## Amari, Shun-ichi

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 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
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### 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
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### 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)

### 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 0367.92005
Amari, Shun-ichi
1977
Differential-geometrical methods in statistics. Zbl 0559.62001
Amari, Shun-ichi
1985
Methods of information geometry. Transl. from the Japanese by Daishi Harada. Zbl 0960.62005
Amari, Shun-ichi; Nagaoka, Hiroshi
2000
Information geometry and its applications. Zbl 1350.94001
Amari, Shun-ichi
2016
Differential geometry of curved exponential families. Curvatures and information loss. Zbl 0507.62026
Amari, Shun-ichi
1982
Differential geometry in statistical inference. Zbl 0694.62001
Amari, S.-I.; Barndorff-Nielsen, O. E.; Kass, R. E.; Lauritzen, S. L.; Rao, C. R.
1987
Families of alpha-, beta- and gamma-divergences: flexible and robust measures of similarities. Zbl 1229.94030
Cichocki, Andrzej; Amari, Shun-Ichi
2010
Neural theory of association and concept-formation. Zbl 0364.92016
Amari, S.-I.
1977
Existence and stability of local excitations in homogeneous neural fields. Zbl 0406.92010
Kishimoto, K.; Amari, S.
1979
Information geometry on hierarchy of probability distributions. Zbl 0997.94009
Amari, Shun-ichi
2001
Characteristics of random nets of analog neuron-like elements. Zbl 0247.92006
Amari, Shun-Ichi
1972
Differential-geometrical methods in statistics. Corr. 2nd. printing. Zbl 0701.62008
Amari, Shun-ichi
1990
Hierarchical ALS algorithms for nonnegative matrix and 3D tensor factorization. Zbl 1172.94390
Cichocki, Andrzej; Zdunek, Rafal; Amari, Shun-ichi
2007
A method of statistical neurodynamics. Zbl 0277.92003
Amari, Shun-ichi
1974
Learning patterns and pattern sequences by self-organizing nets of threshold elements. Zbl 0245.94024
Amari, Shun-Ichi
1972
Population coding and decoding in a neural field: A computational study. Zbl 0994.92011
Wu, Si; Amari, Shun-ichi; Nakahara, Hiroyuki
2002
Homogeneous nets of neuron-like elements. Zbl 0302.92004
Amari, Shun-Ichi
1975
Topographic organization of nerve fields. Zbl 0477.92008
Amari, Shun-ichi
1980
Geometrical theory of asymptotic ancillarity and conditional inference. Zbl 0484.62046
Amari, Shun-Ichi
1982
Synchronous firing and higher-order interactions in neuron pool. Zbl 1028.92007
Amari, Shun-ichi; Nakahara, Hiroyuki; Wu, Si; Sakai, Yutaka
2003
Identifiability of hidden Markov information sources and their minimum degrees of freedom. Zbl 0742.60041
Ito, Hisashi; Amari, Shun-Ichi; Kobayashi, Kingo
1992
Information-geometric measure for neural spikes. Zbl 1018.68068
Nakahara, Hiroyuki; Amari, Shun-ichi
2002
Formation of topographic maps and columnar microstructures in nerve fields. Zbl 0418.92001
Takeuchi, A.; Amari, S.
1979
Csiszár’s divergences for non-negative matrix factorization: Family of new algorithms. Zbl 1178.94057
Cichocki, Andrzej; Zdunek, Rafal; Amari, Shun-ichi
2006
Geometry of $$q$$-exponential family of probability distributions. Zbl 1306.62073
Amari, Shun-Ichi; Ohara, Atsumi
2011
$$\alpha$$-divergence is unique, belonging to both $$f$$-divergence and Bregman divergence classes. Zbl 1367.94133
Amari, Shun-Ichi
2009
Population coding with correlation and an unfaithful model. Zbl 1011.62116
Wu, Si; Nakahara, Hiroyuki; Amari, Shun-ichi
2001
Differential geometry of a parametric family of invertible linear systems. Riemannian metric, dual affine connections, and divergence. Zbl 0632.93017
Amari, Shun-ichi
1987
Analysis of sparse representation and blind source separation. Zbl 1089.68101
Li, Yuanqing; Cichocki, Andrzej; Amari, Shun-ichi
2004
Dualistic differential geometry of positive definite matrices and its applications to related problems. Zbl 0863.15009
Ohara, Atsumi; Suda, Nobuhide; Amari, Shun-ichi
1996
A theory of adaptive pattern classifiers. Zbl 0189.50101
Amari, S.-i.
