Edit Profile (opens in new tab) Amari, Shun-ichi Co-Author Distance 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. more...less Further Spellings: Amari, Shun’ichi; 甘利 俊; Амари Шун-ичи External Links: MGP · ORCID · Wikidata · Math-Net.Ru · dblp · GND · IdRef Documents Indexed: 179 Publications since 1961, including 16 Books and 2 Additional arXiv Preprints 4 Contributions as Editor · 1 Further Contribution Biographic References: 2 Publications Co-Authors: 104 Co-Authors with 121 Joint Publications 2,477 Co-Co-Authors all top 5 Co-Authors 58 single-authored 15 Cichocki, Andrzej 11 Nakahara, Hiroyuki 10 Wu, Si 9 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 Okada, Masato 4 Park, Hyeyoung 3 Chen, Tianping 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 Yoshida, Yuki 2 Yukawa, Masahiro 2 Zdunek, Rafal 1 Abe, Naoki 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 Feydy, Jean 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 Kurose, Takashi 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 Peyré, Gabriel 1 Rao, Calyampudi Radhakrishna 1 Richmond, Barry J. 1 Sakai, Yutaka 1 Sakamoto, Kotaro 1 Sato, Yuzuru 1 Seghouane, Abd-Krim 1 Séjourné, Thibault 1 Shimizu, Kunio 1 Sonoda, Sho 1 Takeuchi, Kei 1 Tamssaouet, F. ...and 12 more Co-Authors all top 5 Serials 36 Neural Computation 14 IEEE Transactions on Information Theory 5 Biological Cybernetics 5 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 3 Information Geometry 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 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 International Statistical Review 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 Research Notes in Neural Computing 1 Seminar on Mathematical Sciences 1 Journal of Physics A: Mathematical and Theoretical 1 Japanese Journal of Mathematics. 3rd Series 1 Kybernetik 1 International Journal of Systems Science. Principles and Applications of Systems and Integration 1 RIMS Kokyuroku all top 5 Fields 70 Statistics (62-XX) 56 Computer science (68-XX) 44 Biology and other natural sciences (92-XX) 42 Information and communication theory, circuits (94-XX) 33 Differential geometry (53-XX) 11 Probability theory and stochastic processes (60-XX) 7 Numerical analysis (65-XX) 6 Systems theory; control (93-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 General and overarching topics; collections (00-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Integral equations (45-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 137 Publications have been cited 3,017 times in 1,992 Documents Cited by ▼ Year ▼ Methods of information geometry. Transl. from the Japanese by Daishi Harada. Zbl 0960.62005 Amari, Shun-ichi; Nagaoka, Hiroshi 418 2000 Differential-geometrical methods in statistics. Zbl 0559.62001 Amari, Shun-ichi 358 1985 Dynamics of pattern formation in lateral-inhibition type neural fields. Zbl 0367.92005 Amari, Shun-ichi 334 1977 Information geometry and its applications. Zbl 1350.94001 Amari, Shun-ichi 216 2016 Differential geometry in statistical inference. Zbl 0694.62001 Amari, S.-I.; Barndorff-Nielsen, O. E.; Kass, R. E.; Lauritzen, S. L.; Rao, C. R. 119 1987 Differential geometry of curved exponential families. Curvatures and information loss. Zbl 0507.62026 Amari, Shun-ichi 113 1982 Families of alpha-, beta- and gamma-divergences: flexible and robust measures of similarities. Zbl 1229.94030 Cichocki, Andrzej; Amari, Shun-Ichi 71 2010 Information geometry on hierarchy of probability distributions. Zbl 0997.94009 Amari, Shun-ichi 57 2001 Characteristics of random nets of analog neuron-like elements. Zbl 0247.92006 Amari, Shun-Ichi 52 1972 Neural theory of association and concept-formation. Zbl 0364.92016 Amari, S.-I. 51 1977 Existence and stability of local excitations in homogeneous neural fields. Zbl 0406.92010 Kishimoto, K.; Amari, S. 50 1979 Hierarchical ALS algorithms for nonnegative matrix and 3D tensor factorization. Zbl 1172.94390 Cichocki, Andrzej; Zdunek, Rafal; Amari, Shun-ichi 43 2007 Differential-geometrical methods in statistics. Corr. 2nd. printing. Zbl 0701.62008 Amari, Shun-ichi 43 1990 A method of statistical neurodynamics. Zbl 0277.92003 Amari, Shun-ichi 31 1974 Learning patterns and pattern sequences by self-organizing nets of threshold elements. Zbl 0245.94024 Amari, Shun-Ichi 30 1972 Csiszár’s divergences for non-negative matrix factorization: Family of new algorithms. Zbl 1178.94057 Cichocki, Andrzej; Zdunek, Rafal; Amari, Shun-ichi 29 2006 Population coding and decoding in a neural field: A computational study. Zbl 0994.92011 Wu, Si; Amari, Shun-ichi; Nakahara, Hiroyuki 