{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,7]],"date-time":"2024-09-07T18:14:57Z","timestamp":1725732897961},"publisher-location":"Berlin, Heidelberg","reference-count":18,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642386787"},{"type":"electronic","value":"9783642386794"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-38679-4_50","type":"book-chapter","created":{"date-parts":[[2013,6,20]],"date-time":"2013-06-20T11:11:51Z","timestamp":1371726711000},"page":"500-509","source":"Crossref","is-referenced-by-count":5,"title":["Geometrical Complexity of Data Approximators"],"prefix":"10.1007","author":[{"given":"Evgeny M.","family":"Mirkes","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrei","family":"Zinovyev","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander N.","family":"Gorban","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"issue":"6","key":"50_CR1","doi-asserted-by":"publisher","first-page":"716","DOI":"10.1109\/TAC.1974.1100705","volume":"19","author":"A. Hirotugu","year":"1974","unstructured":"Hirotugu, A.: A new look at the statistical model identification. IEEE Transactions on Automatic Control\u00a019(6), 716\u2013723 (1974)","journal-title":"IEEE Transactions on Automatic Control"},{"key":"50_CR2","first-page":"1226","volume":"35","author":"V. Vapnik","year":"1974","unstructured":"Vapnik, V., Chervonenkis, A.: Ordered risk minimization I. Automation and Remote Control\u00a035, 1226\u20131235 (1974)","journal-title":"Automation and Remote Control"},{"key":"50_CR3","doi-asserted-by":"crossref","unstructured":"Gorban, A.N., Zinovyev, A.: Principal graphs and manifolds. In: Olivas, E.S., Guererro, J.D.M., Sober, M.M., Benedito, J.R.M., Lopes, A. (eds.) Handbook of Research on Machine Learning Applications and Trends: Algorithms, Methods and Techniques, Information Science Reference, pp. 28\u201359. IGI Global, Hershey (2009)","DOI":"10.4018\/978-1-60566-766-9.ch002"},{"key":"50_CR4","doi-asserted-by":"crossref","unstructured":"Zinovyev, A., Mirkes, E.: Data complexity measured by principal graphs. Computers and Mathematics with Applications (2013) doi:10.1016\/j.camwa.2012.12.009, arXiv:1212.5841","DOI":"10.1016\/j.camwa.2012.12.009"},{"issue":"3","key":"50_CR5","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1142\/S0129065710002383","volume":"20","author":"A.N. Gorban","year":"2010","unstructured":"Gorban, A.N., Zinovyev, A.: Principal manifolds and graphs in practice: from molecular biology to dynamical systems. International Journal of Neural Systems\u00a020(3), 219\u2013232 (2010)","journal-title":"International Journal of Neural Systems"},{"key":"50_CR6","unstructured":"Blakeslee, S.: Lost on earth: wealth of data found in space, An Edward Ng\u2019s quote from the article in New York Times (March 1990)"},{"key":"50_CR7","unstructured":"Burnham, K.P., Anderson, D.R.: Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, 2nd edn. Springer (2002)"},{"issue":"6","key":"50_CR8","doi-asserted-by":"publisher","first-page":"716","DOI":"10.1109\/TAC.1974.1100705","volume":"19","author":"H. Akaike","year":"1974","unstructured":"Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control\u00a019(6), 716\u2013723 (1974)","journal-title":"IEEE Transactions on Automatic Control"},{"key":"50_CR9","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1006\/jmps.1999.1283","volume":"44","author":"I.J. Myung","year":"2000","unstructured":"Myung, I.J.: The Importance of Complexity in Model Selection. Journal of Mathematical Psychology\u00a044, 190\u2013204 (2000)","journal-title":"Journal of Mathematical Psychology"},{"key":"50_CR10","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1006\/jmps.1999.1284","volume":"44","author":"M.R. Forster","year":"2000","unstructured":"Forster, M.R.: Key Concepts in Model Selection: Performance and Generalizability. Journal of Mathematical Psychology\u00a044, 205\u2013231 (2000)","journal-title":"Journal of Mathematical Psychology"},{"key":"50_CR11","unstructured":"Edmonds, B.: What is complexity? \u2013 The philosophy of complexity per se with application to some examples in evolution. In: Heylighen, F., Aerts, D. (eds.) The Evolution of Complexity. Kluwer, Dordrecht (1998)"},{"issue":"4","key":"50_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0895-7177(96)00103-3","volume":"24","author":"R.J. Brooks","year":"1996","unstructured":"Brooks, R.J., Tobias, A.M.: Choosing the best model: Level of detail, complexity, and model performance. Mathematical and Computer Modelling\u00a024(4), 1\u201314 (1996)","journal-title":"Mathematical and Computer Modelling"},{"issue":"4","key":"50_CR13","doi-asserted-by":"publisher","first-page":"382","DOI":"10.1016\/j.aml.2006.04.022","volume":"20","author":"A.N. Gorban","year":"2007","unstructured":"Gorban, A.N., Sumner, N., Zinovyev, A.: Topological grammars for data approximation. Applied Mathematics Letters\u00a020(4), 382\u2013386 (2007)","journal-title":"Applied Mathematics Letters"},{"issue":"1","key":"50_CR14","first-page":"1","volume":"1","author":"A.N. Kolmogorov","year":"1965","unstructured":"Kolmogorov, A.N.: Three approaches to the quantitative definition of information. Problems of Information Transmission\u00a01(1), 1\u20137 (1965)","journal-title":"Problems of Information Transmission"},{"key":"50_CR15","unstructured":"Alahakoon, D., Halgamuge, S.K., Sirinivasan, B.: A self growing cluster development approach to data mining. In: Proceedings of IEEE International Conference on Systems, Man and Cybernetics, San Diego, USA, pp. 2901\u20132906 (1998)"},{"key":"50_CR16","unstructured":"PCA Master applet, Mirkes, E., University of Leicester (2011) http:\/\/bioinfo.curie.fr\/projects\/elmap"},{"key":"50_CR17","unstructured":"Kohonen, T.: The Self-Organizing Map (SOM)., http:\/\/www.cis.hut.fi\/projects\/somtoolbox\/theory\/somalgorithm.shtml"},{"key":"50_CR18","series-title":"LNSE","volume-title":"Principal Manifolds for Data Visualisation and Dimension Reduction","year":"2008","unstructured":"Gorban, A.N., K\u00e9gl, B., Wunch, D.C., Zinovyev, A. (eds.): Principal Manifolds for Data Visualisation and Dimension Reduction. LNSE, vol.\u00a058. Springer, Heidelberg (2008)"}],"container-title":["Lecture Notes in Computer Science","Advances in Computational Intelligence"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-38679-4_50","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,15]],"date-time":"2019-07-15T19:29:11Z","timestamp":1563218951000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-38679-4_50"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642386787","9783642386794"],"references-count":18,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-38679-4_50","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2013]]}}}