1967
Differential geometry of Edgeworth expansions in curved exponential family. Zbl 0527.62034
Amari, Shun-ichi; Kumon, Masayuki
1983
Field theory of self-organizing neural nets. Zbl 0543.92007
Amari, Shun-ichi
1983
Geometrical theory of higher-order asymptotics of test, interval estimator and conditional inference. Zbl 0527.62031
Kumon, M.; Amari, S.
1983
A mathematical foundation for statistical neurodynamics. Zbl 0356.92002
Amari, Shun-Ichi; Yoshida, Kiyonori; Kanatani, Ken-Ichi
1977
Estimating spiking irregularities under changing environments. Zbl 1106.92015
Miura, Keiji; Okada, Masato; Amari, Shunichi
2006
Integration of stochastic models by minimizing $$\alpha$$-divergence. Zbl 1138.62002
Amari, Shun-ichi
2007
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
2018
Gradient systems in view of information geometry. Zbl 0883.53020
Fujiwara, Akio; Amari, Shun-ichi
1995
Mathematical theory on formation of category detecting nerve cells. Zbl 0383.92003
Amari, Shun-ichi; Takeuchi, Akikazu
1978
Dynamics of learning near singularities in layered networks. Zbl 1138.68048
Wei, Haikun; Zhang, Jun; Cousseau, Florent; Ozeki, Tomoko; Amari, Shun-Ichi
2008
Methods of information geometry. Translation from the Japanese by Daishi Harada. Reprint of the 2000 edition. Zbl 1146.62001
Amari, Shun-ichi; Nagaoka, Hiroshi
2008
Information geometry of estimating functions in semi-parametric statistical models. Zbl 0881.62034
Amari, Shun-ichi; Kawanabe, Motoaki
1997
Singularities affect dynamics of learning in neuromanifolds. Zbl 1092.68636
Amari, Shun-ichi; Park, Hyeyoung; Ozeki, Tomoko
2006
Underdetermined blind source separation based on sparse representation. Zbl 1373.94647
Li, Yuanqing; Amari, S.; Cichocki, A.; Ho, D. W. C.; Xie, Shengli
2006
Computing with continuous attractors: stability and online aspects. Zbl 1080.68638
Wu, Si; Amari, Shun-ichi
2005
Geometrical structures of FIR manifold and multichannel blind deconvolution. Zbl 0999.93013
Zhang, L.-Q.; Cichocki, A.; Amari, S.
