Skip to main content
SpringerLink
Log in

High Dimensional Neural Networks and Applications

  • Chapter
Intelligent Autonomous Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 275))

Abstract

Intelligent systems are emerging computing systems developed based on intelligent techniques. These techniques take advantage of artificial neural networks to emulate intelligent behavior. Extensive studies carried out during the past several years have revealed that neural networks enjoy numerous practical advantages over conventional methods. They are more fault-tolerant, less sensitive to noise and mostly used for their human-like characteristics (learning and generalization). They have been accepted as powerful tools for correlating data without making strong assumptions about the problems. Traditional neural networks’s parameters are usually real numbers for dealing with real-valued data. However, high-dimensional data also appear in practical applications and consequently, high-dimensional neural networks have been proposed. They have also presented improved results even in case of real-valued problems. As a prelude, we provide a brief overview of the existing methodologies in high-dimensional neural computation. Our particular point of view is to describe several real-world applications, in which the use of these techniques really helps in achieving the goals of intelligent system.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. McCulloch, W.S., Pitts, W.: A logical calculation of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics 5, 115–133 (1943)

    Article  MATH  MathSciNet  Google Scholar 

  2. Giles, C.L., Maxwell, T.: Learning, invariance and generalization in a high-order neural network. Applied Optics 26(23), 4972–4978 (1987)

    Article  Google Scholar 

  3. Cha, H.: Channel equalization using adaptive complex radial basis function networks. IEEE J. Select. Areas Communication 9, 122–131 (1995)

    Google Scholar 

  4. Jianping, D., Sundararajan, N., Saratchandran, P.: Communication channel equalization using complex-valued minimal radial basis function neural networks. IEEE Trans. on Neural Networks 13(3), 687–696 (2002)

    Article  Google Scholar 

  5. Igel, C., Husken, M.: Empirical evaluation of the improved Rprop learning algorithms. Neurocomputing 50, 105–123 (2003)

    Article  MATH  Google Scholar 

  6. Watanabe, A., Miyauchi, A., Miyauchi, M.: A method to interpret 3D motion using neural networks. IEICE Trans. on Fundamentals of Electronics and Computer Science E77-A(8), 1363–1370 (1994)

    Google Scholar 

  7. Nitta, T.: A 3D vector version of the back-propagation algorithm. In: Proc. of IJCNN 1992, Beijing, vol. 2, pp. 511–516 (1992)

    Google Scholar 

  8. Aizenberg, N.N., Ivaskiv, Y.L., Pospelov, D.A.: About one generalization of the threshold function. Doklady Akademii Nauk SSSR (The Reports of the Academy of Sciences of the USSR) 196(6), 1287–1290 (1971) (in Russian)

    MathSciNet  Google Scholar 

  9. Aizenberg, I., Moraga, C.: Multilayer feed-forward neural network based on multi-valued neurons (MLMVN) and a backpropagation learning algorithm. Soft Computing 11(2), 169–183 (2007)

    Article  Google Scholar 

  10. Aizenberg, I., Aizenberg, N., Vandewalle, J.: Multi-valued and universal binary neurons: theory, learning, applications. Kluwer Academic Publishers, Dordrecht (2000)

    Google Scholar 

  11. Kim, T., Adali, T.: Approximation by fully complex multilayer perceptrons. Neural Computation 15, 1641–1666 (2003)

    Article  MATH  Google Scholar 

  12. Piazza, F., Benvenuto, N.: On the complex back-propagation algorithm. IEEE Transaction on Signal Processing 40(4), 967–969 (1992)

    Article  Google Scholar 

  13. Goh, S.L.: A complex-valued RTRL algorithm for recurrent neural networks. Neural Computation 16, 2699–2713 (2003)

    Article  Google Scholar 

  14. Leung, H., Haykin, S.: The complex back-propagation algorithm. IEEE Transaction on Signal Processing 39(9), 2101–2104 (1991)

    Article  Google Scholar 

  15. Nitta, T.: An extension of the back-propagation to complex numbers. Neural Networks 10(8), 1391–1415 (1997)

    Article  Google Scholar 

  16. Nitta, T.: Orthogonality of decision boundaries in complex-valued neural networks. Neural Computation 16(1), 73–97 (2004)

    Article  MATH  Google Scholar 

  17. Nitta, T.: Solving the XOR problem and the detection of symmetry using a single complex-valued neuron. Neural Networks 16, 1101–1105 (2003)

