Edit Profile (opens in new tab) Amari, Shun-ichi Compute Distance To: Compute Author ID: amari.shun-ichi Published as: Amari, Shun-ichi; Amari, Shun-Ichi; Amari, S.; Amari, S.-i.; Amari, S.-I.; Amari, Shunichi; Amari, S. I.; Amari, Sh. Further Spellings: Amari, Shun’ichi; 甘利 俊; Амари Шун-ичи External Links: MGP · ORCID · Wikidata · Math-Net.Ru · dblp · GND · IdRef Documents Indexed: 173 Publications since 1961, including 16 Books 3 Contributions as Editor · 1 Further Contribution Biographic References: 2 Publications Co-Authors: 94 Co-Authors with 117 Joint Publications 1,963 Co-Co-Authors all top 5 Co-Authors 54 single-authored 15 Cichocki, Andrzej 11 Nakahara, Hiroyuki 10 Wu, Si 7 Karakida, Ryo 6 Han, Te Sun 6 Kawanabe, Motoaki 5 Burnashev, Marat V. 5 Kumon, Masayuki 5 Ohara, Atsumi 5 Ozeki, Tomoko 4 Li, Yuanqing 4 Murata, Noboru 4 Oizumi, Masafumi 4 Park, Hyeyoung 3 Chen, Tianping 3 Okada, Masato 3 Zhang, Liqing 2 Akaho, Shotaro 2 Arbib, Michael A. 2 Cruces, Sergio 2 Douglas, Scott C. 2 Guan, Cuntai 2 Ikeda, Shiro 2 Kang, Kukjin 2 Lu, Wenlian 2 Ma, Jinwen 2 Matsuda, Takeru 2 Matsuzoe, Hiroshi 2 Nagaoka, Hiroshi 2 Nielsen, Frank 2 Nock, Richard 2 Suda, Nobuhide 2 Takeuchi, Akikazu 2 Tanaka, Toshiyuki 2 Tsuchiya, Naotsugu 2 Wei, Haikun 2 Yang, Howard Hua 2 Yukawa, Masahiro 2 Zdunek, Rafal 1 Abe, Naoki 1 Ait Oumeziane, F. 1 Akahira, Masafumi 1 Aki, Sigeo 1 Ay, Nihat 1 Barndorff-Nielsen, Ole Eiler 1 Bollé, D. 1 Bös, Siegfried 1 Chakravarthy, V. S. 1 Chen, Danmei 1 Chen, Zhe 1 Cheung, Chi Chiu 1 Choi, Seungjin 1 Cousseau, Florent 1 Cuturi, Marco 1 Dominguez Carreta, D. R. C. 1 Eguchi, Shinto 1 Fellous, Jean-Marc 1 Feng, Jianfeng 1 Fujiwara, Akio 1 Fung, C. C. Alan 1 Gao, Dengpan 1 Ge, Fei 1 Hamaguchi, Kosuke 1 Hikosaka, Okihide 1 Ho, Daniel W. C. 1 Iri, Masao 1 Isogai, Eiichi 1 Ito, Hisashi 1 Jeong, Kwangjin 1 Kagekawa, K. 1 Kanatani, Kenichi 1 Kasabov, Nikola K. 1 Kass, Robert E. 1 Kobayashi, Kingo 1 Kuboki, Hisataka 1 Kurata, Koji 1 Lauritzen, Steffen Lilholt 1 Lu, Yao 1 Magdoom, K. N. 1 Massolo, G. 1 Meenakshisundaram, N. 1 Miura, Keiji 1 Müller, Klaus-Robert 1 Niranjan, Mahesan 1 Okamoto, Ichi 1 Oshima, Nobunori 1 Rao, Calyampudi Radhakrishna 1 Richmond, Barry J. 1 Sakai, Yutaka 1 Sato, Yuzuru 1 Seghouane, Abd-Krim 1 Shimizu, Kunio 1 Takeuchi, Kei 1 Tamssaouet, F. 1 Tatsuno, Masami 1 Watanabe, Sumio 1 Waxman, David 1 Xie, Shengli 1 Xu, Lei 1 Yoshida, Kiyonori ...and 3 more Co-Authors all top 5 Serials 36 Neural Computation 14 IEEE Transactions on Information Theory 5 Biological Cybernetics 4 Neural Networks 4 Neurocomputing 4 Entropy 3 Annals of the Institute of Statistical Mathematics 3 The Annals of Statistics 3 Signal Processing 3 IEEE Transactions on Signal Processing 3 Journal of VLSI Signal Processing Systems for Signal, Image, and Video Technology 3 RIMS Kokyuroku 2 Problems of Information Transmission 2 Theory of Probability and its Applications 2 Biometrika 2 IEEE Transactions on Systems, Man, and Cybernetics 2 Neural Processing Letters 2 Lecture Notes in Statistics 2 Translations of Mathematical Monographs 2 International Journal of Systems Science. Principles and Applications of Systems and Integration 1 Modern Physics Letters B 1 International Journal of Engineering Science 1 Journal of Mathematical Biology 1 Bulletin of Mathematical Biology 1 IEEE Transactions on Computers 1 Journal of Computer and System Sciences 1 Kybernetika 1 Mathematical Systems Theory 1 Physica D 1 New Generation Computing 1 Algorithmica 1 Differential Geometry and its Applications 1 Linear Algebra and its Applications 1 Proceedings of the National Academy of Sciences of the United States of America 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 SIAM Journal on Applied Mathematics 1 Bernoulli 1 New Journal of Physics 1 Journal of Statistical Mechanics: Theory and Experiment 1 IEEE Transactions on Electronic Computers 1 Applied Mathematical Sciences 1 Bulletin of the International Statistical Institute 1 Institute of Mathematical Statistics Lecture Notes - Monograph Series 1 Lecture Notes in Biomathematics 1 Seminar on Mathematical Sciences 1 Japanese Journal of Mathematics. 