메뉴 건너뛰기




Volumn 23, Issue 1, 2012, Pages 175-182

Nonlinear system modeling with random matrices: Echo state networks revisited

Author keywords

Circular law; concentration of measure; echo state networks; echo state property; random matrix theory; recurrent neural networks

Indexed keywords

CIRCULAR LAW; CONCENTRATION OF MEASURE; ECHO STATE NETWORKS; ECHO STATE PROPERTY; RANDOM MATRIX THEORY;

EID: 84866504536     PISSN: 2162237X     EISSN: 21622388     Source Type: Journal    
DOI: 10.1109/TNNLS.2011.2178562     Document Type: Article
Times cited : (82)

References (31)
  • 1
    • 1842421269 scopus 로고    scopus 로고
    • Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication
    • Apr
    • H. Jaeger and H. Haas, "Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication," Science, vol. 304, no. 5667, pp. 78-80, Apr. 2004.
    • (2004) Science , vol.304 , Issue.5667 , pp. 78-80
    • Jaeger, H.1    Haas, H.2
  • 3
    • 0036834701 scopus 로고    scopus 로고
    • Real-time computing without stable states: A new framework for neural computation based on perturbations
    • Nov
    • W. Maass, T. Natschläger, and H. Markram, "Real-time computing without stable states: A new framework for neural computation based on perturbations," Neural Comput., vol. 14, no. 11, pp. 2531-2560, Nov. 2002.
    • (2002) Neural Comput , vol.14 , Issue.11 , pp. 2531-2560
    • Maass, W.1    Natschläger, T.2    Markram, H.3
  • 4
    • 34047166022 scopus 로고    scopus 로고
    • Support vector echo-state machine for chaotic timeseries prediction
    • Mar
    • Z. Shi and M. Han, "Support vector echo-state machine for chaotic timeseries prediction," IEEE Trans. Neural Netw., vol. 18, no. 2, pp. 359-372, Mar. 2007.
    • (2007) IEEE Trans. Neural Netw , vol.18 , Issue.2 , pp. 359-372
    • Shi, Z.1    Han, M.2
  • 5
    • 34249802596 scopus 로고    scopus 로고
    • An associative memory readout for ESNs with applications to dynamical pattern recognition
    • Apr
    • M. C. Ozturk and J. C. Príncipe, "An associative memory readout for ESNs with applications to dynamical pattern recognition," Neural Netw., vol. 20, no. 3, pp. 377-390, Apr. 2007.
    • (2007) Neural Netw , vol.20 , Issue.3 , pp. 377-390
    • Ozturk, M.C.1    Príncipe, J.C.2
  • 6
    • 34249867443 scopus 로고    scopus 로고
    • Automatic speech recognition using a predictive echo state network classifier
    • Apr
    • M. D. Skowronski and J. G. Harris, "Automatic speech recognition using a predictive echo state network classifier," Neural Netw., vol. 20, no. 3, pp. 414-423, Apr. 2007.
    • (2007) Neural Netw , vol.20 , Issue.3 , pp. 414-423
    • Skowronski, M.D.1    Harris, J.G.2
  • 8
    • 34548609011 scopus 로고    scopus 로고
    • Collective behavior of a small-world recurrent neural system with scale-free distribution
    • Sep
    • Z. Deng and Y. Zhang, "Collective behavior of a small-world recurrent neural system with scale-free distribution," IEEE Trans. Neural Netw., vol. 18, no. 5, pp. 1364-1375, Sep. 2007.
    • (2007) IEEE Trans. Neural Netw , vol.18 , Issue.5 , pp. 1364-1375
    • Deng, Z.1    Zhang, Y.2
  • 9
    • 34249819041 scopus 로고    scopus 로고
    • Decoupled echo state networks with lateral inhibition
    • Y. Xue, L. Yang, and S. Haykin, "Decoupled echo state networks with lateral inhibition," Neural Netw., vol. 20, no. 3, pp. 365-376, 2007.
    • (2007) Neural Netw , vol.20 , Issue.3 , pp. 365-376
    • Xue, Y.1    Yang, L.2    Haykin, S.3
  • 10
