{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T10:20:46Z","timestamp":1773656446340,"version":"3.50.1"},"reference-count":23,"publisher":"Pleiades Publishing Ltd","issue":"11","license":[{"start":{"date-parts":[[2018,11,1]],"date-time":"2018-11-01T00:00:00Z","timestamp":1541030400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2018,11,1]],"date-time":"2018-11-01T00:00:00Z","timestamp":1541030400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Autom Remote Control"],"published-print":{"date-parts":[[2018,11]]},"DOI":"10.1134\/s0005117918110085","type":"journal-article","created":{"date-parts":[[2018,11,16]],"date-time":"2018-11-16T03:26:54Z","timestamp":1542338814000},"page":"2038-2051","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Entropy Dimension Reduction Method for Randomized Machine Learning Problems"],"prefix":"10.1134","volume":"79","author":[{"given":"Yu. S.","family":"Popkov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu. A.","family":"Dubnov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. Yu.","family":"Popkov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"137","published-online":{"date-parts":[[2018,11,16]]},"reference":[{"key":"890_CR1","volume-title":"Prikladnaya statistika. Klassifikatsiya i snizhenie razmernosti","author":"S.A. Aivazyan","year":"1989","unstructured":"Aivazyan, S.A. and Mkhitaryan, V.S., Prikladnaya statistika. Klassifikatsiya i snizhenie razmernosti (Applied Statistics. Classification and Dimension Reduction), Moscow: Finansy i Statistika, 1989."},{"key":"890_CR2","volume-title":"Raspoznavanie obrazov. Vvedenie v metody statisticheskogo obucheniya","author":"A.B. Merkov","year":"2010","unstructured":"Merkov, A.B., Raspoznavanie obrazov. Vvedenie v metody statisticheskogo obucheniya (Pattern Recognition. Introduction to the Methods of Statistical Learning), Moscow: URSS, 2010."},{"key":"890_CR3","doi-asserted-by":"crossref","unstructured":"Friedman, J., Hastie, T., and Tibshirani, R., The Elements of Statistical Learning, Springer Series in Statistics, Berlin: Springer, 2001, vol.1.","DOI":"10.1007\/978-0-387-21606-5_1"},{"key":"890_CR4","doi-asserted-by":"crossref","unstructured":"Popkov, Yu.S., Dubnov, Yu.A., and Popkov, A.Yu., Randomized Machine Learning: Statement, Solution, Applications, in Intelligent Systems (IS), 2016 IEEE 8th Int. Conf., 2016, pp. 27\u201339.","DOI":"10.1109\/IS.2016.7737456"},{"issue":"1","key":"890_CR5","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1137\/060657704","volume":"51","author":"A.M. Bruckstein","year":"2009","unstructured":"Bruckstein, A.M., Donoho, D.L., and Elad, M., From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images, SIAM Rev., 2009, vol. 51, no. 1, pp. 34\u201381.","journal-title":"SIAM Rev."},{"key":"890_CR6","volume-title":"Statisticheskie vyvody i svyazi","author":"M. Kendall","year":"1973","unstructured":"Kendall, M., Stewart, A., Gal\u2019chuk, L.I., and Terekhin, A.T., Statisticheskie vyvody i svyazi (Statistical Inferences and Couplings), Moscow: Nauka, 1973."},{"key":"890_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-1904-8","volume-title":"Principal Component Analysis","author":"I.T. Jolliffe","year":"1986","unstructured":"Jolliffe, I.T., Principal Component Analysis, New York: Springer, 1986."},{"key":"890_CR8","volume-title":"Handbook of Blind Source Separation. Independent Component Analysis and Applications","author":"P. Comon","year":"2010","unstructured":"Comon, P. and Jutten, C., Handbook of Blind Source Separation. Independent Component Analysis and Applications, Oxford: Academic, 2010."},{"key":"890_CR9","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1016\/j.csda.2006.11.006","volume":"52","author":"M.W. Berry","year":"2007","unstructured":"Berry, M.W. and Browne, M., Algorithms and Applications for Approximate Nonnegative Matrix Factorization, Comput. Statist. Data Analysis, 2007, vol. 52, pp. 155\u2013173.","journal-title":"Comput. Statist. Data Analysis"},{"issue":"3","key":"890_CR10","doi-asserted-by":"publisher","first-page":"490","DOI":"10.1134\/S0005117917030092","volume":"78","author":"B.T. Polyak","year":"2017","unstructured":"Polyak, B.T. and Khlebnikov, M.V., Principal Component Analysis: Robust Versions, Autom. Remote Control, 2017, vol. 78, no. 3, pp. pp. 490\u2013506.","journal-title":"Autom. Remote Control"},{"key":"890_CR11","first-page":"189","volume":"26","author":"W.B. Johnson","year":"1984","unstructured":"Johnson, W.B. and Lindenstrauss, J., Extensions of Lipshitz Mapping into Hilbert Space, Modern Anal. Probab., Am. Math. Soc., 1984, vol. 26, pp. 189\u2013206.","journal-title":"Modern Anal. Probab., Am. Math. Soc."},{"key":"890_CR12","first-page":"274","volume-title":"PODS\u201901, Am. Math. Soc.","author":"D. Achlioptas","year":"2001","unstructured":"Achlioptas, D., Database-friendly Random Projections, PODS\u201901, Am. Math. Soc., 2001, pp. 274\u2013281."