3rd Series 1 Kybernetik 1 Information Geometry all top 5 Fields 64 Statistics (62-XX) 55 Computer science (68-XX) 42 Biology and other natural sciences (92-XX) 41 Information and communication theory, circuits (94-XX) 31 Differential geometry (53-XX) 11 Probability theory and stochastic processes (60-XX) 7 Numerical analysis (65-XX) 7 Systems theory; control (93-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 General and overarching topics; collections (00-XX) 3 Integral equations (45-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Mechanics of deformable solids (74-XX) 2 Operations research, mathematical programming (90-XX) 1 History and biography (01-XX) 1 Algebraic geometry (14-XX) 1 Ordinary differential equations (34-XX) 1 Partial differential equations (35-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Convex and discrete geometry (52-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Quantum theory (81-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 123 Publications have been cited 2,220 times in 1,528 Documents Cited by ▼ Year ▼ Dynamics of pattern formation in lateral-inhibition type neural fields. Zbl 0367.92005Amari, Shun-ichi 291 1977 Differential-geometrical methods in statistics. Zbl 0559.62001Amari, Shun-ichi 245 1985 Methods of information geometry. Transl. from the Japanese by Daishi Harada. Zbl 0960.62005Amari, Shun-ichi; Nagaoka, Hiroshi 220 2000 Information geometry and its applications. Zbl 1350.94001Amari, Shun-ichi 102 2016 Differential geometry of curved exponential families. Curvatures and information loss. Zbl 0507.62026Amari, Shun-ichi 89 1982 Differential geometry in statistical inference. Zbl 0694.62001Amari, S.-I.; Barndorff-Nielsen, O. E.; Kass, R. E.; Lauritzen, S. L.; Rao, C. R. 68 1987 Families of alpha-, beta- and gamma-divergences: flexible and robust measures of similarities. Zbl 1229.94030Cichocki, Andrzej; Amari, Shun-Ichi 49 2010 Neural theory of association and concept-formation. Zbl 0364.92016Amari, S.-I. 48 1977 Existence and stability of local excitations in homogeneous neural fields. Zbl 0406.92010Kishimoto, K.; Amari, S. 47 1979 Information geometry on hierarchy of probability distributions. Zbl 0997.94009Amari, Shun-ichi 47 2001 Characteristics of random nets of analog neuron-like elements. Zbl 0247.92006Amari, Shun-Ichi 46 1972 Differential-geometrical methods in statistics. Corr. 2nd. printing. Zbl 0701.62008Amari, Shun-ichi 33 1990 Hierarchical ALS algorithms for nonnegative matrix and 3D tensor factorization. Zbl 1172.94390Cichocki, Andrzej; Zdunek, Rafal; Amari, Shun-ichi 33 2007 A method of statistical neurodynamics. Zbl 0277.92003Amari, Shun-ichi 29 1974 Learning patterns and pattern sequences by self-organizing nets of threshold elements. Zbl 0245.94024Amari, Shun-Ichi 28 1972 Population coding and decoding in a neural field: A computational study. Zbl 0994.92011Wu, Si; Amari, Shun-ichi; Nakahara, Hiroyuki 28 2002 Homogeneous nets of neuron-like elements. Zbl 0302.92004Amari, Shun-Ichi 25 1975 Topographic organization of nerve fields. Zbl 0477.92008Amari, Shun-ichi 24 1980 Geometrical theory of asymptotic ancillarity and conditional inference. Zbl 0484.62046Amari, Shun-Ichi 24 1982 Synchronous firing and higher-order interactions in neuron pool. Zbl 1028.92007Amari, Shun-ichi; Nakahara, Hiroyuki; Wu, Si; Sakai, Yutaka 23 2003 Identifiability of hidden Markov information sources and their minimum degrees of freedom. Zbl 0742.60041Ito, Hisashi; Amari, Shun-Ichi; Kobayashi, Kingo 22 1992 Information-geometric measure for neural spikes. Zbl 1018.68068Nakahara, Hiroyuki; Amari, Shun-ichi 21 2002 Formation of topographic maps and columnar microstructures in nerve fields. Zbl 0418.92001Takeuchi, A.; Amari, S. 20 1979 Csiszár’s divergences for non-negative matrix factorization: Family of new algorithms. Zbl 1178.94057Cichocki, Andrzej; Zdunek, Rafal; Amari, Shun-ichi 20 2006 Geometry of \(q\)-exponential family of probability distributions. Zbl 1306.62073Amari, Shun-Ichi; Ohara, Atsumi 20 2011 \(\alpha\)-divergence is unique, belonging to both \(f\)-divergence and Bregman divergence classes. Zbl 1367.94133Amari, Shun-Ichi 20 2009 Population coding with correlation and an unfaithful model. Zbl 1011.62116Wu, Si; Nakahara, Hiroyuki; Amari, Shun-ichi 18 2001 Differential geometry of a parametric family of invertible linear systems. Riemannian metric, dual affine connections, and divergence. Zbl 0632.93017Amari, Shun-ichi 18 1987 Analysis of sparse representation and blind source separation. Zbl 1089.68101Li, Yuanqing; Cichocki, Andrzej; Amari, Shun-ichi 17 2004 Dualistic differential geometry of positive definite matrices and its applications to related problems. Zbl 0863.15009Ohara, Atsumi; Suda, Nobuhide; Amari, Shun-ichi 16 1996 A theory of adaptive pattern classifiers. Zbl 0189.50101Amari, S.