    • 33846023013 scopus 로고    scopus 로고
    • Analysis and design of echo state networks
    • Jan
    • M. C. Ozturk, D. Xu, and J. C. Príncipe, "Analysis and design of echo state networks," Neural Comput., vol. 19, no. 1, pp. 111-138, Jan. 2007.
    • (2007) Neural Comput , vol.19 , Issue.1 , pp. 111-138
    • Ozturk, M.C.1    Xu, D.2    Príncipe, J.C.3
  • 11
    • 78651275150 scopus 로고    scopus 로고
    • An augmented echo state network for nonlinear adaptive filtering of complex noncircular signals
    • Jan.
    • Y. Xia, B. Jelfs, M. Van Hulle, J. Príncipe, and D. Mandic, "An augmented echo state network for nonlinear adaptive filtering of complex noncircular signals," IEEE Trans. Neural Netw., vol. 22, no. 1, pp. 74-83, Jan. 2011.
    • (2011) IEEE Trans. Neural Netw , vol.22 , Issue.1 , pp. 74-83
    • Xia, Y.1    Jelfs, B.2    Van Hulle, M.3    Príncipe, J.4    Mandic, D.5
  • 12
    • 80052405292 scopus 로고    scopus 로고
    • Echo state Gaussian process
    • Sep.
    • S. Chatzis and Y. Demiris, "Echo state Gaussian process," IEEE Trans. Neural Netw., vol. 22, no. 9, pp. 1435-1445, Sep. 2011.
    • (2011) IEEE Trans. Neural Netw , vol.22 , Issue.9 , pp. 1435-1445
    • Chatzis, S.1    Demiris, Y.2
  • 13
    • 78651295386 scopus 로고    scopus 로고
    • Minimum complexity echo state network
    • Jan.
    • A. Rodan and P. Tino, "Minimum complexity echo state network," IEEE Trans. Neural Netw., vol. 22, no. 1, pp. 131-144, Jan. 2011.
    • (2011) IEEE Trans. Neural Netw , vol.22 , Issue.1 , pp. 131-144
    • Rodan, A.1    Tino, P.2
  • 14
    • 68649088777 scopus 로고    scopus 로고
    • Reservoir computing approaches to recurrent neural network training
    • Aug
    • M. Lukosevicius and H. Jaeger, "Reservoir computing approaches to recurrent neural network training," Comput. Sci. Rev., vol. 3, no. 3, pp. 127-149, Aug. 2009.
    • (2009) Comput. Sci. Rev , vol.3 , Issue.3 , pp. 127-149
    • Lukosevicius, M.1    Jaeger, H.2
  • 15
    • 26444565569 scopus 로고
    • Finding structure in time
    • J. L. Elman, "Finding structure in time," Cognit. Sci., vol. 14, no. 2, pp. 179-211, 1990.
    • (1990) Cognit. Sci , vol.14 , Issue.2 , pp. 179-211
    • Elman, J.L.1
  • 16
    • 72249111101 scopus 로고
    • Attractor dynamics and parallelism in a connectionist sequential machine
    • J. Diederich, Ed. Los Alamitos, CA: IEEE Computer Society Press, Jan
    • M. I. Jordan, "Attractor dynamics and parallelism in a connectionist sequential machine," in Artificial Neural Networks: Concept Learning (IEEE Computer Society Neural Networks Technology), J. Diederich, Ed. Los Alamitos, CA: IEEE Computer Society Press, Jan. 1990, pp. 112-127.
    • (1990) Artificial Neural Networks: Concept Learning (IEEE Computer Society Neural Networks Technology) , pp. 112-127
    • Jordan, M.I.1
  • 17
    • 33646536035 scopus 로고    scopus 로고
    • A tighter bound for the echo state property
    • May
    • M. Buehner and P. Young, "A tighter bound for the echo state property," IEEE Trans. Neural Netw., vol. 17, no. 3, pp. 820-824, May 2006.
    • (2006) IEEE Trans. Neural Netw , vol.17 , Issue.3 , pp. 820-824
    • Buehner, M.1    Young, P.2
  • 18
    • 58049158689 scopus 로고    scopus 로고
    • Echo state network
    • H. Jaeger, "Echo state network," Scholarpedia, vol. 2, no. 9, p. 2330, 2007.
    • (2007) Scholarpedia , vol.2 , Issue.9 , pp. 2330
    • Jaeger, H.1
  • 20
    • 0031068715 scopus 로고    scopus 로고
