{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T10:34:22Z","timestamp":1764239662749},"reference-count":65,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"5","license":[{"start":{"date-parts":[[2011,5,1]],"date-time":"2011-05-01T00:00:00Z","timestamp":1304208000000},"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."],"published-print":{"date-parts":[[2011,5]]},"DOI":"10.1109\/tnn.2011.2109395","type":"journal-article","created":{"date-parts":[[2011,3,22]],"date-time":"2011-03-22T15:31:42Z","timestamp":1300807902000},"page":"687-700","source":"Crossref","is-referenced-by-count":27,"title":["Extended Hamiltonian Learning on Riemannian Manifolds: Theoretical Aspects"],"prefix":"10.1109","volume":"22","author":[{"given":"S","family":"Fiori","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP.2010.5496011"},{"key":"ref38","first-page":"477","article-title":"Implementing decisions in binary decision trees using independent component analysis","author":"pajunen","year":"2000","journal-title":"Proc Int Workshop Independent Compon Anal Blind Signal Separat"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479895290954"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP.1997.604600"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP.1999.759931"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1162\/089976699300015990"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1049\/ip-vis:20030511"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1109\/18.212280"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2007.08.014"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050432"},{"key":"ref60","doi-asserted-by":"crossref","first-page":"281","DOI":"10.24033\/asens.1673","article-title":"A classification of Monge–Ampére equations","volume":"26","author":"lychagin","year":"1993","journal-title":"Ann Sci cole Normale Supr"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1162\/089976698300017746"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-008-9025-1"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2003.10.002"},{"key":"ref28","first-page":"140","article-title":"Orthogonal nonnegative matrix factorization: Multiplicative updates on Stiefel manifolds","author":"yoo","year":"2008","journal-title":"Proc Intell Data Eng Autom Learn"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1162\/neco.2008.03-07-489"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2004.11.035"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2005.852860"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP.1996.550159"},{"key":"ref2","author":"hairer","year":"2006","journal-title":"Geometric Numerical Integration Structure-Preserving Algorithms for Ordinary Differential Equations"},{"key":"ref1","author":"zurada","year":"1992","journal-title":"Introduction to Artificial Neural Systems"},{"key":"ref20","first-page":"70","article-title":"Fluid flow versus geometric dynamics","author":"isvoranu","year":"2005","journal-title":"Proc 5th Conf Balkan Soc Geometers"},{"key":"ref22","author":"cichocki","year":"1993","journal-title":"Neural Networks for Optimization and Signal Processing"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2010.2043445"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1016\/0893-6080(92)90006-5"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1109\/72.248453"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1109\/SAM.2002.1191070"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2004.02.007"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-56542-7"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2002.803545"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.88.097904"},{"key":"ref58","author":"guillemin","year":"1984","journal-title":"Symplectic Techniques in Physics"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1111\/j.1475-1313.2004.00239.x"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1097\/00006324-199404000-00009"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479803436937"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1000625"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1007\/s12559-009-9026-7"},{"key":"ref52","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.1016\/S0165-1684(03)00002-1","article-title":"Computation of symmetric positive definite Toeplitz matrices by the hybrid steepest descent method","volume":"83","author":"slavakis","year":"2003","journal-title":"Signal Process"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-6080(98)00116-6"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2002.1000121"},{"key":"ref40","first-page":"810","article-title":"Learning lie groups for invariant visual perception","author":"rao","year":"1999","journal-title":"Proc Adv Neural Inf Process Syst 11"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1142\/S012906570200114X"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-5193(84)80179-4"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1016\/0306-4522(80)90191-8"},{"key":"ref15","author":"spivak","year":"1979","journal-title":"A Comprehensive Introduction to Differential Geometry"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1515\/9781400830244"},{"key":"ref17","author":"gelfand","year":"2000","journal-title":"Calculus of Variations"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1016\/0309-1708(84)90006-X"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1002\/zamm.19750550605"},{"key":"ref4","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2851-4","author":"lee","year":"1998","journal-title":"Independent Component Analysis Theory and Applications"},{"key":"ref3","author":"diamantaras","year":"1996","journal-title":"Principal component Neural Networks Theory and Applications"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.18.11.620"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2004.824258"},{"key":"ref8","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-21792-5","author":"marsden","year":"1999","journal-title":"Texts in Applied Mathematics 27"},{"key":"ref7","author":"lanczos","year":"1986","journal-title":"The Variational Principles of Mechanics"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1137\/050622729"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1007\/BF00941312"},{"key":"ref46","first-page":"743","article-title":"Quasi-geodesic neural learning algorithms over the orthogonal group: A tutorial","volume":"6","author":"fiori","year":"2005","journal-title":"J Mach Learn Res"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.2307\/2347791"},{"key":"ref48","author":"grubii","year":"2005","journal-title":"Efficient Rank Reduction of Correlation Matrices"},{"key":"ref47","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/11679363_37","article-title":"Riemannian optimization method on the flag manifold for independent subspace analysis","volume":"3889","author":"nishimori","year":"2006","journal-title":"Proc 6th Int Conf Independent Compon Anal Blind Signal Separat"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2005.1458"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2004.1382"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2004.841784"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-3758(01)00195-1"}],"container-title":["IEEE Transactions on Neural Networks"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx5\/72\/5762843\/05735228.pdf?arnumber=5735228","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,10]],"date-time":"2021-10-10T23:52:24Z","timestamp":1633909944000},"score":1,"resource":{"primary":{"URL":"http:\/\/ieeexplore.ieee.org\/document\/5735228\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,5]]},"references-count":65,"journal-issue":{"issue":"5"},"URL":"https:\/\/doi.org\/10.1109\/tnn.2011.2109395","relation":{},"ISSN":["1045-9227","1941-0093"],"issn-type":[{"value":"1045-9227","type":"print"},{"value":"1941-0093","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,5]]}}}