2002
Conformal transformation of kernel functions: A data-dependent way to improve support vector machine classifiers. Zbl 1008.68741
Wu, Si; Amari, Shun-Ichi
2002
Traveling bumps and their collisions in a two-dimensional neural field. Zbl 1217.92028
Lu, Yao; Sato, Yuzuru; Amari, Shun-ichi
2011
Estimation in the presence of infinitely many nuisance parameters - Geometry of estimating functions. Zbl 0665.62029
Amari, Shun-Ichi; Kumon, Masayuki
1988
Asymptotic theory of sequential estimation: Differential geometrical approach. Zbl 0737.62067
Okamoto, Ichi; Amari, Shun-Ichi; Takeuchi, Kei
1991
Dynamics and computation of continuous attractors. Zbl 1148.68450
Wu, Si; Hamaguchi, Kosuke; Amari, Shun-Ichi
2008
Flexible independent component analysis. Zbl 0965.68132
Choi, Seungjin; Cichocki, Andrzej; Amari, Shun-Ichi
2000
Exponential convergence of delayed dynamical systems. Zbl 1083.34534
Chen, Tianping; Amari, Shunichi
2001
Global convergence rate of recurrently connected neural networks. Zbl 1079.68584
Chen, Tianping; Lu, Wenlian; Amari, Shun-ichi
2002
Information processing in a neuron ensemble with the multiplicative correlation structure. Zbl 1044.92003
Wu, Si; Amari, Shun-ichi; Nakahara, Hiroyuki
2004
Theory of information space: A differential-geometrical foundation of statistics. Zbl 0433.62004
Amari, Shun-ichi
1980
Information-theoretic approach to blind separation of sources in non-linear mixture. Zbl 1006.94514
Hua Yang, Howard; Amari, Shun-ichi; Cichocki, Andrzej
1998
Log-determinant divergences revisited: alpha-beta and gamma log-det divergences. Zbl 1338.94034
Cichocki, Andrzej; Cruces, Sergio; Amari, Shun-ichi
2015
Unified framework for information integration based on information geometry. Zbl 1407.62037
Oizumi, Masafumi; Tsuchiya, Naotsugu; Amari, Shun-ichi
2016
Statistical inference under multiterminal rate restrictions: A differential geometric approach. Zbl 0673.62008
Amari, Shun-ichi; Han, Te Sun
1989
Sequential Bayesian decoding with a population of neurons. Zbl 1085.68657
Wu, Si; Chen, Danmei; Niranjan, Mahesan; Amari, Shun-ichi
2003
Learned parametric mixture based ICA algorithm. Zbl 0911.68159
Xu, Lei; Cheung, Chi Chiu; Amari, Shun-ichi
1998
Equiaffine structures on statistical manifolds and Bayesian statistics. Zbl 1106.53008
Matsuzoe, Hiroshi; Takeuchi, Jun-Ichi; Amari, Shun-Ichi
2006
Difficulty of singularity in population coding. Zbl 1079.62007
Amari, Shun-ichi; Nakahara, Hiroyuki
2005
Estimation of a structural parameter in the presence of a large number of nuisance parameters. Zbl 0571.62025
Kumon, Masayuki; Amari, Shun-ichi
1984
Information-geometric measures as robust estimators of connection strengths and external inputs. Zbl 1167.92007
Tatsuno, Masami; Fellous, Jean-Marc; Amari, Shun-Ichi
2009
Mathematical theory of neural learning. Zbl 0712.68079
Amari, Shun-ichi
1991
Dynamics of learning near singularities in radial basis function networks. Zbl 1254.68230
Wei, Haikun; Amari, Shun-Ichi
2008
Information geometry of turbo and low-density parity-check codes. Zbl 1303.94134
Ikeda, Shiro; Tanaka, Toshiyuki; Amari, Shun-Ichi
2004
Differential geometric structures of stable state feedback systems with dual connections. Zbl 0821.93029
Ohara, Atsumi; Amari, Shun-Ichi
1994
Statistical inference under multiterminal data compression. Zbl 0933.94014
Han, Te Sun; Amari, Shun-ichi
1998
Measure of correlation orthogonal to change in firing rate. Zbl 1178.68391
Amari, Shun-ichi
2009
Attention modulation of neural tuning through peak and base rate. Zbl 0988.92007
Nakahara, Hiroyuki; Wu, Si; Amari, Shun-ichi
2001
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.
2006
Discrimination with spike times and ISI distributions. Zbl 1137.92007
Kang, Kukjin; Amari, Shun-Ichi
2008
$$\alpha$$-parallel prior and its properties. Zbl 1147.62322
Takeuchi, J.; Amari, S.