},{"issue":"8","key":"890_CR13","first-page":"1236","volume":"27","author":"H.C. Peng","year":"2005","unstructured":"Peng, H.C., Long, F., and Ding, C., Feature Selection Based on Mutual Information: Criteria of Maxdependency, Max-relevance, and Min-redundancy, IEEE Trans. Pattern Anal. Machine Intelligence, 2005, vol. 27, no. 8, pp. 1236\u20131238.","journal-title":"IEEE Trans. Pattern Anal. Machine Intelligence"},{"key":"890_CR14","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/j.neucom.2012.06.036","volume":"101","author":"Y. Zhang","year":"2013","unstructured":"Zhang, Y., Li, S., Wang, T., and Zhang, Z., Divergence-based Feature Selection for Separate Classes, Neurocomputing, 2013, vol. 101, pp. 32\u201342.","journal-title":"Neurocomputing"},{"issue":"2","key":"890_CR15","doi-asserted-by":"publisher","first-page":"287","DOI":"10.3166\/ejc.7.287-310","volume":"7","author":"M. Vidyasagar","year":"2001","unstructured":"Vidyasagar, M., Randomized Algorithms for Robust Controller Synthesis Using Statistical Learning Theory: A Tutorial Overview, Eur. J. Cont., 2001, vol. 7, no. 2, pp. 287\u2013310.","journal-title":"Eur. J. Cont."},{"key":"890_CR16","volume-title":"Randomizirovannye algoritmy otsenivaniya i optimizatsii pri pochti proizvol\u2019nykh pomekhakh","author":"O.N. Granichin","year":"2003","unstructured":"Granichin, O.N. and Polyak, B.T., Randomizirovannye algoritmy otsenivaniya i optimizatsii pri pochti proizvol\u2019nykh pomekhakh (Randimized Algorithms for Estimation and Optimization under Almost Arbitrary Noise), Moscow: Nauka, 2003."},{"key":"890_CR17","volume-title":"An Introduction to Probability Theory and Its Applications","author":"W. Feller","year":"1967","unstructured":"Feller, W., An Introduction to Probability Theory and Its Applications, New York: Wiley, 1957. Translated under the title Vvedenie v teoriyu veroyatnostei i ee prilozheniya, Moscow: Mir, 1967."},{"key":"890_CR18","volume-title":"Macrosystems Theory and Its Applications","author":"Yu.S. Popkov","year":"1995","unstructured":"Popkov, Yu.S., Macrosystems Theory and Its Applications, Lecture Notes in Control and Information Sciences, vol. 203, Berlin: Springer, 1995."},{"key":"890_CR19","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4321-0","volume-title":"The Cross-Entropy Method","author":"R.Y. Rubinstein","year":"2004","unstructured":"Rubinstein, R.Y. and Kroese, D.P., The Cross-Entropy Method, New York: Springer, 2004."},{"issue":"4","key":"890_CR20","doi-asserted-by":"publisher","first-page":"656","DOI":"10.1002\/j.1538-7305.1949.tb00928.x","volume":"28","author":"C.E. Shannon","year":"1949","unstructured":"Shannon, C.E., Communication Theory of Secrecy Systems, Bell Labs Techn. J., 1949, vol. 28, no. 4, pp. 656\u2013715.","journal-title":"Bell Labs Techn. J."},{"issue":"4","key":"890_CR21","doi-asserted-by":"publisher","first-page":"620","DOI":"10.1103\/PhysRev.106.620","volume":"106","author":"E.T. Jaynes","year":"1957","unstructured":"Jaynes, E.T., Information Theory and Statistical Mechanics, Phys. Rev., 1957, vol. 106, no. 4, pp. 620\u2013630.","journal-title":"Phys. Rev."},{"key":"890_CR22","volume-title":"Matrix Differential Calculus with Applications in Statistics and Econometrics","author":"J.R. Magnus","year":"1988","unstructured":"Magnus, J.R. and Neudecker, H., Matrix Differential Calculus with Applications in Statistics and Econometrics, New York: Wiley, 1988."},{"issue":"1","key":"890_CR23","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1214\/aoms\/1177729694","volume":"22","author":"S. Kullback","year":"1951","unstructured":"Kullback, S. and Leibler, R.A., On Information and Sufficiency, Ann. Math. Statist., 1951, vol. 22, no. 1, pp. 79\u201386.","journal-title":"Ann. Math. Statist."}],"container-title":["Automation and Remote Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0005117918110085.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1134\/S0005117918110085","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0005117918110085.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T22:32:35Z","timestamp":1773613955000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1134\/S0005117918110085"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11]]},"references-count":23,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2018,11]]}},"alternative-id":["890"],"URL":"https:\/\/doi.org\/10.1134\/s0005117918110085","relation":{},"ISSN":["0005-1179","1608-3032"],"issn-type":[{"value":"0005-1179","type":"print"},{"value":"1608-3032","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11]]},"assertion":[{"value":"24 January 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 November 2018","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}