29 2002 Geometry of \(q\)-exponential family of probability distributions. Zbl 1306.62073 Amari, Shun-Ichi; Ohara, Atsumi 29 2011 Homogeneous nets of neuron-like elements. Zbl 0302.92004 Amari, Shun-Ichi 28 1975 \(\alpha\)-divergence is unique, belonging to both \(f\)-divergence and Bregman divergence classes. Zbl 1367.94133 Amari, Shun-Ichi 27 2009 Information geometry connecting Wasserstein distance and Kullback-Leibler divergence via the entropy-relaxed transportation problem. Zbl 1409.62020 Amari, Shun-ichi; Karakida, Ryo; Oizumi, Masafumi 27 2018 Synchronous firing and higher-order interactions in neuron pool. Zbl 1028.92007 Amari, Shun-ichi; Nakahara, Hiroyuki; Wu, Si; Sakai, Yutaka 25 2003 Topographic organization of nerve fields. Zbl 0477.92008 Amari, Shun-ichi 25 1980 Geometrical theory of asymptotic ancillarity and conditional inference. Zbl 0484.62046 Amari, Shun-Ichi 25 1982 Identifiability of hidden Markov information sources and their minimum degrees of freedom. Zbl 0742.60041 Ito, Hisashi; Amari, Shun-Ichi; Kobayashi, Kingo 24 1992 Information-geometric measure for neural spikes. Zbl 1018.68068 Nakahara, Hiroyuki; Amari, Shun-ichi 22 2002 Analysis of sparse representation and blind source separation. Zbl 1089.68101 Li, Yuanqing; Cichocki, Andrzej; Amari, Shun-ichi 22 2004 Dualistic differential geometry of positive definite matrices and its applications to related problems. Zbl 0863.15009 Ohara, Atsumi; Suda, Nobuhide; Amari, Shun-ichi 21 1996 Formation of topographic maps and columnar microstructures in nerve fields. Zbl 0418.92001 Takeuchi, A.; Amari, S. 21 1979 Gradient systems in view of information geometry. Zbl 0883.53020 Fujiwara, Akio; Amari, Shun-ichi 19 1995 A theory of adaptive pattern classifiers. Zbl 0189.50101 Amari, S.-i. 19 1967 Differential geometry of a parametric family of invertible linear systems. Riemannian metric, dual affine connections, and divergence. Zbl 0632.93017 Amari, Shun-ichi 19 1987 Population coding with correlation and an unfaithful model. Zbl 1011.62116 Wu, Si; Nakahara, Hiroyuki; Amari, Shun-ichi 18 2001 Integration of stochastic models by minimizing \(\alpha\)-divergence. Zbl 1138.62002 Amari, Shun-ichi 16 2007 Methods of information geometry. Translation from the Japanese by Daishi Harada. Reprint of the 2000 edition. Zbl 1146.62001 Amari, Shun-ichi; Nagaoka, Hiroshi 16 2008 Differential geometry of Edgeworth expansions in curved exponential family. Zbl 0527.62034 Amari, Shun-ichi; Kumon, Masayuki 16 1983 Field theory of self-organizing neural nets. Zbl 0543.92007 Amari, Shun-ichi 16 1983 Estimating spiking irregularities under changing environments. Zbl 1106.92015 Miura, Keiji; Okada, Masato; Amari, Shunichi 15 2006 A mathematical foundation for statistical neurodynamics. Zbl 0356.92002 Amari, Shun-Ichi; Yoshida, Kiyonori; Kanatani, Ken-Ichi 15 1977 Underdetermined blind source separation based on sparse representation. Zbl 1373.94647 Li, Yuanqing; Amari, S.; Cichocki, A.; Ho, D. W. C.; Xie, Shengli 15 2006 Geometrical theory of higher-order asymptotics of test, interval estimator and conditional inference. Zbl 0527.62031 Kumon, M.; Amari, S. 15 1983 Information geometry of estimating functions in semi-parametric statistical models. Zbl 0881.62034 Amari, Shun-ichi; Kawanabe, Motoaki 14 1997 Dynamics of learning near singularities in layered networks. Zbl 1138.68048 Wei, Haikun; Zhang, Jun; Cousseau, Florent; Ozeki, Tomoko; Amari, Shun-Ichi 14 2008 Estimation in the presence of infinitely many nuisance parameters - Geometry of estimating functions. Zbl 0665.62029 Amari, Shun-Ichi; Kumon, Masayuki 13 1988 Mathematical theory on formation of category detecting nerve cells. Zbl 0383.92003 Amari, Shun-ichi; Takeuchi, Akikazu 13 1978 Geometrical structures of FIR manifold and multichannel blind deconvolution. Zbl 0999.93013 Zhang, L.-Q.; Cichocki, A.; Amari, S. 12 2002 Singularities affect dynamics of learning in neuromanifolds. Zbl 1092.68636 Amari, Shun-ichi; Park, Hyeyoung; Ozeki, Tomoko 12 2006 Log-determinant divergences revisited: alpha-beta and gamma log-det divergences. Zbl 1338.94034 Cichocki, Andrzej; Cruces, Sergio; Amari, Shun-ichi 12 2015 Flexible independent component analysis. Zbl 0965.68132 Choi, Seungjin; Cichocki, Andrzej; Amari, Shun-Ichi 11 2000 Computing with continuous attractors: stability and online aspects. Zbl 1080.68638 Wu, Si; Amari, Shun-ichi 11 2005 Conformal transformation of kernel functions: A data-dependent way to improve support vector machine classifiers. Zbl 1008.68741 Wu, Si; Amari, Shun-Ichi 10 2002 Unified framework