2005
On conformal divergences and their population minimizers. Zbl 1359.94347
Nock, Richard; Nielsen, Frank; Amari, Shun-Ichi
2016
Dynamical analysis of contrastive divergence learning: restricted Boltzmann machines with Gaussian visible units. Zbl 1414.68062
Karakida, Ryo; Okada, Masato; Amari, Shun-ichi
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
1982
Learning coefficients of layered models when the true distribution mismatches the singularities. Zbl 1085.68138
Watanabe, Sumio; Amari, Shun-ichi
2003
Stoachastic reasoning, free energy, and information geometry. Zbl 1090.68106
Ikeda, Shiro; Tanaka, Toshiyuki; Amari, Shun-ichi
2004
Differential geometrical method in asymptotics of statistical inference. Zbl 0693.62034
Amari, Shun-ichi
1987
Identification of directed influence: Granger causality, Kullback-Leibler divergence, and complexity. Zbl 1311.92115
Seghouane, Abd-Krim; Amari, Shun-Ichi
2012
Dynamical stability of formation of cortical maps. Zbl 0672.92005
Amari, Shun-ichi
1989
Dualistic theory of non-Riemannian material manifolds. Zbl 0503.73094
Amari, Shun-ichi
1981
Information geometry of the EM algorithm for neural networks. Zbl 0939.62501
Amari, Shun-ichi; Kawanabe, Motoaki
1994
Backpropagation and stochastic gradient descent method. Zbl 0782.68094
Amari, Shun-ichi
1993
Parameter estimation with multiterminal data compression. Zbl 0844.62005
Han, Te Sun; Amari, Shun-ichi
1995
Dreaming of mathematical neuroscience for half a century. Zbl 1258.92006
Amari, Shun-Ichi
2013
Sequential extraction of minor components. Zbl 1008.68732
Chen, Tianping; Amari, Shun-Ichi; Murata, Noboru
2001
Correlation and independence in the neural code. Zbl 1101.68746
Amari, Shun-ichi; Nakahara, Hiroyuki
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
2006
Geometry of information integration. Zbl 1414.62023
Amari, Shun-ichi; Tsuchiya, Naotsugu; Oizumi, Masafumi
2018
Information geometry of Wasserstein divergence. Zbl 1425.94037
Karakida, Ryo; Amari, Shun-ichi
2017
Competitive and cooperative aspects in dynamics of neural excitation and self-organization. Zbl 0494.92010
Amari, Shun-ichi
1982
Differential geometry of statistical inference. Zbl 0533.62023
Amari, Shun-ichi
1983
Estimation of network parameters in semiparametric stochastic perceptron. Zbl 0814.68109
Kawanabe, Motoaki; Amari, Shun-ichi
1994
Improving generalization performance of natural gradient learning using optimized regularization by NIC. Zbl 1097.68603
Park, Hyeyoung; Murata, Noboru; Amari, Shun-ichi
2004
Topographic organization of nerve fields. Zbl 0427.92008
Amari, Shun-ichi
1978
Information geometry for regularized optimal transport and barycenters of patterns. Zbl 1478.53020
Amari, Shun-Ichi; Karakida, Ryo; Oizumi, Masafumi; Cuturi, Marco
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
2018
Geometry of information integration. Zbl 1414.62023
Amari, Shun-ichi; Tsuchiya, Naotsugu; Oizumi, Masafumi
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
2018
Information geometry of Wasserstein divergence. Zbl 1425.94037
Karakida, Ryo; Amari, Shun-ichi
2017
Information geometry and its applications. Zbl 1350.94001
Amari, Shun-ichi
2016
Unified framework for information integration based on information geometry. Zbl 1407.62037
Oizumi, Masafumi; Tsuchiya, Naotsugu; Amari, Shun-ichi
2016
On conformal divergences and their population minimizers. Zbl 1359.94347
Nock, Richard; Nielsen, Frank; Amari, Shun-Ichi
2016
Dynamical analysis of contrastive divergence learning: restricted Boltzmann machines with Gaussian visible units. Zbl 1414.68062
Karakida, Ryo; Okada, Masato; Amari, Shun-ichi
