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Volumn 21, Issue 7, 2008, Pages 925-935

On Clifford neurons and Clifford multi-layer perceptrons

Author keywords

Backpropagation; Clifford (geometric) algebra; Clifford neural networks; Clifford neurons; Function approximation; Multi layer perceptrons

Indexed keywords

COMPUTER NETWORKS; NEURAL NETWORKS; PATTERN RECOGNITION SYSTEMS;

EID: 51049088188     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neunet.2008.03.004     Document Type: Article
Times cited : (122)

References (31)
  • 1
    • 0031104970 scopus 로고    scopus 로고
    • Multilayer perceptrons to approximate quaternion valued functions
    • Arena P., Fortuna L., Muscato G., and Xibilia M.G. Multilayer perceptrons to approximate quaternion valued functions. Neural Networks 10 2 (1997) 334-342
    • (1997) Neural Networks , vol.10 , Issue.2 , pp. 334-342
    • Arena, P.1    Fortuna, L.2    Muscato, G.3    Xibilia, M.G.4
  • 2
    • 0242393023 scopus 로고    scopus 로고
    • Neural networks in multidimensional domains
    • Springer-Verlag
    • Arena P., Fortuna L., Muscato G., and Xibilia M.G. Neural networks in multidimensional domains. LNCIS Vol. 234 (1998), Springer-Verlag
    • (1998) LNCIS , vol.234
    • Arena, P.1    Fortuna, L.2    Muscato, G.3    Xibilia, M.G.4
  • 5
    • 51049085487 scopus 로고    scopus 로고
    • Buchholz, S. (2005). A theory of neural computation with Clifford-algebra. Technical report number 0504. Christian-Albrechts-Universität zu Kiel, Institut für Informatik und Praktische Mathematik
    • Buchholz, S. (2005). A theory of neural computation with Clifford-algebra. Technical report number 0504. Christian-Albrechts-Universität zu Kiel, Institut für Informatik und Praktische Mathematik
  • 6
    • 84937434115 scopus 로고    scopus 로고
    • Learning geometric transformations with Clifford neurons
    • 2nd International workshop on algebraic frames for the perception-action cycle. Sommer G., and Zeevi Y. (Eds). AFPAC 2000, Kiel, Springer-Verlag
    • Buchholz S., and Sommer G. Learning geometric transformations with Clifford neurons. In: Sommer G., and Zeevi Y. (Eds). 2nd International workshop on algebraic frames for the perception-action cycle. AFPAC 2000, Kiel. LNCS Vol. 1888 (2000), Springer-Verlag 144-153
    • (2000) LNCS , vol.1888 , pp. 144-153
    • Buchholz, S.1    Sommer, G.2
  • 7
    • 51049102480 scopus 로고    scopus 로고
    • Buchholz, S., & Sommer, G. (2000). Quaternionic spinor MLP. In 8th European symposium on artificial neural networks (pp. 377-382)
    • Buchholz, S., & Sommer, G. (2000). Quaternionic spinor MLP. In 8th European symposium on artificial neural networks (pp. 377-382)
  • 8
    • 12944276312 scopus 로고    scopus 로고
    • Clifford algebra multilayer perceptrons
    • Sommer G. (Ed), Springer-Verlag, Heidelberg
    • Buchholz S., and Sommer G. Clifford algebra multilayer perceptrons. In: Sommer G. (Ed). Geometric computing with Clifford algebra (2001), Springer-Verlag, Heidelberg 315-334
    • (2001) Geometric computing with Clifford algebra , pp. 315-334
    • Buchholz, S.1    Sommer, G.2
  • 9
    • 38149069761 scopus 로고    scopus 로고
    • Buchholz, S., Tachibana, K., & Hitzer, E. (2007). Optimal learning rates for clifford neurons. In International conference on artificial neural networks (pp. 864-873). Vol. 1
    • Buchholz, S., Tachibana, K., & Hitzer, E. (2007). Optimal learning rates for clifford neurons. In International conference on artificial neural networks (pp. 864-873). Vol. 1
  • 11
    • 0024861871 scopus 로고
    • Approximation by superposition of a sigmoidal function
    • Cybenko G. Approximation by superposition of a sigmoidal function. Mathematics of Control, Signals and Systems 2 (1989) 303-314
