×
Author ID: amari.shun-ichi Recent zbMATH articles by "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
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

Publications by Year

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 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

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.