2016
$$\ell_p$$-regularized least squares $$(0<p<1)$$ and critical path. Zbl 1359.94207
Yukawa, Masahiro; Amari, Shun-Ichi
2016
Log-determinant divergences revisited: alpha-beta and gamma log-det divergences. Zbl 1338.94034
Cichocki, Andrzej; Cruces, Sergio; Amari, Shun-ichi
2015
Standard divergence in manifold of dual affine connections. Zbl 1396.53044
Amari, Shun-ichi; Ay, Nihat
2015
On clustering histograms with $$k$$-means by using mixed $$\alpha$$-divergences. Zbl 1341.62186
Nielsen, Frank; Nock, Richard; Amari, Shun-ichi
2014
Heaviside world: excitation and self-organization of neural fields. Zbl 1462.92008
Amari, Shun-Ichi
2014
Dreaming of mathematical neuroscience for half a century. Zbl 1258.92006
Amari, Shun-Ichi
2013
Identification of directed influence: Granger causality, Kullback-Leibler divergence, and complexity. Zbl 1311.92115
Seghouane, Abd-Krim; Amari, Shun-Ichi
2012
Conformal geometry of escort probability and its applications. Zbl 1262.82004
Ohara, Atsumi; Matsuzoe, Hiroshi; Amari, Shun-Ichi
2012
Geometry of $$q$$-exponential family of probability distributions. Zbl 1306.62073
Amari, Shun-Ichi; Ohara, Atsumi
2011
Traveling bumps and their collisions in a two-dimensional neural field. Zbl 1217.92028
Lu, Yao; Sato, Yuzuru; Amari, Shun-ichi
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.
2011
Families of alpha-, beta- and gamma-divergences: flexible and robust measures of similarities. Zbl 1229.94030
Cichocki, Andrzej; Amari, Shun-Ichi
2010
$$\alpha$$-divergence is unique, belonging to both $$f$$-divergence and Bregman divergence classes. Zbl 1367.94133
Amari, Shun-Ichi
2009
Information-geometric measures as robust estimators of connection strengths and external inputs. Zbl 1167.92007
Tatsuno, Masami; Fellous, Jean-Marc; Amari, Shun-Ichi
2009
Measure of correlation orthogonal to change in firing rate. Zbl 1178.68391
Amari, Shun-ichi
2009
Dynamics of learning near singularities in layered networks. Zbl 1138.68048
Wei, Haikun; Zhang, Jun; Cousseau, Florent; Ozeki, Tomoko; Amari, Shun-Ichi
2008
Methods of information geometry. Translation from the Japanese by Daishi Harada. Reprint of the 2000 edition. Zbl 1146.62001
Amari, Shun-ichi; Nagaoka, Hiroshi
2008
Dynamics and computation of continuous attractors. Zbl 1148.68450
Wu, Si; Hamaguchi, Kosuke; Amari, Shun-Ichi
2008
Dynamics of learning near singularities in radial basis function networks. Zbl 1254.68230
Wei, Haikun; Amari, Shun-Ichi
2008
Discrimination with spike times and ISI distributions. Zbl 1137.92007
Kang, Kukjin; Amari, Shun-Ichi
2008
Hierarchical ALS algorithms for nonnegative matrix and 3D tensor factorization. Zbl 1172.94390
Cichocki, Andrzej; Zdunek, Rafal; Amari, Shun-ichi
2007
Integration of stochastic models by minimizing $$\alpha$$-divergence. Zbl 1138.62002
Amari, Shun-ichi
2007
Csiszár’s divergences for non-negative matrix factorization: Family of new algorithms. Zbl 1178.94057
Cichocki, Andrzej; Zdunek, Rafal; Amari, Shun-ichi
2006
Estimating spiking irregularities under changing environments. Zbl 1106.92015
Miura, Keiji; Okada, Masato; Amari, Shunichi
2006
Singularities affect dynamics of learning in neuromanifolds. Zbl 1092.68636
Amari, Shun-ichi; Park, Hyeyoung; Ozeki, Tomoko
2006
Underdetermined blind source separation based on sparse representation. Zbl 1373.94647
Li, Yuanqing; Amari, S.; Cichocki, A.; Ho, D. W. C.; Xie, Shengli
2006
Equiaffine structures on statistical manifolds and Bayesian statistics. Zbl 1106.53008
Matsuzoe, Hiroshi; Takeuchi, Jun-Ichi; Amari, Shun-Ichi
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.