    Article  Google Scholar 

  18. Jacobs, R.A.: Increased rates of convergence through learning rate adaptation. Neural Networks 1(4), 295–307 (1988)

    Article  Google Scholar 

  19. Nitta, T.: An analysis of the fundamental structure of complex-valued neurons. Neural Processing Letters 12, 239–246 (2000)

    Article  MATH  Google Scholar 

  20. Brown, J.W., Churchill, R.V.: Complex Variables and Applications, 7th edn. McGraw-Hill, New York (2003)

    Google Scholar 

  21. Nitta, T.: Three-dimensional vector valued neural network and its generalization abilIty. Neural Information Processing – Letters and Reviews 10(10), 237–242 (2006)

    Google Scholar 

  22. Tripathi, B.K., Chandra, B., Kalra, P.K.: The generalized product neuron model in complex domain. In: Proc. of International Conference on Neural Information Processing, Auckland, New Zealand (2008)

    Google Scholar 

  23. Turk, M., Pentaland, A.P.: Face recognition using eigenfaces. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, pp. 586–591 (1991)

    Google Scholar 

  24. Bartlett, M.S., Movellan, J.R., Sejnowski, T.J.: Face recognition by independent component analysis. IEEE Transaction on Neural Networks 3(6), 1450–1464 (2002)

    Article  Google Scholar 

  25. Rattan, S., Hsieh, W., Ruessink, B.G.: Nonlinear complex principal component analysis and its applications. In: Proceedings of International Joint Conference on Neural Networks, Montreal, Canada (2005)

    Google Scholar 

  26. Calhoun, V., Adali, T.: Complex ICA for FMRI analysis: performance of several approaches. In: Proc. of ICASSP (2003)

    Google Scholar 

  27. Kalra, P.K., Yadav, R.N., John, J.: Time series prediction with single multiplicative neuron model. Applied Soft Computing 7, 1157–1163 (2007)

    Article  Google Scholar 

  28. Gorman, R.P., Sejnowski, T.J.: Analysis of hidden units in a layered network trained to classify sonar targets. Neural Networks 1, 75–89 (1988)

    Article  Google Scholar 

  29. Tripathi, B.K., Kalra, P.K.: A complex valued heterogeneous neural network. In: Proc. of a Workshop on Complex Valued Neural Network, International Joint Conference on Artificial Intelligence, Hyderabad, India (2007)

    Google Scholar 

  30. Van Ooyen, A., Nienhuis, B.: Improving the convergence of the back-propagation algorithm. Neural Networks 5(3), 465–472 (1992)

    Article  Google Scholar 

  31. Chen, X., Tang, Z., Vairappan, C., Li, S., Okada, T.: A modified error back-propagation algorithm for complex-value neural networks. International Journal of Neural System 15(6), 435–443 (2005)

    Article  Google Scholar 

  32. http://www-2.cs.cmu.edu/afs/cs/project/ai-repository/ai/areas/neural/bench/cmu

  33. Blake, C.L., Merz, C.J.: UCI Repository of machine learning database. University of California, Department of Information and computer science (1998), http://www.ics.uci.edu/mealrn/MLRepository.html

  34. ORL database, http://www.cam-orl.co.uk/facedatabase.html

  35. Gupta, M.M., Homma, N.: Static and Dynamic Neural Networks: From Fundamentals to Advanced Theory. Wiley, Chichester (2003)

    Book  Google Scholar 

  36. Hirose, A.: Complex-Valued Neural Networks. Springer, New York (2006)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. 107-ACES, Indian Institute of Technology, Kanpur, India

    B. K. Tripathi

  2. Indian Institute of Technology, Rajasthan, India

    P. K. Kalra

Authors
  1. B. K. Tripathi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. K. Kalra
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur, India

    Dilip Kumar Pratihar

  2. School of Electrical and Information Engineering, University of South Australia, Mawson Lakes Campus, Adelaide, South Australia, Australia

    Lakhmi C. Jain

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Tripathi, B.K., Kalra, P.K. (2010). High Dimensional Neural Networks and Applications. In: Pratihar, D.K., Jain, L.C. (eds) Intelligent Autonomous Systems. Studies in Computational Intelligence, vol 275. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11676-6_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-11676-6_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11675-9

  • Online ISBN: 978-3-642-11676-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation