{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T10:27:09Z","timestamp":1648636029697},"reference-count":46,"publisher":"Elsevier BV","issue":"10","license":[{"start":{"date-parts":[[2002,10,1]],"date-time":"2002-10-01T00:00:00Z","timestamp":1033430400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Signal Processing"],"published-print":{"date-parts":[[2002,10]]},"DOI":"10.1016\/s0165-1684(02)00281-5","type":"journal-article","created":{"date-parts":[[2002,10,11]],"date-time":"2002-10-11T23:23:42Z","timestamp":1034378622000},"page":"1389-1410","source":"Crossref","is-referenced-by-count":6,"title":["Contravariant adaptation on structured matrix spaces"],"prefix":"10.1016","volume":"82","author":[{"given":"Todd K.","family":"Moon","sequence":"first","affiliation":[]},{"given":"Jacob H.","family":"Gunther","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0165-1684(02)00281-5_BIB1","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/BF01692059","article-title":"Differential geometry of a parametric family of invertible linear systems\u2014Riemannian metric, dual affine connections, and divergence","volume":"20","author":"Amari","year":"1987","journal-title":"Math. Systems Theory"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB2","unstructured":"S.-I. Amari, Gradient learning in structured parameter space: adaptive blind separation of signal sources, in: Proceedings of World Congress on Neural Networks, 1996."},{"key":"10.1016\/S0165-1684(02)00281-5_BIB3","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1162\/089976698300017746","article-title":"Natural gradient works efficiently in learning","volume":"10","author":"Amari","year":"1998","journal-title":"Neural Comput."},{"key":"10.1016\/S0165-1684(02)00281-5_BIB4","series-title":"Differential Geometry in Statistical Inference","author":"Amari","year":"1987"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB5","unstructured":"S. Amari, A. Cichocki, H. Yang, A new learning algorithm for blind signal separation, in: D. Touretzky, M. Mozer, H. Hasselmo (Eds.), Advances in Neural Information Processing, Vol. 8, MIT Press, Cambridge, MA, 1996, pp. 757\u2013763."},{"key":"10.1016\/S0165-1684(02)00281-5_BIB6","doi-asserted-by":"crossref","unstructured":"S. Amari, S.C. Douglas, Why natural gradient? in: Proc. ICASSP 2 (1998) 1213\u20131216.","DOI":"10.1109\/ICASSP.1998.675489"},{"issue":"1","key":"10.1016\/S0165-1684(02)00281-5_BIB7","first-page":"31","article-title":"Differential and algebraic geometry of multilayer perceptrons","volume":"84 A","author":"Amari","year":"2001","journal-title":"IEICE Trans. Fundam."},{"key":"10.1016\/S0165-1684(02)00281-5_BIB8","doi-asserted-by":"crossref","first-page":"1129","DOI":"10.1162\/neco.1995.7.6.1129","article-title":"An information-maximization approach to blind separation and blind deconvolution","volume":"7","author":"Bell","year":"1995","journal-title":"Neural Comput."},{"key":"10.1016\/S0165-1684(02)00281-5_BIB9","doi-asserted-by":"crossref","unstructured":"N. Bienati, U. Spagnolini, M. Zecca, An adaptive blind signal separation based on the joint optimization of givens rotations, in: Proc. ICASSP VI (2001) 2809\u20132812.","DOI":"10.1109\/ICASSP.2001.940230"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB10","series-title":"Tensor Analysis on Manifolds","author":"Bishop","year":"1980"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB11","series-title":"An Introduction to Differentiable Manifolds and Riemannian, Geometry","author":"Boothby","year":"1986"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB12","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1109\/PROC.1976.10067","article-title":"Nonlinear systems and differential geometry","volume":"64","author":"Brockett","year":"1976","journal-title":"Proc. IEEE"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB13","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/0005-1098(76)90080-7","article-title":"Volterra series and geometric control theory","volume":"12","author":"Brockett","year":"1976","journal-title":"Automatica"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB14","series-title":"Control Theory and Singular Riemannian Geometry","author":"Brockett","year":"1981"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB15","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1023\/A:1007992709392","article-title":"Differential and numerically invariant signature curves applied to object recognition","volume":"26","author":"Calabi","year":"1998","journal-title":"Int. J. Comput. Vision"},{"issue":"10","key":"10.1016\/S0165-1684(02)00281-5_BIB16","doi-asserted-by":"crossref","first-page":"2009","DOI":"10.1109\/5.720250","article-title":"Blind signal separation","volume":"9","author":"Cardoso","year":"1988","journal-title":"Proc. IEEE"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB17","doi-asserted-by":"crossref","unstructured":"J.-F. Cardoso, S.-I. Amari, Maximum likelihood source separation: equivariance and adaptivity, in: 11th IFAC Symposium on System Identification, Fukuoka, Japan, 1997, pp. 1063\u20131068.","DOI":"10.1016\/S1474-6670(17)42973-9"},{"issue":"44","key":"10.1016\/S0165-1684(02)00281-5_BIB18","doi-asserted-by":"crossref","first-page":"3017","DOI":"10.1109\/78.553476","article-title":"Equivariant adaptive source separation","volume":"12","author":"Cardoso","year":"1996","journal-title":"IEEE Trans. Signal Process."},{"key":"10.1016\/S0165-1684(02)00281-5_BIB19","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/0165-1684(94)90029-9","article-title":"Independent component analysis, a new concept?","volume":"36","author":"Comon","year":"1994","journal-title":"Signal Process."