2006
Correlation and independence in the neural code. Zbl 1101.68746
Amari, Shun-ichi; Nakahara, Hiroyuki
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
2006
Computing with continuous attractors: stability and online aspects. Zbl 1080.68638
Wu, Si; Amari, Shun-ichi
2005
Difficulty of singularity in population coding. Zbl 1079.62007
Amari, Shun-ichi; Nakahara, Hiroyuki
2005
$$\alpha$$-parallel prior and its properties. Zbl 1147.62322
Takeuchi, J.; Amari, S.
2005
$$\alpha$$-parallel prior and its properties. Zbl 1288.62043
Takeuchi, Jun-ichi; Amari, Shun-ichi
2005
Analysis of sparse representation and blind source separation. Zbl 1089.68101
Li, Yuanqing; Cichocki, Andrzej; Amari, Shun-ichi
2004
Information processing in a neuron ensemble with the multiplicative correlation structure. Zbl 1044.92003
Wu, Si; Amari, Shun-ichi; Nakahara, Hiroyuki
2004
Information geometry of turbo and low-density parity-check codes. Zbl 1303.94134
Ikeda, Shiro; Tanaka, Toshiyuki; Amari, Shun-Ichi
2004
Stoachastic reasoning, free energy, and information geometry. Zbl 1090.68106
Ikeda, Shiro; Tanaka, Toshiyuki; Amari, Shun-ichi
2004
Improving generalization performance of natural gradient learning using optimized regularization by NIC. Zbl 1097.68603
Park, Hyeyoung; Murata, Noboru; Amari, Shun-ichi
2004
Synchronous firing and higher-order interactions in neuron pool. Zbl 1028.92007
Amari, Shun-ichi; Nakahara, Hiroyuki; Wu, Si; Sakai, Yutaka
2003
Sequential Bayesian decoding with a population of neurons. Zbl 1085.68657
Wu, Si; Chen, Danmei; Niranjan, Mahesan; Amari, Shun-ichi
2003
Learning coefficients of layered models when the true distribution mismatches the singularities. Zbl 1085.68138
Watanabe, Sumio; Amari, Shun-ichi
2003
On some singularities in parameter estimation problems. Zbl 1085.94005
Amari, S.; Burnashev, M. V.
2003
Population coding and decoding in a neural field: A computational study. Zbl 0994.92011
Wu, Si; Amari, Shun-ichi; Nakahara, Hiroyuki
2002
Information-geometric measure for neural spikes. Zbl 1018.68068
Nakahara, Hiroyuki; Amari, Shun-ichi
2002
Geometrical structures of FIR manifold and multichannel blind deconvolution. Zbl 0999.93013
Zhang, L.-Q.; Cichocki, A.; Amari, S.
2002
Conformal transformation of kernel functions: A data-dependent way to improve support vector machine classifiers. Zbl 1008.68741
Wu, Si; Amari, Shun-Ichi
2002
Global convergence rate of recurrently connected neural networks. Zbl 1079.68584
Chen, Tianping; Lu, Wenlian; Amari, Shun-ichi
2002
On density estimation under relative entropy loss criterion. Zbl 1021.94007
Burnashev, M. V.; Amari, S.