for information integration based on information geometry. Zbl 1407.62037 Oizumi, Masafumi; Tsuchiya, Naotsugu; Amari, Shun-ichi 10 2016 Traveling bumps and their collisions in a two-dimensional neural field. Zbl 1217.92028 Lu, Yao; Sato, Yuzuru; Amari, Shun-ichi 10 2011 Asymptotic theory of sequential estimation: Differential geometrical approach. Zbl 0737.62067 Okamoto, Ichi; Amari, Shun-Ichi; Takeuchi, Kei 10 1991 Theory of information space: A differential-geometrical foundation of statistics. Zbl 0433.62004 Amari, Shun-ichi 9 1980 Dynamics and computation of continuous attractors. Zbl 1148.68450 Wu, Si; Hamaguchi, Kosuke; Amari, Shun-Ichi 9 2008 Backpropagation and stochastic gradient descent method. Zbl 0782.68094 Amari, Shun-ichi 8 1993 Equiaffine structures on statistical manifolds and Bayesian statistics. Zbl 1106.53008 Matsuzoe, Hiroshi; Takeuchi, Jun-Ichi; Amari, Shun-Ichi 8 2006 Dynamical analysis of contrastive divergence learning: restricted Boltzmann machines with Gaussian visible units. Zbl 1414.68062 Karakida, Ryo; Okada, Masato; Amari, Shun-ichi 8 2016 Information-theoretic approach to blind separation of sources in non-linear mixture. Zbl 1006.94514 Hua Yang, Howard; Amari, Shun-ichi; Cichocki, Andrzej 8 1998 Statistical inference under multiterminal rate restrictions: A differential geometric approach. Zbl 0673.62008 Amari, Shun-ichi; Han, Te Sun 8 1989 Statistical inference under multiterminal data compression. Zbl 0933.94014 Han, Te Sun; Amari, Shun-ichi 8 1998 Global convergence rate of recurrently connected neural networks. Zbl 1079.68584 Chen, Tianping; Lu, Wenlian; Amari, Shun-ichi 8 2002 Information processing in a neuron ensemble with the multiplicative correlation structure. Zbl 1044.92003 Wu, Si; Amari, Shun-ichi; Nakahara, Hiroyuki 8 2004 Exponential convergence of delayed dynamical systems. Zbl 1083.34534 Chen, Tianping; Amari, Shunichi 8 2001 Estimation of a structural parameter in the presence of a large number of nuisance parameters. Zbl 0571.62025 Kumon, Masayuki; Amari, Shun-ichi 8 1984 On conformal divergences and their population minimizers. Zbl 1359.94347 Nock, Richard; Nielsen, Frank; Amari, Shun-Ichi 8 2016 Learned parametric mixture based ICA algorithm. Zbl 0911.68159 Xu, Lei; Cheung, Chi Chiu; Amari, Shun-ichi 7 1998 Information geometry of turbo and low-density parity-check codes. Zbl 1303.94134 Ikeda, Shiro; Tanaka, Toshiyuki; Amari, Shun-Ichi 7 2004 Difficulty of singularity in population coding. Zbl 1079.62007 Amari, Shun-ichi; Nakahara, Hiroyuki 7 2005 Sequential Bayesian decoding with a population of neurons. Zbl 1085.68657 Wu, Si; Chen, Danmei; Niranjan, Mahesan; Amari, Shun-ichi 7 2003 Information geometry for regularized optimal transport and barycenters of patterns. Zbl 1478.53020 Amari, Shun-Ichi; Karakida, Ryo; Oizumi, Masafumi; Cuturi, Marco 7 2019 Dynamical stability of formation of cortical maps. Zbl 0672.92005 Amari, Shun-ichi 6 1989 \(\alpha\)-parallel prior and its properties. Zbl 1147.62322 Takeuchi, J.; Amari, S. 6 2005 Information-geometric measures as robust estimators of connection strengths and external inputs. Zbl 1167.92007 Tatsuno, Masami; Fellous, Jean-Marc; Amari, Shun-Ichi 6 2009 Learning coefficients of layered models when the true distribution mismatches the singularities. Zbl 1085.68138 Watanabe, Sumio; Amari, Shun-ichi 6 2003 Information geometry. Zbl 1472.53023 Amari, Shun-ichi 6 2021 Dynamics of learning near singularities in radial basis function networks. Zbl 1254.68230 Wei, Haikun; Amari, Shun-Ichi 6 2008 Mathematical theory of neural learning. Zbl 0712.68079 Amari, Shun-ichi 6 1991 Differential geometric structures of stable state feedback systems with dual connections. Zbl 0821.93029 Ohara, Atsumi; Amari, Shun-Ichi 5 1994 Attention modulation of neural tuning through peak and base rate. Zbl 0988.92007 Nakahara, Hiroyuki; Wu, Si; Amari, Shun-ichi 5 2001 Measure of correlation orthogonal to change in firing rate. Zbl 1178.68391 Amari, Shun-ichi 5 2009 Discrimination with spike times and ISI distributions. Zbl 1137.92007 Kang, Kukjin; Amari, Shun-Ichi 5 2008 A comparison of descriptive models of a single spike train by information-geometric measure. Zbl 1087.92010 Nakahara, Hiroyuki; Amari, Shun-ichi; Richmond, Barry J. 5 2006 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 5 1982 Probability estimation for recoverability analysis of blind source separation based on sparse representation. Zbl 1309.94045 Li, Yuanqing; Amari, Shun-Ichi; Cichocki, Andrzej; Guan, Cuntai 4 2006 Parameter estimation with multiterminal data compression. Zbl 0844.62005 