-i. 16 1967 Differential geometry of Edgeworth expansions in curved exponential family. Zbl 0527.62034Amari, Shun-ichi; Kumon, Masayuki 15 1983 Field theory of self-organizing neural nets. Zbl 0543.92007Amari, Shun-ichi 15 1983 Geometrical theory of higher-order asymptotics of test, interval estimator and conditional inference. Zbl 0527.62031Kumon, M.; Amari, S. 14 1983 A mathematical foundation for statistical neurodynamics. Zbl 0356.92002Amari, Shun-Ichi; Yoshida, Kiyonori; Kanatani, Ken-Ichi 14 1977 Estimating spiking irregularities under changing environments. Zbl 1106.92015Miura, Keiji; Okada, Masato; Amari, Shunichi 14 2006 Integration of stochastic models by minimizing \(\alpha\)-divergence. Zbl 1138.62002Amari, Shun-ichi 14 2007 Information geometry connecting Wasserstein distance and Kullback-Leibler divergence via the entropy-relaxed transportation problem. Zbl 1409.62020Amari, Shun-ichi; Karakida, Ryo; Oizumi, Masafumi 13 2018 Gradient systems in view of information geometry. Zbl 0883.53020Fujiwara, Akio; Amari, Shun-ichi 13 1995 Mathematical theory on formation of category detecting nerve cells. Zbl 0383.92003Amari, Shun-ichi; Takeuchi, Akikazu 13 1978 Dynamics of learning near singularities in layered networks. Zbl 1138.68048Wei, Haikun; Zhang, Jun; Cousseau, Florent; Ozeki, Tomoko; Amari, Shun-Ichi 13 2008 Methods of information geometry. Translation from the Japanese by Daishi Harada. Reprint of the 2000 edition. Zbl 1146.62001Amari, Shun-ichi; Nagaoka, Hiroshi 12 2008 Information geometry of estimating functions in semi-parametric statistical models. Zbl 0881.62034Amari, Shun-ichi; Kawanabe, Motoaki 11 1997 Singularities affect dynamics of learning in neuromanifolds. Zbl 1092.68636Amari, Shun-ichi; Park, Hyeyoung; Ozeki, Tomoko 11 2006 Underdetermined blind source separation based on sparse representation. Zbl 1373.94647Li, Yuanqing; Amari, S.; Cichocki, A.; Ho, D. W. C.; Xie, Shengli 10 2006 Computing with continuous attractors: stability and online aspects. Zbl 1080.68638Wu, Si; Amari, Shun-ichi 10 2005 Geometrical structures of FIR manifold and multichannel blind deconvolution. Zbl 0999.93013Zhang, L.-Q.; Cichocki, A.; Amari, S. 10 2002 Conformal transformation of kernel functions: A data-dependent way to improve support vector machine classifiers. Zbl 1008.68741Wu, Si; Amari, Shun-Ichi 10 2002 Traveling bumps and their collisions in a two-dimensional neural field. Zbl 1217.92028Lu, Yao; Sato, Yuzuru; Amari, Shun-ichi 10 2011 Estimation in the presence of infinitely many nuisance parameters - Geometry of estimating functions. Zbl 0665.62029Amari, Shun-Ichi; Kumon, Masayuki 9 1988 Asymptotic theory of sequential estimation: Differential geometrical approach. Zbl 0737.62067Okamoto, Ichi; Amari, Shun-Ichi; Takeuchi, Kei 9 1991 Dynamics and computation of continuous attractors. Zbl 1148.68450Wu, Si; Hamaguchi, Kosuke; Amari, Shun-Ichi 9 2008 Flexible independent component analysis. Zbl 0965.68132Choi, Seungjin; Cichocki, Andrzej; Amari, Shun-Ichi 8 2000 Exponential convergence of delayed dynamical systems. Zbl 1083.34534Chen, Tianping; Amari, Shunichi 8 2001 Global convergence rate of recurrently connected neural networks. Zbl 1079.68584Chen, Tianping; Lu, Wenlian; Amari, Shun-ichi 8 2002 Information processing in a neuron ensemble with the multiplicative correlation structure. Zbl 1044.92003Wu, Si; Amari, Shun-ichi; Nakahara, Hiroyuki 8 2004 Theory of information space: A differential-geometrical foundation of statistics. Zbl 0433.62004Amari, Shun-ichi 8 1980 Information-theoretic approach to blind separation of sources in non-linear mixture. Zbl 1006.94514Hua Yang, Howard; Amari, Shun-ichi; Cichocki, Andrzej 8 1998 Log-determinant divergences revisited: alpha-beta and gamma log-det divergences. Zbl 1338.94034Cichocki, Andrzej; Cruces, Sergio; Amari, Shun-ichi 8 2015 Unified framework for information integration based on information geometry. Zbl 1407.62037Oizumi, Masafumi; Tsuchiya, Naotsugu; Amari, Shun-ichi 7 2016 Statistical inference under multiterminal rate restrictions: A differential geometric approach. Zbl 0673.62008Amari, Shun-ichi; Han, Te Sun 7 1989 Sequential Bayesian decoding with a population of neurons. Zbl 1085.68657Wu, Si; Chen, Danmei; Niranjan, Mahesan; Amari, Shun-ichi 7 2003 Learned parametric mixture based ICA algorithm. Zbl 0911.68159Xu, Lei; Cheung, Chi Chiu; Amari, Shun-ichi 7 1998 Equiaffine structures on statistical manifolds and Bayesian statistics. Zbl 1106.53008Matsuzoe, Hiroshi; Takeuchi, Jun-Ichi; Amari, Shun-Ichi 7 2006 Difficulty of singularity in population coding. Zbl 1079.62007Amari, Shun-ichi; Nakahara, Hiroyuki 