2002
Asymptotic behaviors of population codes. Zbl 1007.68766
Wu, Si; Amari, Shun-ichi; Nakahara, Hiroyuki
2002
Information geometry on hierarchy of probability distributions. Zbl 0997.94009
Amari, Shun-ichi
2001
Population coding with correlation and an unfaithful model. Zbl 1011.62116
Wu, Si; Nakahara, Hiroyuki; Amari, Shun-ichi
2001
Exponential convergence of delayed dynamical systems. Zbl 1083.34534
Chen, Tianping; Amari, Shunichi
2001
Attention modulation of neural tuning through peak and base rate. Zbl 0988.92007
Nakahara, Hiroyuki; Wu, Si; Amari, Shun-ichi
2001
Sequential extraction of minor components. Zbl 1008.68732
Chen, Tianping; Amari, Shun-Ichi; Murata, Noboru
2001
Methods of information geometry. Transl. from the Japanese by Daishi Harada. Zbl 0960.62005
Amari, Shun-ichi; Nagaoka, Hiroshi
2000
Flexible independent component analysis. Zbl 0965.68132
Choi, Seungjin; Cichocki, Andrzej; Amari, Shun-Ichi
2000
Statistical analysis of learning dynamics. Zbl 0922.68094
Murata, Noboru; Amari, Shun-ichi
1999
Information-theoretic approach to blind separation of sources in non-linear mixture. Zbl 1006.94514
Hua Yang, Howard; Amari, Shun-ichi; Cichocki, Andrzej
1998
Learned parametric mixture based ICA algorithm. Zbl 0911.68159
Xu, Lei; Cheung, Chi Chiu; Amari, Shun-ichi
1998
Statistical inference under multiterminal data compression. Zbl 0933.94014
Han, Te Sun; Amari, Shun-ichi
1998
Strategy under the unknown stochastic environment: The nonparametric lop-pass problem. Zbl 0910.68172
Hiraoka, K.; Amari, S.
1998
Robust techniques for independent component analysis (ICA) with noisy data. Zbl 0911.68161
Cichocki, A.; Douglas, S. C.; Amari, S.
1998
Information geometry of estimating functions in semi-parametric statistical models. Zbl 0881.62034
Amari, Shun-ichi; Kawanabe, Motoaki
1997
Estimating functions in semiparametric statistical models. Zbl 0945.62026
Amari, S.; Kawanabe, M.
1997
Information geometry. Zbl 0873.53004
Amari, S.-I.
1997
Dualistic differential geometry of positive definite matrices and its applications to related problems. Zbl 0863.15009
Ohara, Atsumi; Suda, Nobuhide; Amari, Shun-ichi
1996
Gradient systems in view of information geometry. Zbl 0883.53020
Fujiwara, Akio; Amari, Shun-ichi
1995
Parameter estimation with multiterminal data compression. Zbl 0844.62005
Han, Te Sun; Amari, Shun-ichi
1995
Differential geometric structures of stable state feedback systems with dual connections. Zbl 0821.93029
Ohara, Atsumi; Amari, Shun-Ichi
1994
Information geometry of the EM algorithm for neural networks. Zbl 0939.62501
Amari, Shun-ichi; Kawanabe, Motoaki
1994
Estimation of network parameters in semiparametric stochastic perceptron. Zbl 0814.68109
Kawanabe, Motoaki; Amari, Shun-ichi
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
1994
Backpropagation and stochastic gradient descent method. Zbl 0782.68094
Amari, Shun-ichi
1993
Mathematical methods of neurocomputing. Zbl 0821.92003
Amari, Shun-Ichi
1993
Differential geometry of estimating functions. Zbl 0810.62026
Amari, Shun-ichi
1993
Identifiability of hidden Markov information sources and their minimum degrees of freedom. Zbl 0742.60041
Ito, Hisashi; Amari, Shun-Ichi; Kobayashi, Kingo
1992
Asymptotic theory of sequential estimation: Differential geometrical approach. Zbl 0737.62067
Okamoto, Ichi; Amari, Shun-Ichi; Takeuchi, Kei
1991
Mathematical theory of neural learning. Zbl 0712.68079
Amari, Shun-ichi
1991
Differential-geometrical methods in statistics. Corr. 2nd. printing. Zbl 0701.62008
Amari, Shun-ichi
1990
Statistical inference under multiterminal rate restrictions: A differential geometric approach. Zbl 0673.62008
Amari, Shun-ichi; Han, Te Sun
1989
Dynamical stability of formation of cortical maps. Zbl 0672.92005
Amari, Shun-ichi
1989
Fisher information under restriction of Shannon information in multi-terminal situations. Zbl 0703.62005
Amari, Shun-Ichi
1989
Estimation in the presence of infinitely many nuisance parameters - Geometry of estimating functions. Zbl 0665.62029
Amari, Shun-Ichi; Kumon, Masayuki
1988
Differential geometry in statistical inference. Zbl 0694.62001
Amari, S.-I.; Barndorff-Nielsen, O. E.; Kass, R. E.; Lauritzen, S. L.; Rao, C. R.
