal of Neural Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129065710002383","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T16:50:46Z","timestamp":1565110246000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129065710002383"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,6]]},"references-count":32,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2012,4,30]]},"published-print":{"date-parts":[[2010,6]]}},"alternative-id":["10.1142\/S0129065710002383"],"URL":"https:\/\/doi.org\/10.1142\/s0129065710002383","relation":{},"ISSN":["0129-0657","1793-6462"],"issn-type":[{"value":"0129-0657","type":"print"},{"value":"1793-6462","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,6]]}}}