7 2005 Estimation of a structural parameter in the presence of a large number of nuisance parameters. Zbl 0571.62025Kumon, Masayuki; Amari, Shun-ichi 6 1984 Information-geometric measures as robust estimators of connection strengths and external inputs. Zbl 1167.92007Tatsuno, Masami; Fellous, Jean-Marc; Amari, Shun-Ichi 6 2009 Mathematical theory of neural learning. Zbl 0712.68079Amari, Shun-ichi 6 1991 Dynamics of learning near singularities in radial basis function networks. Zbl 1254.68230Wei, Haikun; Amari, Shun-Ichi 6 2008 Information geometry of turbo and low-density parity-check codes. Zbl 1303.94134Ikeda, Shiro; Tanaka, Toshiyuki; Amari, Shun-Ichi 6 2004 Differential geometric structures of stable state feedback systems with dual connections. Zbl 0821.93029Ohara, Atsumi; Amari, Shun-Ichi 5 1994 Statistical inference under multiterminal data compression. Zbl 0933.94014Han, Te Sun; Amari, Shun-ichi 5 1998 Measure of correlation orthogonal to change in firing rate. Zbl 1178.68391Amari, Shun-ichi 5 2009 Attention modulation of neural tuning through peak and base rate. Zbl 0988.92007Nakahara, Hiroyuki; Wu, Si; Amari, Shun-ichi 5 2001 A comparison of descriptive models of a single spike train by information-geometric measure. Zbl 1087.92010Nakahara, Hiroyuki; Amari, Shun-ichi; Richmond, Barry J. 5 2006 Discrimination with spike times and ISI distributions. Zbl 1137.92007Kang, Kukjin; Amari, Shun-Ichi 5 2008 \(\alpha\)-parallel prior and its properties. Zbl 1147.62322Takeuchi, J.; Amari, S. 5 2005 On conformal divergences and their population minimizers. Zbl 1359.94347Nock, Richard; Nielsen, Frank; Amari, Shun-Ichi 5 2016 Dynamical analysis of contrastive divergence learning: restricted Boltzmann machines with Gaussian visible units. Zbl 1414.68062Karakida, Ryo; Okada, Masato; Amari, Shun-ichi 4 2016 Competition and cooperation in neural nets. Proceedings of the U.S.-Japan Joint Seminar held at Kyoto, Japan, February 15-19, 1982. Zbl 0477.00041 4 1982 Learning coefficients of layered models when the true distribution mismatches the singularities. Zbl 1085.68138Watanabe, Sumio; Amari, Shun-ichi 4 2003 Stoachastic reasoning, free energy, and information geometry. Zbl 1090.68106Ikeda, Shiro; Tanaka, Toshiyuki; Amari, Shun-ichi 4 2004 Differential geometrical method in asymptotics of statistical inference. Zbl 0693.62034Amari, Shun-ichi 4 1987 Identification of directed influence: Granger causality, Kullback-Leibler divergence, and complexity. Zbl 1311.92115Seghouane, Abd-Krim; Amari, Shun-Ichi 4 2012 Dynamical stability of formation of cortical maps. Zbl 0672.92005Amari, Shun-ichi 3 1989 Dualistic theory of non-Riemannian material manifolds. Zbl 0503.73094Amari, Shun-ichi 3 1981 Information geometry of the EM algorithm for neural networks. Zbl 0939.62501Amari, Shun-ichi; Kawanabe, Motoaki 3 1994 Backpropagation and stochastic gradient descent method. Zbl 0782.68094Amari, Shun-ichi 3 1993 Parameter estimation with multiterminal data compression. Zbl 0844.62005Han, Te Sun; Amari, Shun-ichi 3 1995 Dreaming of mathematical neuroscience for half a century. Zbl 1258.92006Amari, Shun-Ichi 3 2013 Sequential extraction of minor components. Zbl 1008.68732Chen, Tianping; Amari, Shun-Ichi; Murata, Noboru 3 2001 Correlation and independence in the neural code. Zbl 1101.68746Amari, Shun-ichi; Nakahara, Hiroyuki 3 2006 Probability estimation for recoverability analysis of blind source separation based on sparse representation. Zbl 1309.94045Li, Yuanqing; Amari, Shun-Ichi; Cichocki, Andrzej; Guan, Cuntai 3 2006 Geometry of information integration. Zbl 1414.62023Amari, Shun-ichi; Tsuchiya, Naotsugu; Oizumi, Masafumi 2 2018 Information geometry of Wasserstein divergence. Zbl 1425.94037Karakida, Ryo; Amari, Shun-ichi 2 2017 Competitive and cooperative aspects in dynamics of neural excitation and self-organization. Zbl 0494.92010Amari, Shun-ichi 2 1982 Differential geometry of statistical inference. Zbl 0533.62023Amari, Shun-ichi 2 1983 Estimation of network parameters in semiparametric stochastic perceptron. Zbl 0814.68109Kawanabe, Motoaki; Amari, Shun-ichi 2 1994 Improving generalization performance of natural gradient learning using optimized regularization by NIC. Zbl 1097.68603Park, Hyeyoung; Murata, Noboru; Amari, Shun-ichi 2 2004 Topographic organization of nerve fields. Zbl 0427.92008Amari, Shun-ichi 2 1978 Information geometry for regularized optimal transport and barycenters of patterns. Zbl 1478.53020Amari, Shun-Ichi; Karakida, Ryo; Oizumi, Masafumi; Cuturi, Marco 