Han, Te Sun; Amari, Shun-ichi 4 1995 Stoachastic reasoning, free energy, and information geometry. Zbl 1090.68106 Ikeda, Shiro; Tanaka, Toshiyuki; Amari, Shun-ichi 4 2004 \(\ell_p\)-regularized least squares \((0<p<1)\) and critical path. Zbl 1359.94207 Yukawa, Masahiro; Amari, Shun-Ichi 4 2016 Differential geometrical method in asymptotics of statistical inference. Zbl 0693.62034 Amari, Shun-ichi 4 1987 Fisher information under restriction of Shannon information in multi-terminal situations. Zbl 0703.62005 Amari, Shun-Ichi 4 1989 Identification of directed influence: Granger causality, Kullback-Leibler divergence, and complexity. Zbl 1311.92115 Seghouane, Abd-Krim; Amari, Shun-Ichi 4 2012 Dreaming of mathematical neuroscience for half a century. Zbl 1258.92006 Amari, Shun-Ichi 4 2013 Conformal geometry of escort probability and its applications. Zbl 1262.82004 Ohara, Atsumi; Matsuzoe, Hiroshi; Amari, Shun-Ichi 4 2012 Dualistic theory of non-Riemannian material manifolds. Zbl 0503.73094 Amari, Shun-ichi 4 1981 Sequential extraction of minor components. Zbl 1008.68732 Chen, Tianping; Amari, Shun-Ichi; Murata, Noboru 3 2001 Statistical analysis of learning dynamics. Zbl 0922.68094 Murata, Noboru; Amari, Shun-ichi 3 1999 Information geometry of the EM algorithm for neural networks. Zbl 0939.62501 Amari, Shun-ichi; Kawanabe, Motoaki 3 1994 Correlation and independence in the neural code. Zbl 1101.68746 Amari, Shun-ichi; Nakahara, Hiroyuki 3 2006 Heaviside world: excitation and self-organization of neural fields. Zbl 1462.92008 Amari, Shun-Ichi 3 2014 Wasserstein statistics in one-dimensional location scale models. Zbl 07473253 Amari, Shun-ichi; Matsuda, Takeru 2 2022 Optimal transportation plans with escort entropy regularization. Zbl 1493.62028 Kurose, Takashi; Yoshizawa, Shintaro; Amari, Shun-ichi 1 2022 Information geometry. Zbl 1472.53023 Amari, Shun-ichi 6 2021 Pathological spectra of the Fisher information metric and its variants in deep neural networks. Zbl 1522.68497 Karakida, Ryo; Akaho, Shotaro; Amari, Shun-Ichi 2 2021 Wasserstein statistics in one-dimensional location-scale models. Zbl 07495249 Amari, Shun-ichi; Matsuda, Takeru 1 2021 Universal statistics of Fisher information in deep neural networks: mean field approach. Zbl 07330526 Karakida, Ryo; Akaho, Shotaro; Amari, Shun-ichi 3 2020 Any target function exists in a neighborhood of any sufficiently wide random network: a geometrical perspective. Zbl 1490.68196 Amari, Shun-ichi 1 2020 Information geometry for regularized optimal transport and barycenters of patterns. Zbl 1478.53020 Amari, Shun-Ichi; Karakida, Ryo; Oizumi, Masafumi; Cuturi, Marco 7 2019 Statistical mechanical analysis of learning dynamics of two-layer perceptron with multiple output units. Zbl 1509.82102 Yoshida, Yuki; Karakida, Ryo; Okada, Masato; Amari, Shun-Ichi 2 2019 Information geometry connecting Wasserstein distance and Kullback-Leibler divergence via the entropy-relaxed transportation problem. Zbl 1409.62020 Amari, Shun-ichi; Karakida, Ryo; Oizumi, Masafumi 27 2018 Dynamics of learning in MLP: natural gradient and singularity revisited. Zbl 1472.68128 Amari, Shun-ichi; Ozeki, Tomoko; Karakida, Ryo; Yoshida, Yuki; Okada, Masato 3 2018 Geometry of information integration. Zbl 1414.62023 Amari, Shun-ichi; Tsuchiya, Naotsugu; Oizumi, Masafumi 2 2018 Modelling and temporal evaluation of networked control systems using timed automata with guards and (max,+) algebra. Zbl 1482.93235 Tamssaouet, F.; Amari, S. 2 2018 Information geometry of Wasserstein divergence. Zbl 1425.94037 Karakida, Ryo; Amari, Shun-ichi 2 2017 Information geometry and its applications. Zbl 1350.94001 Amari, Shun-ichi 216 2016 Unified framework for information integration based on information geometry. Zbl 1407.62037 Oizumi, Masafumi; Tsuchiya, Naotsugu; Amari, Shun-ichi 10 2016 Dynamical analysis of contrastive divergence learning: restricted Boltzmann machines with Gaussian visible units. Zbl 1414.68062 Karakida, Ryo; Okada, Masato; Amari, Shun-ichi 8 2016 On conformal divergences and their population minimizers. Zbl 1359.94347 Nock, Richard; Nielsen, Frank; Amari, Shun-Ichi 8 2016 \(\ell_p\)-regularized least squares \((0<p<1)\) and critical path. Zbl 1359.94207 Yukawa, Masahiro; Amari, Shun-Ichi 4 2016 Log-determinant divergences revisited: alpha-beta and gamma log-det divergences. Zbl 1338.94034 Cichocki, Andrzej; Cruces, Sergio; Amari, Shun-ichi 12 2015 Standard divergence in manifold of dual affine connections. Zbl 1396.53044 Amari, Shun-ichi; Ay, Nihat 1 2015 Heaviside world: excitation and self-organization of neural