    • (1989) Mathematics of Control, Signals and Systems , vol.2 , pp. 303-314
    • Cybenko, G.1
  • 12
    • 33745812636 scopus 로고    scopus 로고
    • Using the algebra of dual quaternions for motion alignment
    • Sommer G. (Ed), Springer-Verlag
    • Daniilidis K. Using the algebra of dual quaternions for motion alignment. In: Sommer G. (Ed). Geometric computing with Clifford algebras (2001), Springer-Verlag 489-499
    • (2001) Geometric computing with Clifford algebras , pp. 489-499
    • Daniilidis, K.1
  • 15
    • 0003998814 scopus 로고
    • Longmans Green, London Chelsea, New York, 1969
    • Hamilton W.R. Elements of quaternions (1866), Longmans Green, London Chelsea, New York, 1969
    • (1866) Elements of quaternions
    • Hamilton, W.R.1
  • 16
    • 0024878952 scopus 로고    scopus 로고
    • Hecht-Nielsen, R. (1989). Theory of the back-propagation neural network. In Proc. IEEE IJCNN (pp. 593-605)
    • Hecht-Nielsen, R. (1989). Theory of the back-propagation neural network. In Proc. IEEE IJCNN (pp. 593-605)
  • 17
    • 0004199140 scopus 로고
    • Addison-Wesley Publishing Company, Inc.
    • Hecht-Nielsen R. Neurocomputing (1991), Addison-Wesley Publishing Company, Inc.
    • (1991) Neurocomputing
    • Hecht-Nielsen, R.1
  • 20
    • 0024880831 scopus 로고
    • Multilayer feedforward networks are universal approximators
    • Hornik K., Stinchcombe M., and White H. Multilayer feedforward networks are universal approximators. Neural Networks 2 (1989) 359-366
    • (1989) Neural Networks , vol.2 , pp. 359-366
    • Hornik, K.1    Stinchcombe, M.2    White, H.3
  • 21
    • 85143190590 scopus 로고    scopus 로고
    • Kim, T., & Adali, T. (2001). Complex backpropagtion neural network using elementary transcendetal activation functions. In Proc. of IEEE ICASSP (pp. 1281-1284)
    • Kim, T., & Adali, T. (2001). Complex backpropagtion neural network using elementary transcendetal activation functions. In Proc. of IEEE ICASSP (pp. 1281-1284)
  • 22
    • 0038159963 scopus 로고    scopus 로고
    • Approximation by fully-complex multilayer perceptrons
    • Kim T., and Adali T. Approximation by fully-complex multilayer perceptrons. Neural Networks 15 7 (2003) 1641-1666
    • (2003) Neural Networks , vol.15 , Issue.7 , pp. 1641-1666
    • Kim, T.1    Adali, T.2
  • 24
    • 0000044667 scopus 로고
    • Eigenvalues of covariance matrices: Application to neural-network learning
    • LeCun Y., Kanter I., and Solla S.A. Eigenvalues of covariance matrices: Application to neural-network learning. Physical Review Letters 66 18 (1991) 2396-2399
    • (1991) Physical Review Letters , vol.66 , Issue.18 , pp. 2396-2399
    • LeCun, Y.1    Kanter, I.2    Solla, S.A.3
  • 26
    • 51049100090 scopus 로고    scopus 로고
    • Pearson, J. K. (1994). Clifford networks. Ph.D. thesis. University of Kent
    • Pearson, J. K. (1994). Clifford networks. Ph.D. thesis. University of Kent
  • 28
    • 51049116970 scopus 로고    scopus 로고
    • Rosenhahn, B. (2003). Pose estimation revisited. Technical report number 0308. Christian-Albrechts-Universität zu Kiel, Institut für Informatik und Praktische Mathematik
    • Rosenhahn, B. (2003). Pose estimation revisited. Technical report number 0308. Christian-Albrechts-Universität zu Kiel, Institut für Informatik und Praktische Mathematik
  • 29
    • 84949184246 scopus 로고    scopus 로고
    • Algbraic aspects of designing behavior based systems
    • Proc. Int. Workshop AFPAC'97. Sommer G., and Koenderink J.J. (Eds), Springer-Verlag
    • Sommer G. Algbraic aspects of designing behavior based systems. In: Sommer G., and Koenderink J.J. (Eds). Proc. Int. Workshop AFPAC'97. LNCS Vol. 1315 (1997), Springer-Verlag 1-28
    • (1997) LNCS , vol.1315 , pp. 1-28
    • Sommer, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.