2 2019 Information geometry connecting Wasserstein distance and Kullback-Leibler divergence via the entropy-relaxed transportation problem. Zbl 1409.62020Amari, Shun-ichi; Karakida, Ryo; Oizumi, Masafumi 13 2018 Geometry of information integration. Zbl 1414.62023Amari, Shun-ichi; Tsuchiya, Naotsugu; Oizumi, Masafumi 2 2018 Dynamics of learning in MLP: natural gradient and singularity revisited. Zbl 1472.68128Amari, Shun-ichi; Ozeki, Tomoko; Karakida, Ryo; Yoshida, Yuki; Okada, Masato 1 2018 Information geometry of Wasserstein divergence. Zbl 1425.94037Karakida, Ryo; Amari, Shun-ichi 2 2017 Information geometry and its applications. Zbl 1350.94001Amari, Shun-ichi 102 2016 Unified framework for information integration based on information geometry. Zbl 1407.62037Oizumi, Masafumi; Tsuchiya, Naotsugu; Amari, Shun-ichi 7 2016 On conformal divergences and their population minimizers. Zbl 1359.94347Nock, Richard; Nielsen, Frank; Amari, Shun-Ichi 5 2016 Dynamical analysis of contrastive divergence learning: restricted Boltzmann machines with Gaussian visible units. Zbl 1414.68062Karakida, Ryo; Okada, Masato; Amari, Shun-ichi 4 2016 \(\ell_p\)-regularized least squares \((0<p<1)\) and critical path. Zbl 1359.94207Yukawa, Masahiro; Amari, Shun-Ichi 2 2016 Log-determinant divergences revisited: alpha-beta and gamma log-det divergences. Zbl 1338.94034Cichocki, Andrzej; Cruces, Sergio; Amari, Shun-ichi 8 2015 Standard divergence in manifold of dual affine connections. Zbl 1396.53044Amari, Shun-ichi; Ay, Nihat 1 2015 On clustering histograms with \(k\)-means by using mixed \(\alpha\)-divergences. Zbl 1341.62186Nielsen, Frank; Nock, Richard; Amari, Shun-ichi 1 2014 Heaviside world: excitation and self-organization of neural fields. Zbl 1462.92008Amari, Shun-Ichi 1 2014 Dreaming of mathematical neuroscience for half a century. Zbl 1258.92006Amari, Shun-Ichi 3 2013 Identification of directed influence: Granger causality, Kullback-Leibler divergence, and complexity. Zbl 1311.92115Seghouane, Abd-Krim; Amari, Shun-Ichi 4 2012 Conformal geometry of escort probability and its applications. Zbl 1262.82004Ohara, Atsumi; Matsuzoe, Hiroshi; Amari, Shun-Ichi 2 2012 Geometry of \(q\)-exponential family of probability distributions. Zbl 1306.62073Amari, Shun-Ichi; Ohara, Atsumi 20 2011 Traveling bumps and their collisions in a two-dimensional neural field. Zbl 1217.92028Lu, Yao; Sato, Yuzuru; Amari, Shun-ichi 10 2011 Modeling basal ganglia for understanding Parkinsonian reaching movements. Zbl 1208.92013Magdoom, K. N.; Subramanian, D.; Chakravarthy, V. S.; Ravindran, B.; Amari, Shun-Ichi; Meenakshisundaram, N. 2 2011 Families of alpha-, beta- and gamma-divergences: flexible and robust measures of similarities. Zbl 1229.94030Cichocki, Andrzej; Amari, Shun-Ichi 49 2010 \(\alpha\)-divergence is unique, belonging to both \(f\)-divergence and Bregman divergence classes. Zbl 1367.94133Amari, Shun-Ichi 20 2009 Information-geometric measures as robust estimators of connection strengths and external inputs. Zbl 1167.92007Tatsuno, Masami; Fellous, Jean-Marc; Amari, Shun-Ichi 6 2009 Measure of correlation orthogonal to change in firing rate. Zbl 1178.68391Amari, Shun-ichi 5 2009 Dynamics of learning near singularities in layered networks. Zbl 1138.68048Wei, Haikun; Zhang, Jun; Cousseau, Florent; Ozeki, Tomoko; Amari, Shun-Ichi 13 2008 Methods of information geometry. Translation from the Japanese by Daishi Harada. Reprint of the 2000 edition. Zbl 1146.62001Amari, Shun-ichi; Nagaoka, Hiroshi 12 2008 Dynamics and computation of continuous attractors. Zbl 1148.68450Wu, Si; Hamaguchi, Kosuke; Amari, Shun-Ichi 9 2008 Dynamics of learning near singularities in radial basis function networks. Zbl 1254.68230Wei, Haikun; Amari, Shun-Ichi 6 2008 Discrimination with spike times and ISI distributions. Zbl 1137.92007Kang, Kukjin; Amari, Shun-Ichi 5 2008 Hierarchical ALS algorithms for nonnegative matrix and 3D tensor factorization. Zbl 1172.94390Cichocki, Andrzej; Zdunek, Rafal; Amari, Shun-ichi 33 2007 Integration of stochastic models by minimizing \(\alpha\)-divergence. Zbl 1138.62002Amari, Shun-ichi 14 2007 Csiszár’s divergences for non-negative matrix factorization: Family of new algorithms. Zbl 1178.94057Cichocki, Andrzej; Zdunek, Rafal; Amari, Shun-ichi 20 2006 Estimating spiking irregularities under changing environments. Zbl 1106.92015Miura, Keiji; Okada, Masato; Amari, Shunichi 14 2006 Singularities affect dynamics of learning in neuromanifolds. Zbl 1092.68636Amari, Shun-ichi; Park, Hyeyoung; Ozeki, Tomoko 