fields. Zbl 1462.92008 Amari, Shun-Ichi 3 2014 On clustering histograms with \(k\)-means by using mixed \(\alpha\)-divergences. Zbl 1341.62186 Nielsen, Frank; Nock, Richard; Amari, Shun-ichi 2 2014 Dreaming of mathematical neuroscience for half a century. Zbl 1258.92006 Amari, Shun-Ichi 4 2013 Achieving precise mechanical control in intrinsically noisy systems. Zbl 1451.82040 Lu, Wenlian; Feng, Jianfeng; Amari, Shun-Ichi; Waxman, David 1 2013 Identification of directed influence: Granger causality, Kullback-Leibler divergence, and complexity. Zbl 1311.92115 Seghouane, Abd-Krim; Amari, Shun-Ichi 4 2012 Conformal geometry of escort probability and its applications. Zbl 1262.82004 Ohara, Atsumi; Matsuzoe, Hiroshi; Amari, Shun-Ichi 4 2012 Geometry of \(q\)-exponential family of probability distributions. Zbl 1306.62073 Amari, Shun-Ichi; Ohara, Atsumi 29 2011 Traveling bumps and their collisions in a two-dimensional neural field. Zbl 1217.92028 Lu, Yao; Sato, Yuzuru; Amari, Shun-ichi 10 2011 Modeling basal ganglia for understanding Parkinsonian reaching movements. Zbl 1208.92013 Magdoom, K. N.; Subramanian, D.; Chakravarthy, V. S.; Ravindran, B.; Amari, Shun-Ichi; Meenakshisundaram, N. 2 2011 On optimal data compression in multiterminal statistical inference. Zbl 1365.94194 Amari, Shun-ichi 2 2011 Families of alpha-, beta- and gamma-divergences: flexible and robust measures of similarities. Zbl 1229.94030 Cichocki, Andrzej; Amari, Shun-Ichi 71 2010 \(\alpha\)-divergence is unique, belonging to both \(f\)-divergence and Bregman divergence classes. Zbl 1367.94133 Amari, Shun-Ichi 27 2009 Information-geometric measures as robust estimators of connection strengths and external inputs. Zbl 1167.92007 Tatsuno, Masami; Fellous, Jean-Marc; Amari, Shun-Ichi 6 2009 Measure of correlation orthogonal to change in firing rate. Zbl 1178.68391 Amari, Shun-ichi 5 2009 Methods of information geometry. Translation from the Japanese by Daishi Harada. Reprint of the 2000 edition. Zbl 1146.62001 Amari, Shun-ichi; Nagaoka, Hiroshi 16 2008 Dynamics of learning near singularities in layered networks. Zbl 1138.68048 Wei, Haikun; Zhang, Jun; Cousseau, Florent; Ozeki, Tomoko; Amari, Shun-Ichi 14 2008 Dynamics and computation of continuous attractors. Zbl 1148.68450 Wu, Si; Hamaguchi, Kosuke; Amari, Shun-Ichi 9 2008 Dynamics of learning near singularities in radial basis function networks. Zbl 1254.68230 Wei, Haikun; Amari, Shun-Ichi 6 2008 Discrimination with spike times and ISI distributions. Zbl 1137.92007 Kang, Kukjin; Amari, Shun-Ichi 5 2008 Hierarchical ALS algorithms for nonnegative matrix and 3D tensor factorization. Zbl 1172.94390 Cichocki, Andrzej; Zdunek, Rafal; Amari, Shun-ichi 43 2007 Integration of stochastic models by minimizing \(\alpha\)-divergence. Zbl 1138.62002 Amari, Shun-ichi 16 2007 Csiszár’s divergences for non-negative matrix factorization: Family of new algorithms. Zbl 1178.94057 Cichocki, Andrzej; Zdunek, Rafal; Amari, Shun-ichi 29 2006 Estimating spiking irregularities under changing environments. Zbl 1106.92015 Miura, Keiji; Okada, Masato; Amari, Shunichi 15 2006 Underdetermined blind source separation based on sparse representation. Zbl 1373.94647 Li, Yuanqing; Amari, S.; Cichocki, A.; Ho, D. W. C.; Xie, Shengli 15 2006 Singularities affect dynamics of learning in neuromanifolds. Zbl 1092.68636 Amari, Shun-ichi; Park, Hyeyoung; Ozeki, Tomoko 12 2006 Equiaffine structures on statistical manifolds and Bayesian statistics. Zbl 1106.53008 Matsuzoe, Hiroshi; Takeuchi, Jun-Ichi; Amari, Shun-Ichi 8 2006 A comparison of descriptive models of a single spike train by information-geometric measure. Zbl 1087.92010 Nakahara, Hiroyuki; Amari, Shun-ichi; Richmond, Barry J. 5 2006 Probability estimation for recoverability analysis of blind source separation based on sparse representation. Zbl 1309.94045 Li, Yuanqing; Amari, Shun-Ichi; Cichocki, Andrzej; Guan, Cuntai 4 2006 Correlation and independence in the neural code. Zbl 1101.68746 Amari, Shun-ichi; Nakahara, Hiroyuki 3 2006 Computing with continuous attractors: stability and online aspects. Zbl 1080.68638 Wu, Si; Amari, Shun-ichi 11 2005 Difficulty of singularity in population coding. Zbl 1079.62007 Amari, Shun-ichi; Nakahara, Hiroyuki 7 2005 \(\alpha\)-parallel prior and its properties. Zbl 1147.62322 Takeuchi, J.; Amari, S. 6 2005 \(\alpha\)-parallel prior and its properties. Zbl 1288.62043 Takeuchi, Jun-ichi; Amari, Shun-ichi 1 2005 Analysis of sparse representation and blind source separation. Zbl 1089.68101 Li, Yuanqing; Cichocki, Andrzej; Amari, Shun-ichi 22 2004 Information processing