1987
Differential geometry of a parametric family of invertible linear systems. Riemannian metric, dual affine connections, and divergence. Zbl 0632.93017
Amari, Shun-ichi
1987
Differential geometrical method in asymptotics of statistical inference. Zbl 0693.62034
Amari, Shun-ichi
1987
Differential-geometrical methods in statistics. Zbl 0559.62001
Amari, Shun-ichi
1985
Estimation of a structural parameter in the presence of a large number of nuisance parameters. Zbl 0571.62025
Kumon, Masayuki; Amari, Shun-ichi
1984
Differential geometry of Edgeworth expansions in curved exponential family. Zbl 0527.62034
Amari, Shun-ichi; Kumon, Masayuki
1983
Field theory of self-organizing neural nets. Zbl 0543.92007
Amari, Shun-ichi
1983
...and 23 more Documents
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### 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
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### 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. Theory and Methods 15 Journal of Mathematical Biology 14 Bulletin of Mathematical Biology 14 Chaos 13 Physica A 12 Journal of Statistical Physics 12 Kybernetika 12 Statistics & Probability Letters 12 SIAM Journal on Applied Dynamical Systems 11 Journal of Computational and Applied Mathematics 11 Machine Learning 11 Journal of Mathematical Imaging and Vision 11 Bernoulli 10 Journal of Mathematical Analysis and Applications 10 Circuits, Systems, and Signal Processing 10 Japan Journal of Industrial and Applied Mathematics 10 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 8 Computers & Mathematics with Applications 8 Reports on Mathematical Physics 8 Differential Geometry and its Applications 8 Computational Statistics and Data Analysis 8 International Journal of Computer Vision 8 Journal of Machine Learning Research (JMLR) 7 Journal of Geometry and Physics 7 Applied Mathematics. Series B (English Edition) 7 Journal of Statistical Mechanics: Theory and Experiment 6 Chaos, Solitons and Fractals 6 Applied Mathematics and Computation 6 Automatica 6 Information Sciences 6 Journal of Differential Equations 6 Signal Processing 6 Stochastic Processes and their Applications 6 Computational Optimization and Applications 6 Nonlinear Analysis. Real World Applications 6 Journal of Theoretical Biology 5 International Journal of Theoretical Physics 5 Physics Letters. A 5 Journal of Mathematical Psychology 5 Statistical Science 5 Pattern Recognition 5 SIAM Journal on Scientific Computing 5 Journal of Mathematical Sciences (New York) 5 Balkan Journal of Geometry and its Applications (BJGA) 5 Differential Equations and Dynamical Systems 5 International Electronic Journal of Geometry 5 Electronic Journal of Statistics 5 Sankhyā. Series A 5 Statistics and Computing 5 Bayesian Analysis 4 The Canadian Journal of Statistics 4 Communications in Mathematical Physics 4 Journal of Computer and System Sciences 4 Statistics 4 Probability Theory and Related Fields 4 Sequential Analysis 4 Journal of Scientific Computing 4 Journal of Global Optimization 4 European Journal of Operational Research 4 International Journal of Computer Mathematics 4 Open Systems & Information Dynamics 4 International Journal of Quantum Information 4 Journal of the Japan Statistical Society. Japanese Issue 3 Modern Physics Letters B 3 General Relativity and Gravitation 3 Journal of the Franklin Institute 3 Letters in Mathematical Physics 3 Reviews in Mathematical Physics 3 The Annals of Probability 3 Results in Mathematics 3 Journal of Time Series Analysis 3 New Generation Computing 3 MCSS. Mathematics of Control, Signals, and Systems 3 Multidimensional Systems and Signal Processing 3 The Annals of Applied Probability 3 SIAM Journal on Applied Mathematics 3 SIAM Journal on Mathematical Analysis 3 SIAM Review 3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. 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
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### 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)

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