11 2006 Underdetermined blind source separation based on sparse representation. Zbl 1373.94647Li, Yuanqing; Amari, S.; Cichocki, A.; Ho, D. W. C.; Xie, Shengli 10 2006 Equiaffine structures on statistical manifolds and Bayesian statistics. Zbl 1106.53008Matsuzoe, Hiroshi; Takeuchi, Jun-Ichi; Amari, Shun-Ichi 7 2006 A comparison of descriptive models of a single spike train by information-geometric measure. Zbl 1087.92010Nakahara, Hiroyuki; Amari, Shun-ichi; Richmond, Barry J. 5 2006 Correlation and independence in the neural code. Zbl 1101.68746Amari, Shun-ichi; Nakahara, Hiroyuki 3 2006 Probability estimation for recoverability analysis of blind source separation based on sparse representation. Zbl 1309.94045Li, Yuanqing; Amari, Shun-Ichi; Cichocki, Andrzej; Guan, Cuntai 3 2006 Computing with continuous attractors: stability and online aspects. Zbl 1080.68638Wu, Si; Amari, Shun-ichi 10 2005 Difficulty of singularity in population coding. Zbl 1079.62007Amari, Shun-ichi; Nakahara, Hiroyuki 7 2005 \(\alpha\)-parallel prior and its properties. Zbl 1147.62322Takeuchi, J.; Amari, S. 5 2005 \(\alpha\)-parallel prior and its properties. Zbl 1288.62043Takeuchi, Jun-ichi; Amari, Shun-ichi 1 2005 Analysis of sparse representation and blind source separation. Zbl 1089.68101Li, Yuanqing; Cichocki, Andrzej; Amari, Shun-ichi 17 2004 Information processing in a neuron ensemble with the multiplicative correlation structure. Zbl 1044.92003Wu, Si; Amari, Shun-ichi; Nakahara, Hiroyuki 8 2004 Information geometry of turbo and low-density parity-check codes. Zbl 1303.94134Ikeda, Shiro; Tanaka, Toshiyuki; Amari, Shun-Ichi 6 2004 Stoachastic reasoning, free energy, and information geometry. Zbl 1090.68106Ikeda, Shiro; Tanaka, Toshiyuki; Amari, Shun-ichi 4 2004 Improving generalization performance of natural gradient learning using optimized regularization by NIC. Zbl 1097.68603Park, Hyeyoung; Murata, Noboru; Amari, Shun-ichi 2 2004 Synchronous firing and higher-order interactions in neuron pool. Zbl 1028.92007Amari, Shun-ichi; Nakahara, Hiroyuki; Wu, Si; Sakai, Yutaka 23 2003 Sequential Bayesian decoding with a population of neurons. Zbl 1085.68657Wu, Si; Chen, Danmei; Niranjan, Mahesan; Amari, Shun-ichi 7 2003 Learning coefficients of layered models when the true distribution mismatches the singularities. Zbl 1085.68138Watanabe, Sumio; Amari, Shun-ichi 4 2003 On some singularities in parameter estimation problems. Zbl 1085.94005Amari, S.; Burnashev, M. V. 1 2003 Population coding and decoding in a neural field: A computational study. Zbl 0994.92011Wu, Si; Amari, Shun-ichi; Nakahara, Hiroyuki 28 2002 Information-geometric measure for neural spikes. Zbl 1018.68068Nakahara, Hiroyuki; Amari, Shun-ichi 21 2002 Geometrical structures of FIR manifold and multichannel blind deconvolution. Zbl 0999.93013Zhang, L.-Q.; Cichocki, A.; Amari, S. 10 2002 Conformal transformation of kernel functions: A data-dependent way to improve support vector machine classifiers. Zbl 1008.68741Wu, Si; Amari, Shun-Ichi 10 2002 Global convergence rate of recurrently connected neural networks. Zbl 1079.68584Chen, Tianping; Lu, Wenlian; Amari, Shun-ichi 8 2002 On density estimation under relative entropy loss criterion. Zbl 1021.94007Burnashev, M. V.; Amari, S. 1 2002 Asymptotic behaviors of population codes. Zbl 1007.68766Wu, Si; Amari, Shun-ichi; Nakahara, Hiroyuki 1 2002 Information geometry on hierarchy of probability distributions. Zbl 0997.94009Amari, Shun-ichi 47 2001 Population coding with correlation and an unfaithful model. Zbl 1011.62116Wu, Si; Nakahara, Hiroyuki; Amari, Shun-ichi 18 2001 Exponential convergence of delayed dynamical systems. Zbl 1083.34534Chen, Tianping; Amari, Shunichi 8 2001 Attention modulation of neural tuning through peak and base rate. Zbl 0988.92007Nakahara, Hiroyuki; Wu, Si; Amari, Shun-ichi 5 2001 Sequential extraction of minor components. Zbl 1008.68732Chen, Tianping; Amari, Shun-Ichi; Murata, Noboru 3 2001 Methods of information geometry. Transl. from the Japanese by Daishi Harada. Zbl 0960.62005Amari, Shun-ichi; Nagaoka, Hiroshi 220 2000 Flexible independent component analysis. Zbl 0965.68132Choi, Seungjin; Cichocki, Andrzej; Amari, Shun-Ichi 8 2000 Statistical analysis of learning dynamics. Zbl 0922.68094Murata, Noboru; Amari, Shun-ichi 2 1999 Information-theoretic approach to blind separation of sources in non-linear mixture. Zbl 1006.94514Hua Yang, Howard; Amari, Shun-ichi; Cichocki, Andrzej 8 1998 Learned parametric mixture based ICA algorithm. Zbl 