in a neuron ensemble with the multiplicative correlation structure. Zbl 1044.92003 Wu, Si; Amari, Shun-ichi; Nakahara, Hiroyuki 8 2004 Information geometry of turbo and low-density parity-check codes. Zbl 1303.94134 Ikeda, Shiro; Tanaka, Toshiyuki; Amari, Shun-Ichi 7 2004 Stoachastic reasoning, free energy, and information geometry. Zbl 1090.68106 Ikeda, Shiro; Tanaka, Toshiyuki; Amari, Shun-ichi 4 2004 Improving generalization performance of natural gradient learning using optimized regularization by NIC. Zbl 1097.68603 Park, Hyeyoung; Murata, Noboru; Amari, Shun-ichi 2 2004 Synchronous firing and higher-order interactions in neuron pool. Zbl 1028.92007 Amari, Shun-ichi; Nakahara, Hiroyuki; Wu, Si; Sakai, Yutaka 25 2003 Sequential Bayesian decoding with a population of neurons. Zbl 1085.68657 Wu, Si; Chen, Danmei; Niranjan, Mahesan; Amari, Shun-ichi 7 2003 Learning coefficients of layered models when the true distribution mismatches the singularities. Zbl 1085.68138 Watanabe, Sumio; Amari, Shun-ichi 6 2003 On some singularities in parameter estimation problems. Zbl 1085.94005 Amari, S.; Burnashev, M. V. 1 2003 Population coding and decoding in a neural field: A computational study. Zbl 0994.92011 Wu, Si; Amari, Shun-ichi; Nakahara, Hiroyuki 29 2002 Information-geometric measure for neural spikes. Zbl 1018.68068 Nakahara, Hiroyuki; Amari, Shun-ichi 22 2002 Geometrical structures of FIR manifold and multichannel blind deconvolution. Zbl 0999.93013 Zhang, L.-Q.; Cichocki, A.; Amari, S. 12 2002 Conformal transformation of kernel functions: A data-dependent way to improve support vector machine classifiers. Zbl 1008.68741 Wu, Si; Amari, Shun-Ichi 10 2002 Global convergence rate of recurrently connected neural networks. Zbl 1079.68584 Chen, Tianping; Lu, Wenlian; Amari, Shun-ichi 8 2002 Asymptotic behaviors of population codes. Zbl 1007.68766 Wu, Si; Amari, Shun-ichi; Nakahara, Hiroyuki 1 2002 On density estimation under relative entropy loss criterion. Zbl 1021.94007 Burnashev, M. V.; Amari, S. 1 2002 Information geometry on hierarchy of probability distributions. Zbl 0997.94009 Amari, Shun-ichi 57 2001 Population coding with correlation and an unfaithful model. Zbl 1011.62116 Wu, Si; Nakahara, Hiroyuki; Amari, Shun-ichi 18 2001 Exponential convergence of delayed dynamical systems. Zbl 1083.34534 Chen, Tianping; Amari, Shunichi 8 2001 Attention modulation of neural tuning through peak and base rate. Zbl 0988.92007 Nakahara, Hiroyuki; Wu, Si; Amari, Shun-ichi 5 2001 Sequential extraction of minor components. Zbl 1008.68732 Chen, Tianping; Amari, Shun-Ichi; Murata, Noboru 3 2001 The minimum entropy and cumulants based contrast functions for blind source extraction. Zbl 0982.68843 Cruces, Sergio; Cichocki, Andrzej; Amari, Shun-ichi 1 2001 On some estimation problems with information constraints. Zbl 1113.62301 Burnashev, M. V.; Han, T. S.; Amari, S. 1 2001 Methods of information geometry. Transl. from the Japanese by Daishi Harada. Zbl 0960.62005 Amari, Shun-ichi; Nagaoka, Hiroshi 418 2000 Flexible independent component analysis. Zbl 0965.68132 Choi, Seungjin; Cichocki, Andrzej; Amari, Shun-Ichi 11 2000 On some testing of hypothesis problems with information constraints. Zbl 0990.62003 Burnashev, M. V.; Amari, Sh.; Han, T. S. 2 2000 Statistical analysis of learning dynamics. Zbl 0922.68094 Murata, Noboru; Amari, Shun-ichi 3 1999 Information-theoretic approach to blind separation of sources in non-linear mixture. Zbl 1006.94514 Hua Yang, Howard; Amari, Shun-ichi; Cichocki, Andrzej 8 1998 Statistical inference under multiterminal data compression. Zbl 0933.94014 Han, Te Sun; Amari, Shun-ichi 8 1998 Learned parametric mixture based ICA algorithm. Zbl 0911.68159 Xu, Lei; Cheung, Chi Chiu; Amari, Shun-ichi 7 1998 Strategy under the unknown stochastic environment: The nonparametric lop-pass problem. Zbl 0910.68172 Hiraoka, K.; Amari, S. 1 1998 Robust techniques for independent component analysis (ICA) with noisy data. Zbl 0911.68161 Cichocki, A.; Douglas, S. C.; Amari, S. 1 1998 Information geometry of estimating functions in semi-parametric statistical models. Zbl 0881.62034 Amari, Shun-ichi; Kawanabe, Motoaki 14 1997 Estimating functions in semiparametric statistical models. Zbl 0945.62026 Amari, S.; Kawanabe, M. 2 1997 Information geometry. Zbl 0873.53004 Amari, S.