},{"key":"10.1016\/S0165-1684(02)00281-5_BIB20","series-title":"Matrix Groups","author":"Curtis","year":"1984"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB21","series-title":"The Geometry of Physics","author":"Frankel","year":"1997"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB22","unstructured":"I. Gohberg, I. Fel'dman, Convolution equations and projection methods for their solutions, Transl. Math. Monographs, Amer. Math. Soc. 41, 86 (1974)."},{"key":"10.1016\/S0165-1684(02)00281-5_BIB23","first-page":"201","article-title":"On the inversion of finite Toeplitz matrices and their continuous analogs","volume":"2","author":"Gohberg","year":"1972","journal-title":"Mat. Issled."},{"key":"10.1016\/S0165-1684(02)00281-5_BIB24","series-title":"Matrix Computations","author":"Golub","year":"1996"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB25","series-title":"Adaptive Filter Theory","author":"Haykin","year":"1996"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB26","series-title":"Nonlinear Control Systems","author":"Isidori","year":"1995"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB27","doi-asserted-by":"crossref","first-page":"1287","DOI":"10.1364\/JOSA.62.001287","article-title":"Color distance and geodesics in color 3 space","volume":"62","author":"Jain","year":"1972","journal-title":"J. Opt. Soc. Amer."},{"key":"10.1016\/S0165-1684(02)00281-5_BIB28","series-title":"Linear Systems","author":"Kailath","year":"1980"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB29","series-title":"Tensor Calculus, Shaum's Outlines","author":"Kay","year":"1988"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB30","series-title":"Nonholonomic motion planning","first-page":"235","article-title":"A differential geometric approach to motion planning","author":"Lafferriere","year":"1993"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB31","series-title":"Independent Component Analysis: Theory and Applications","author":"Lee","year":"1998"},{"issue":"2","key":"10.1016\/S0165-1684(02)00281-5_BIB32","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1162\/089976699300016719","article-title":"Independent component analysis using an extended infomax algorithm for mixed sub-gaussian and super-gaussian sources","volume":"11","author":"Lee","year":"1999","journal-title":"Neural Comput."},{"key":"10.1016\/S0165-1684(02)00281-5_BIB33","series-title":"Tensors, Differential Forms and Variational Principles","author":"Lovelock","year":"1989"},{"issue":"3","key":"10.1016\/S0165-1684(02)00281-5_BIB34","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1109\/78.905865","article-title":"Manifold studies of nonlinear antenna arry geometries","volume":"49","author":"Manikas","year":"2001","journal-title":"IEEE Trans. Signal Process"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB35","series-title":"Mathematical Methods and Algorithms for Signal Processing","author":"Moon","year":"2000"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB36","series-title":"Nonlinear Dynamic Control Systems","author":"Nijmeijer","year":"1990"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB37","series-title":"Elementary Differential Geometry","author":"O'Neill","year":"1997"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB38","series-title":"Applications of Lie Groups to Differential Equations","author":"Olver","year":"1990"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB39","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1023\/A:1006295328209","article-title":"Affine invariant detection","volume":"59","author":"Olver","year":"1999","journal-title":"Acta Appl. Math."},{"key":"10.1016\/S0165-1684(02)00281-5_BIB40","doi-asserted-by":"crossref","unstructured":"G. Orsak, S. Douglas, Code-length based universal extraction for blind signal separation, in: Proc. ICASSP 6 (2000) 3422\u20133425.","DOI":"10.1109\/ICASSP.2000.860136"},{"issue":"11","key":"10.1016\/S0165-1684(02)00281-5_BIB41","doi-asserted-by":"crossref","first-page":"2768","DOI":"10.1109\/78.542183","article-title":"Blind separation of instantaneous mixture of sources via independent component analysis","volume":"44","author":"Pham","year":"1998","journal-title":"IEEE Trans. Signal Process."},{"key":"10.1016\/S0165-1684(02)00281-5_BIB42","unstructured":"S.T. Smith, Geometric optimization methods for adaptive filtering, Ph.D. Thesis, Harvard University, September, 1993."},{"key":"10.1016\/S0165-1684(02)00281-5_BIB43","doi-asserted-by":"crossref","unstructured":"X. Sun, S. Douglas, Adaptive paraunitary filter banks for contrast-based multichannel blind deconvolution, in: Proc. ICASSP 5 (2001) 2753\u20132756.","DOI":"10.1109\/ICASSP.2001.940216"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB44","doi-asserted-by":"crossref","unstructured":"R. Thomas, T. Moon, Projective residual vector quantization and mapped residual pooling, in: Proc. ICASSP (2000) IV-1891\u20131894.","DOI":"10.1109\/ICASSP.2000.859197"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB45","series-title":"Diagrammatica: The Path to Feynman Diagrams","author":"Veltman","year":"1994"},{"key":"10.1016\/S0165-1684(02)00281-5_BIB46","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1109\/42.563665","article-title":"A geometric snake model for segmentation of medical imagery","volume":"16","author":"Yezzi","year":"1997","journal-title":"IEEE Trans. Med. Imag."}],"container-title":["Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0165168402002815?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0165168402002815?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2020,3,5]],"date-time":"2020-03-05T14:16:15Z","timestamp":1583417775000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0165168402002815"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,10]]},"references-count":46,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2002,10]]}},"alternative-id":["S0165168402002815"],"URL":"https:\/\/doi.org\/10.1016\/s0165-1684(02)00281-5","relation":{},"ISSN":["0165-1684"],"issn-type":[{"value":"0165-1684","type":"print"}],"subject":[],"published":{"date-parts":[[2002,10]]}}}