0911.68159Xu, Lei; Cheung, Chi Chiu; Amari, Shun-ichi 7 1998 Statistical inference under multiterminal data compression. Zbl 0933.94014Han, Te Sun; Amari, Shun-ichi 5 1998 Strategy under the unknown stochastic environment: The nonparametric lop-pass problem. Zbl 0910.68172Hiraoka, K.; Amari, S. 1 1998 Robust techniques for independent component analysis (ICA) with noisy data. Zbl 0911.68161Cichocki, A.; Douglas, S. C.; Amari, S. 1 1998 Information geometry of estimating functions in semi-parametric statistical models. Zbl 0881.62034Amari, Shun-ichi; Kawanabe, Motoaki 11 1997 Estimating functions in semiparametric statistical models. Zbl 0945.62026Amari, S.; Kawanabe, M. 2 1997 Information geometry. Zbl 0873.53004Amari, S.-I. 1 1997 Dualistic differential geometry of positive definite matrices and its applications to related problems. Zbl 0863.15009Ohara, Atsumi; Suda, Nobuhide; Amari, Shun-ichi 16 1996 Gradient systems in view of information geometry. Zbl 0883.53020Fujiwara, Akio; Amari, Shun-ichi 13 1995 Parameter estimation with multiterminal data compression. Zbl 0844.62005Han, Te Sun; Amari, Shun-ichi 3 1995 Differential geometric structures of stable state feedback systems with dual connections. Zbl 0821.93029Ohara, Atsumi; Amari, Shun-Ichi 5 1994 Information geometry of the EM algorithm for neural networks. Zbl 0939.62501Amari, Shun-ichi; Kawanabe, Motoaki 3 1994 Estimation of network parameters in semiparametric stochastic perceptron. Zbl 0814.68109Kawanabe, Motoaki; Amari, Shun-ichi 2 1994 Dualistic differential geometry of positive definite matrices and its application to optimizations and matrix completion problems. Zbl 0822.53008Ohara, Atsumi; Suda, Nobuhide; Amari, Shun-ichi 1 1994 Backpropagation and stochastic gradient descent method. Zbl 0782.68094Amari, Shun-ichi 3 1993 Mathematical methods of neurocomputing. Zbl 0821.92003Amari, Shun-Ichi 2 1993 Differential geometry of estimating functions. Zbl 0810.62026Amari, Shun-ichi 1 1993 Identifiability of hidden Markov information sources and their minimum degrees of freedom. Zbl 0742.60041Ito, Hisashi; Amari, Shun-Ichi; Kobayashi, Kingo 22 1992 Asymptotic theory of sequential estimation: Differential geometrical approach. Zbl 0737.62067Okamoto, Ichi; Amari, Shun-Ichi; Takeuchi, Kei 9 1991 Mathematical theory of neural learning. Zbl 0712.68079Amari, Shun-ichi 6 1991 Differential-geometrical methods in statistics. Corr. 2nd. printing. Zbl 0701.62008Amari, Shun-ichi 33 1990 Statistical inference under multiterminal rate restrictions: A differential geometric approach. Zbl 0673.62008Amari, Shun-ichi; Han, Te Sun 7 1989 Dynamical stability of formation of cortical maps. Zbl 0672.92005Amari, Shun-ichi 3 1989 Fisher information under restriction of Shannon information in multi-terminal situations. Zbl 0703.62005Amari, Shun-Ichi 2 1989 Estimation in the presence of infinitely many nuisance parameters - Geometry of estimating functions. Zbl 0665.62029Amari, Shun-Ichi; Kumon, Masayuki 9 1988 Differential geometry in statistical inference. Zbl 0694.62001Amari, S.-I.; Barndorff-Nielsen, O. E.; Kass, R. E.; Lauritzen, S. L.; Rao, C. R. 68 1987 Differential geometry of a parametric family of invertible linear systems. Riemannian metric, dual affine connections, and divergence. Zbl 0632.93017Amari, Shun-ichi 18 1987 Differential geometrical method in asymptotics of statistical inference. Zbl 0693.62034Amari, Shun-ichi 4 1987 Differential-geometrical methods in statistics. Zbl 0559.62001Amari, Shun-ichi 245 1985 Estimation of a structural parameter in the presence of a large number of nuisance parameters. Zbl 0571.62025Kumon, Masayuki; Amari, Shun-ichi 6 1984 Differential geometry of Edgeworth expansions in curved exponential family. Zbl 0527.62034Amari, Shun-ichi; Kumon, Masayuki 15 1983 Field theory of self-organizing neural nets. Zbl 0543.92007Amari, Shun-ichi 15 1983 ...and 23 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,268 Authors 53 Amari, Shun-ichi 16 Kilpatrick, Zachary P. 14 Coombes, Stephen 14 Eguchi, Shinto 14 Wyller, John A. 13 Ay, Nihat 13 Ohara, Atsumi 13 Okada, Masato 12 Bressloff, Paul C. 12 Komaki, Fumiyasu 11 Aihara, Kazuyuki 11 Laing, Carlo R. 11 Li, Wuchen 10 Nakahara, Hiroyuki 10 Pistone, Giovanni 10 Wu, Si 10 Zhang, Jun 9 Faugeras, Olivier D. 9 Oleynik, Anna 8 Cafaro, Carlo 8 Cichocki, Andrzej 8 Ghosh, Malay 8 Hino, Hideitsu 8 Lánský, Petr 8 Nielsen, Frank 8 Sun, Huafei 8 Vos, Paul W. 8 Wei, Bocheng 8 Zhang, Linghai 7 beim Graben, Peter 7 da Silva, Severino Horácio 7 Fujisawa, Hironori 