-I. 2 1997 Dualistic differential geometry of positive definite matrices and its applications to related problems. Zbl 0863.15009 Ohara, Atsumi; Suda, Nobuhide; Amari, Shun-ichi 21 1996 Gradient systems in view of information geometry. Zbl 0883.53020 Fujiwara, Akio; Amari, Shun-ichi 19 1995 Parameter estimation with multiterminal data compression. Zbl 0844.62005 Han, Te Sun; Amari, Shun-ichi 4 1995 Differential geometric structures of stable state feedback systems with dual connections. Zbl 0821.93029 Ohara, Atsumi; Amari, Shun-Ichi 5 1994 Information geometry of the EM algorithm for neural networks. Zbl 0939.62501 Amari, Shun-ichi; Kawanabe, Motoaki 3 1994 Estimation of network parameters in semiparametric stochastic perceptron. Zbl 0814.68109 Kawanabe, Motoaki; Amari, Shun-ichi 2 1994 Dualistic differential geometry of positive definite matrices and its application to optimizations and matrix completion problems. Zbl 0822.53008 Ohara, Atsumi; Suda, Nobuhide; Amari, Shun-ichi 1 1994 Backpropagation and stochastic gradient descent method. Zbl 0782.68094 Amari, Shun-ichi 8 1993 Mathematical methods of neurocomputing. Zbl 0821.92003 Amari, Shun-Ichi 2 1993 Differential geometry of estimating functions. Zbl 0810.62026 Amari, Shun-ichi 1 1993 Identifiability of hidden Markov information sources and their minimum degrees of freedom. Zbl 0742.60041 Ito, Hisashi; Amari, Shun-Ichi; Kobayashi, Kingo 24 1992 ...and 37 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,913 Authors 59 Amari, Shun-ichi 18 Kilpatrick, Zachary P. 17 Eguchi, Shinto 15 Li, Wuchen 15 Okada, Masato 15 Zhang, Jun 14 Ay, Nihat 14 Coombes, Stephen 14 Ohara, Atsumi 14 Pistone, Giovanni 14 Wyller, John A. 13 Bressloff, Paul C. 13 Komaki, Fumiyasu 11 Aihara, Kazuyuki 11 Cafaro, Carlo 11 Laing, Carlo R. 11 Nielsen, Frank 11 Peyghan, Esmaeil 11 Schnörr, Christoph 10 Ghosh, Malay 10 Hino, Hideitsu 10 Nakahara, Hiroyuki 10 Shi, Yimin 10 Wu, Si 10 Zhang, Fode 9 Faugeras, Olivier D. 9 Hayashi, Masahito 9 Marmo, Giuseppe 9 Matsuzoe, Hiroshi 9 Murata, Noboru 9 Oleynik, Anna 9 Quevedo, Hernando 9 Sun, Huafei 9 Vos, Paul W. 8 Akaho, Shotaro 8 Burlakov, Evgenii O. 8 Ciaglia, Florio Maria 8 Cichocki, Andrzej 8 Lánský, Petr 8 Peng, Linyu 8 Wada, Tatsuaki 8 Wei, Bocheng 8 Wong, Ting-Kam Leonard 8 Zhang, Linghai 7 Avitabile, Daniele 7 beim Graben, Peter 7 da Silva, Severino Horácio 7 Fujisawa, Hironori 7 Gillis, Nicolas 7 Jost, Jürgen 7 Karakida, Ryo 7 Naudts, Jan 7 Ponosov, Arkadiĭ Vladimirovich 7 Shanker, Gauree 6 Bauer, Martin 6 Blaga, Adara-Monica 6 Cao, Jinde 6 Faye, Grégory 6 Felice, Domenico 6 Hutt, Axel 6 Kloeden, Peter Eris 6 Kulhavý, Rudolf 6 Kumon, Masayuki 6 Minh, Ha Quang 6 Modin, Klas 6 Ng, Hon Keung Tony 6 Petra, Stefania 6 Rani, Sarita 6 Reid, Nancy 6 Sei, Tomonari 6 Shahid, Mohammed Hasan 6 Siddiqui, Aliya Naaz 6 Tang, Niansheng 6 Tatsuno, Masami 6 Tayebi, Akbar 6 Yanagimoto, Takemi 6 Zhu, Hongtu 5 Crutchfield, James P. 5 Di Cosmo, Fabio 5 Einevoll, Gaute T. 5 Ermentrout, George Bard 5 Glineur, François 5 He, Xing 5 Kanamori, Takafumi 5 Khan, Gabriel J. H. 5 Kharin, Yuriĭ Sëmenovich 5 Kubokawa, Tatsuya 5 Lima, Pedro Miguel 5 Mancini, Stefano 5 Marriott, Paul 5 Maybank, Stephen John 5 Montúfar, Guido F. 5 Nakamura, Yoshimasa 5 Nannicini, Antonella 5 Ngom, Papa 5 Pázman, Andrej 5 Petz, Dénes 5 Potthast, Roland W. E. 5 Rougier, Nicolas P. 5 Savarino, Fabrizio ...and 2,813 more Authors all top 5 Cited in 425 Serials 178 Neural Computation 81 Biological Cybernetics 77 Information Geometry 62 Neural Networks 49 Physica D 40 Physica A 39 Annals of the Institute of Statistical Mathematics 31 Journal of Multivariate Analysis 31 Journal of Computational Neuroscience 28 Entropy 25 Journal of Statistical Planning and Inference 23 Journal of Physics A: Mathematical and Theoretical 21 Communications in Statistics. Theory and Methods 20 Journal of Mathematical Physics 20 The Annals of Statistics 20 Linear Algebra and its Applications 20 The Journal of Mathematical Neuroscience 17 SIAM Journal on Applied Dynamical Systems 16 Journal of Mathematical Biology 16 Journal of Geometry and Physics 16 Journal of Statistical Mechanics: Theory and Experiment 15 Bulletin of Mathematical Biology 15 Journal of Mathematical Imaging and Vision 15 Chaos 13 Journal of Statistical Physics 13 Statistics & Probability Letters 12 Journal of Mathematical Analysis and Applications 12 Kybernetika 12 Circuits, Systems, and Signal Processing 12 Machine Learning 11 Journal of Computational and Applied Mathematics 11 Bernoulli 10 Japan Journal of Industrial and Applied Mathematics 10 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 10 Journal of Machine Learning Research (JMLR) 10 International Journal of Geometric Methods in Modern Physics 9 Reports on Mathematical Physics 9 Information Sciences 9 Differential Geometry and its Applications 9 Stochastic Processes and