{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T14:03:42Z","timestamp":1765807422904,"version":"3.37.3"},"reference-count":30,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"5","license":[{"start":{"date-parts":[[2018,5,1]],"date-time":"2018-05-01T00:00:00Z","timestamp":1525132800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Neural Netw. Learning Syst."],"published-print":{"date-parts":[[2018,5]]},"DOI":"10.1109\/tnnls.2017.2677446","type":"journal-article","created":{"date-parts":[[2017,3,24]],"date-time":"2017-03-24T05:59:18Z","timestamp":1490335158000},"page":"1689-1702","source":"Crossref","is-referenced-by-count":28,"title":["Hyperbolic Gradient Operator and Hyperbolic Back-Propagation Learning Algorithms"],"prefix":"10.1109","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9628-7920","authenticated-orcid":false,"given":"Tohru","family":"Nitta","sequence":"first","affiliation":[]},{"given":"Yasuaki","family":"Kuroe","sequence":"additional","affiliation":[]}],"member":"263","reference":[{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1541\/ieejeiss.123.1465"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1162\/08997660460734001"},{"key":"ref11","first-page":"560","article-title":"Models of Hopfield-type clifford neural networks and their energy functions&#x2014;Hyperbolic and dual valued networks","author":"kuroe","year":"2011","journal-title":"Proc Int Conf Neural Inf Process (ICONIP)"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2012.2230450"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1109\/IJCNN.1990.137820"},{"key":"ref14","first-page":"1319","article-title":"A complex back-propagation learning","volume":"32","author":"nitta","year":"1991","journal-title":"Trans Inf Process Soc Jpn"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-6080(97)00036-1"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1007\/BF01447872"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1049\/ip-f-1.1983.0003"},{"journal-title":"An Introduction to Complex Function Theory","year":"1995","author":"palka","key":"ref18"},{"journal-title":"Complex Analysis","year":"1990","author":"takahashi","key":"ref19"},{"key":"ref28","first-page":"23","article-title":"Non-constant bounded holomorphic functions of hyperbolic numbers","author":"hitzer","year":"2011","journal-title":"Proc 1st SICE Symp Comput Intell"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.2307\/2687027"},{"key":"ref27","first-page":"318","article-title":"Learning internal representations by error propagation","volume":"1","author":"rumelhart","year":"1986","journal-title":"Parallel Distributed Processing Explorations in the Microstructure of Cognition"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1002\/9781118590072"},{"key":"ref6","first-page":"1417","article-title":"Hyperbolic self-organizing maps for semantic navigation","volume":"14","author":"ontrup","year":"2001","journal-title":"Advances in neural information processing systems"},{"key":"ref29","first-page":"1363","article-title":"A method to interpret 3D motions using neural networks","volume":"e77 a","author":"watanabe","year":"1994","journal-title":"IEICE Trans Fund Electr Commun Comput Sci"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/B978-044450270-4\/50007-3"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/IJCNN.2000.857886"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-44794-6_28"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1002\/9780470742624"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/IJCNN.2008.4634216"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.4018\/978-1-60566-214-5"},{"key":"ref20","first-page":"1","article-title":"The complex gradient operator and the \n$\\mathbb {CR}$\n-calculus","author":"kreutz-delgado","year":"2006","journal-title":"Lect Suppl ECE275A"},{"key":"ref22","first-page":"550","article-title":"Wirtinger calculus based gradient descent and Levenberg-Marquardt learning algorithms in complex-valued neural networks","author":"amin","year":"2011","journal-title":"Proc Int Conf Neural Inf Process (ICONIP)"},{"journal-title":"The complex gradient operator and the CR-Calculus","year":"2009","author":"kreutz-delgado","key":"ref21"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.3390\/info3040756"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2010.2091126"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1007\/BF03041929"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-65308-7"}],"container-title":["IEEE Transactions on Neural Networks and Learning Systems"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/5962385\/8338465\/07885584.pdf?arnumber=7885584","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,29]],"date-time":"2022-01-29T00:05:02Z","timestamp":1643414702000},"score":1,"resource":{"primary":{"URL":"http:\/\/ieeexplore.ieee.org\/document\/7885584\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5]]},"references-count":30,"journal-issue":{"issue":"5"},"URL":"https:\/\/doi.org\/10.1109\/tnnls.2017.2677446","relation":{},"ISSN":["2162-237X","2162-2388"],"issn-type":[{"type":"print","value":"2162-237X"},{"type":"electronic","value":"2162-2388"}],"subject":[],"published":{"date-parts":[[2018,5]]}}}