7 Gillis, Nicolas 7 Hayashi, Masahito 7 Murata, Noboru 7 Peng, Linyu 7 Ponosov, Arkadiĭ Vladimirovich 7 Schnörr, Christoph 7 Shi, Yimin 7 Zhang, Fode 6 Akaho, Shotaro 6 Faye, Grégory 6 Hutt, Axel 6 Kloeden, Peter Eris 6 Kumon, Masayuki 6 Matsuzoe, Hiroshi 6 Tatsuno, Masami 6 Wong, Ting-Kam Leonard 6 Yanagimoto, Takemi 6 Zhu, Hongtu 5 Avitabile, Daniele 5 Burlakov, Evgenii O. 5 Cao, Jinde 5 Einevoll, Gaute T. 5 Felice, Domenico 5 Glineur, François 5 Jost, Jürgen 5 Kanamori, Takafumi 5 Kulhavý, Rudolf 5 Nakamura, Yoshimasa 5 Pázman, Andrej 5 Petz, Dénes 5 Peyghan, Esmaeil 5 Potthast, Roland W. E. 5 Rougier, Nicolas P. 5 Takenouchi, Takashi 5 Tang, Niansheng 5 Tayebi, Akbar 5 Weis, Stephan 5 Xie, Shengli 4 Abdel-All, Nassar Hassan 4 Cessac, Bruno 4 Ciaglia, Florio Maria 4 Crutchfield, James P. 4 Erlhagen, Wolfram 4 Ermentrout, Bard G. 4 Gibilisco, Paolo 4 Giri, Narayan C. 4 Grün, Sonja 4 Hamaguchi, Kosuke 4 Han, Xiaoying 4 Huang, Zhenkun 4 Ibrahim, Joseph George 4 Jenčová, Anna 4 Jirsa, Viktor K. 4 Josić, Krešimir 4 Jupp, Peter E. 4 Karakida, Ryo 4 Kawanabe, Motoaki 4 Knauf, Andreas 4 Komori, Osamu 4 Kubokawa, Tatsuya 4 Kumagai, Atsuya 4 Kuznetsov, Yuri Alexandrovich 4 Lima, Pedro Miguel 4 Mancini, Stefano 4 Marmo, Giuseppe 4 Marriott, Paul 4 Martens, Erik Andreas 4 Maybank, Stephen John ...and 2,168 more Authors all top 5 Cited in 347 Serials 176 Neural Computation 80 Biological Cybernetics 47 Neural Networks 46 Physica D 37 Annals of the Institute of Statistical Mathematics 28 Journal of Computational Neuroscience 28 Entropy 27 Information Geometry 24 Journal of Multivariate Analysis 23 Journal of Statistical Planning and Inference 20 The Journal of Mathematical Neuroscience 19 The Annals of Statistics 18 Linear Algebra and its Applications 17 Journal of Mathematical Physics 17 Communications in Statistics. 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Série VI 3 Calculus of Variations and Partial Differential Equations 3 Mathematical Methods of Statistics 3 Advances in Computational Mathematics 3 Journal of Mathematical Chemistry 3 Nonlinear Dynamics 3 Journal of Applied Statistics 3 Communications in Nonlinear Science and Numerical Simulation ...and 247 more Serials all top 5 Cited in 56 Fields 529 Statistics (62-XX) 489 Biology and other natural sciences (92-XX) 279 Computer science (68-XX) 237 Differential geometry (53-XX) 197 Information and communication theory, circuits (94-XX) 155 Probability theory and stochastic processes (60-XX) 105 Numerical analysis (65-XX) 98 Dynamical systems and ergodic theory (37-XX) 95 Partial differential equations (35-XX) 75 Statistical mechanics, structure of matter (82-XX) 73 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 68 Quantum theory (81-XX) 66 Integral equations (45-XX) 65 Linear and multilinear algebra; matrix theory (15-XX) 59 Ordinary differential equations (34-XX) 58 Systems theory; control (93-XX) 48 Operations research, mathematical programming (90-XX) 33 Operator theory (47-XX) 29 Global analysis, analysis on manifolds (58-XX) 25 Functional analysis (46-XX) 20 Calculus of variations and optimal control; optimization (49-XX) 12 Relativity and gravitational theory (83-XX) 11 Combinatorics (05-XX) 9 Classical thermodynamics, heat transfer (80-XX) 8 Convex and discrete geometry (52-XX) 7 General and overarching topics; collections (00-XX) 7 Measure and integration (28-XX) 7 Mechanics of deformable solids (74-XX) 6 Geometry (51-XX) 5 Topological groups, Lie groups (22-XX) 5 Approximations and expansions (41-XX) 5 Manifolds and cell complexes (57-XX) 5 Mechanics of particles and systems (70-XX) 5 Fluid mechanics (76-XX) 4 Algebraic geometry (14-XX) 4 Nonassociative rings and algebras (17-XX) 4 Geophysics (86-XX) 3 History and biography (01-XX) 3 Group theory and generalizations (20-XX) 3 Real functions (26-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Optics, electromagnetic theory (78-XX) 2 Commutative algebra (13-XX) 2 Category theory; homological algebra (18-XX) 2 Special functions (33-XX) 2 Difference and functional equations (39-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral transforms, operational calculus (44-XX) 2 General topology (54-XX) 2 Astronomy and astrophysics (85-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Number theory (11-XX) 1 Associative rings and algebras (16-XX) 1 Potential theory (31-XX) 1 Abstract harmonic analysis (43-XX) 1 Algebraic topology (55-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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