their Applications 9 International Journal of Computer Vision 8 Computers & Mathematics with Applications 8 Applied Mathematics and Computation 8 Automatica 8 Computational Statistics and Data Analysis 8 Applied Mathematics. Series B (English Edition) 8 International Electronic Journal of Geometry 8 Statistics and Computing 7 Physics Letters. A 7 Journal of Differential Equations 7 Statistical Science 7 SIAM Journal on Scientific Computing 7 Electronic Journal of Statistics 6 Communications in Mathematical Physics 6 International Journal of Theoretical Physics 6 Chaos, Solitons and Fractals 6 International Statistical Review 6 Journal of Mathematical Psychology 6 Signal Processing 6 Computational Optimization and Applications 6 Nonlinear Analysis. Real World Applications 6 Quantum Information Processing 6 Hacettepe Journal of Mathematics and Statistics 6 SIAM Journal on Imaging Sciences 6 Journal of Theoretical Biology 6 Bayesian Analysis 5 General Relativity and Gravitation 5 Reviews in Mathematical Physics 5 Gaṇita 5 Results in Mathematics 5 Statistics 5 Probability Theory and Related Fields 5 Journal of Scientific Computing 5 Journal of Global Optimization 5 Pattern Recognition 5 SIAM Journal on Mathematical Analysis 5 Journal of Mathematical Sciences (New York) 5 Balkan Journal of Geometry and its Applications (BJGA) 5 Differential Equations and Dynamical Systems 5 New Journal of Physics 5 International Journal of Quantum Information 5 Sankhyā. Series A 5 Journal of the Japan Statistical Society. Japanese Issue 4 The Canadian Journal of Statistics 4 Journal of Computational Physics 4 Journal of the Franklin Institute 4 Letters in Mathematical Physics 4 Scandinavian Journal of Statistics 4 Journal of Computer and System Sciences 4 Sequential Analysis 4 International Journal of Approximate Reasoning 4 SIAM Journal on Matrix Analysis and Applications 4 European Journal of Operational Research 4 International Journal of Computer Mathematics 4 SIAM Review 4 Calculus of Variations and Partial Differential Equations 4 Turkish Journal of Mathematics 4 Filomat 4 Open Systems & Information Dynamics 4 Communications in Nonlinear Science and Numerical Simulation ...and 325 more Serials all top 5 Cited in 57 Fields 695 Statistics (62-XX) 535 Biology and other natural sciences (92-XX) 377 Differential geometry (53-XX) 328 Computer science (68-XX) 263 Information and communication theory, circuits (94-XX) 200 Probability theory and stochastic processes (60-XX) 136 Numerical analysis (65-XX) 119 Partial differential equations (35-XX) 117 Dynamical systems and ergodic theory (37-XX) 113 Statistical mechanics, structure of matter (82-XX) 111 Quantum theory (81-XX) 89 Linear and multilinear algebra; matrix theory (15-XX) 88 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 75 Integral equations (45-XX) 71 Systems theory; control (93-XX) 70 Operations research, mathematical programming (90-XX) 63 Ordinary differential equations (34-XX) 43 Global analysis, analysis on manifolds (58-XX) 40 Functional analysis (46-XX) 39 Calculus of variations and optimal control; optimization (49-XX) 37 Operator theory (47-XX) 23 Relativity and gravitational theory (83-XX) 17 Combinatorics (05-XX) 13 Measure and integration (28-XX) 12 Topological groups, Lie groups (22-XX) 11 Convex and discrete geometry (52-XX) 11 Mechanics of deformable solids (74-XX) 11 Classical thermodynamics, heat transfer (80-XX) 9 General and overarching topics; collections (00-XX) 9 Geometry (51-XX) 8 Several complex variables and analytic spaces (32-XX) 8 Mechanics of particles and systems (70-XX) 7 Group theory and generalizations (20-XX) 7 Approximations and expansions (41-XX) 7 Fluid mechanics (76-XX) 7 Geophysics (86-XX) 6 History and biography (01-XX) 6 Algebraic geometry (14-XX) 6 Real functions (26-XX) 6 Manifolds and cell complexes (57-XX) 5 Nonassociative rings and algebras (17-XX) 4 Special functions (33-XX) 4 Integral transforms, operational calculus (44-XX) 4 Optics, electromagnetic theory (78-XX) 4 Astronomy and astrophysics (85-XX) 3 Commutative algebra (13-XX) 3 Difference and functional equations (39-XX) 3 Algebraic topology (55-XX) 2 Mathematical logic and foundations (03-XX) 2 Category theory; homological algebra (18-XX) 2 Potential theory (31-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 General topology (54-XX) 1 Number theory (11-XX) 1 Associative rings and algebras (16-XX) 1 Functions of a complex variable (30-XX) 1 Abstract harmonic analysis (43-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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