    • The probability that a random real Gaussian matrix has k real eigenvalues, related distributions, and the circular law
    • Feb
    • A. Edelman, "The probability that a random real Gaussian matrix has k real eigenvalues, related distributions, and the circular law," J. Multivar. Anal., vol. 60, no. 2, pp. 203-232, Feb. 1997.
    • (1997) J. Multivar. Anal , vol.60 , Issue.2 , pp. 203-232
    • Edelman, A.1
  • 21
    • 0001393752 scopus 로고
    • Circular law
    • V. L. Girko, "Circular law," Theory Probab. Appl., vol. 29, no. 4, pp. 694-706, 1984.
    • (1984) Theory Probab. Appl. , vol.29 , Issue.4 , pp. 694-706
    • Girko, V.L.1
  • 22
    • 0031534271 scopus 로고    scopus 로고
    • Circular law
    • Z. D. Bai, "Circular law," Ann. Probab., vol. 25, no. 1, pp. 494-529, 1997.
    • (1997) Ann. Probab , vol.25 , Issue.1 , pp. 494-529
    • Bai, Z.D.1
  • 23
    • 44249125025 scopus 로고    scopus 로고
    • Random matrices: The circular law
    • T. Tao and V. Vu, "Random matrices: The circular law," Commun. Contemp. Math., vol. 10, no. 2, pp. 261-307, 2008.
    • (2008) Commun. Contemp. Math , vol.10 , Issue.2 , pp. 261-307
    • Tao, T.1    Vu, V.2
  • 24
    • 77957124985 scopus 로고    scopus 로고
    • Random matrices: Universality of ESDs and the circular law
    • T. Tao, V. Vu, and M. Krishnapur, "Random matrices: Universality of ESDs and the circular law," Ann. Prob., vol. 38, no. 5, pp. 2023-2065, 2010.
    • (2010) Ann. Prob , vol.38 , Issue.5 , pp. 2023-2065
    • Tao, T.1    Vu, V.2    Krishnapur, M.3
  • 25
    • 77952883804 scopus 로고    scopus 로고
    • Random matrices: The distribution of the smallest singular values
    • Mar.
    • T. Tao and V. Vu, "Random matrices: The distribution of the smallest singular values," Geometric Funct. Anal., vol. 20, no. 1, pp. 1-43, Mar. 2010.
    • (2010) Geometric Funct. Anal , vol.20 , Issue.1 , pp. 1-43
    • Tao, T.1    Vu, V.2
  • 26
    • 0000263234 scopus 로고
    • Distribution of eigenvalues for some sets of random matrices
    • Apr
    • V. A. Marcenko and L. A. Pastur, "Distribution of eigenvalues for some sets of random matrices," Math. USSR-Sbornik, vol. 1, no. 4, pp. 457-483, Apr. 1967.
    • (1967) Math. USSR-Sbornik , vol.1 , Issue.4 , pp. 457-483
    • Marcenko, V.A.1    Pastur, L.A.2
  • 27
    • 0003059603 scopus 로고
    • Limiting spectral distribution for a class of random matrices
    • Oct
    • Y. Q. Yin, "Limiting spectral distribution for a class of random matrices," J. Multivar. Anal., vol. 20, no. 1, pp. 50-68, Oct. 1986.
    • (1986) J. Multivar. Anal , vol.20 , Issue.1 , pp. 50-68
    • Yin, Y.Q.1
  • 28
    • 0010883127 scopus 로고
    • Limiting behavior of the norm of products of random matrices and two problems of Geman-Hwang
    • Z. D. Bai and Y. Q. Yin, "Limiting behavior of the norm of products of random matrices and two problems of Geman-Hwang," Probab. Theory Rel. Fields, vol. 73, no. 4, pp. 555-569, 1986.
    • (1986) Probab. Theory Rel. Fields , vol.73 , Issue.4 , pp. 555-569
    • Bai, Z.D.1    Yin, Y.Q.2
  • 29
    • 0001136512 scopus 로고
    • On the limit of the largest eigenvalue of the large dimensional sample covariance matrix
    • Y. Q. Yin, Z. D. Bai, and P. R. Krishnaiah, "On the limit of the largest eigenvalue of the large dimensional sample covariance matrix," Prob. Theory Rel. Fields, vol. 78, no. 4, pp. 509-521, 1988.
    • (1988) Prob. Theory Rel. Fields , vol.78 , Issue.4 , pp. 509-521
    • Yin, Y.Q.1    Bai, Z.D.2    Krishnaiah, P.R.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.