Skip to main content
SpringerLink
Log in
Book cover

International Conference on Artificial Intelligence and Soft Computing

ICAISC 2018: Artificial Intelligence and Soft Computing pp 25–34Cite as

On the Global Convergence of the Parzen-Based Generalized Regression Neural Networks Applied to Streaming Data

  • Conference paper
  • First Online:

  • 2183 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10841))

Abstract

In the paper we study global (integral) properties of the Parzen-type recursive algorithm dealing with streaming data in the presence of the time-varying noise. The mean integrated squared error of the regression estimate is shown to converge under several conditions. Simulations results illustrate asymptotic properties of the algorithm and its convergence for a wide spectrum of a time-varying noise.

This is a preview of subscription content, 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 EPUB and 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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Bologna, G., Hayashi, Y.: Characterization of symbolic rules embedded in deep DIMLP networks: a challenge to transparency of deep learning. J. Artif. Intell. Soft Comput. Res. 7(4), 265–286 (2017)

    Article  Google Scholar 

  2. Cao, J., Wang, J.: Global asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 50(1), 34–44 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cao, J., Wang, J.: Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans. Circ. Syst. I Regul. Pap. 52(2), 417–426 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chang, O., Constante, P., Gordon, A., Singana, M.: A novel deep neural network that uses space-time features for tracking and recognizing a moving object. J. Artif. Intell. Soft Comput. Res. 7(2), 125–136 (2017)

    Article  Google Scholar 

  5. Devi, V.S., Meena, L.: Parallel MCNN (pMCNN) with application to prototype selection on large and streaming data. J. Artif. Intell. Soft Comput. Res. 7(3), 155–169 (2017)

    Article  Google Scholar 

  6. Devroye, L., Krzyżak, A.: On the hilbert kernel density estimate. Stat. Probab. Lett. 44(3), 299–308 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  7. Devroye, L., Krzyżak, A.: New multivariate product density estimators. J. Multivar. Anal. 82(1), 88–110 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Diam, A., Last, M., Kandel, A.: Knowledge discovery in data streams with regression tree methods. WIREs Data Min. Knowl. Discov. 2, 69–78 (2012). https://doi.org/10.1002/widm.51

    Article  Google Scholar 

  9. Ditzler, G., Roveri, M., Alippi, C., Polikar, R.: Learning in nonstationary environments: a survey. IEEE Comput. Intell. Mag. 10(4), 12–25 (2015)

    Article  Google Scholar 

  10. Domingos, P., Hulten, G.: Mining high-speed data streams. In: Proceedings of the 6th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 71–80 (2000)

    Google Scholar 

  11. Duda, P., Jaworski, M., Pietruczuk, L., Rutkowski, L.: A novel application of Hoeffding’s inequality to decision trees construction for data streams. In: 2014 International Joint Conference on Neural Networks (IJCNN), pp. 3324–3330. IEEE (2014)

    Google Scholar 

  12. Duda, P., Jaworski, M., Rutkowski, L.: Knowledge discovery in data streams with the orthogonal series-based generalized regression neural networks. Inf. Sci. (2017). https://doi.org/10.1016/j.ins.2017.07.013

    Article  MathSciNet  Google Scholar 

  13. Duda, P., Jaworski, M., Rutkowski, L.: Convergent time-varying regression models for data streams: tracking concept drift by the recursive parzen-based generalized regression neural networks. Int. J. Neural Syst. 28(02), 1750048 (2018)

    Article  Google Scholar 

  14. Duda, P., Pietruczuk, L., Jaworski, M., Krzyzak, A.: On the Cesàro-means-based orthogonal series approach to learning time-varying regression functions. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2016. LNCS (LNAI), vol. 9693, pp. 37–48. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-39384-1_4

    Chapter  Google Scholar 

  15. Ellis, P.: The time-dependent mean and variance of the non-stationary Markovian infinite server system. J. Math. Stat. 6, 68–71 (2010)

    Article  MATH  Google Scholar 

  16. Greblicki, W., Pawlak, M.: Nonparametric System Identification. Cambridge University Press, Cambridge (2008)

    Book  MATH  Google Scholar 

  17. Hulten, G., Spencer, L., Domingos, P.: Mining time-changing data streams. In: Proceedings of the 7th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 97–106 (2001)

    Google Scholar 

  18. Jaworski, M., Duda, P., Rutkowski, L., Najgebauer, P., Pawlak, M.: Heuristic regression function estimation methods for data streams with concept drift. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2017. LNCS (LNAI), vol. 10246, pp. 726–737. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59060-8_65

    Chapter  Google Scholar 

  19. Jaworski, M., Duda, P., Rutkowski, L.: New splitting criteria for decision trees in stationary data streams. IEEE Trans. Neural Netw. Learn. Syst. PP(99), 1–14 (2017). https://doi.org/10.1109/TNNLS.2017.2698204

    Article  Google Scholar 

  20. Krawczyk, B., Minku, L.L., Gama, J., Stefanowski, J., Wozniak, M.: Ensemble learning for data stream analysis: a survey. Inf. Fusion 37, 132–156 (2017)

    Article  Google Scholar 

  21. Li, R., Cao, J., Alsaedi, A., Alsaadi, F.: Exponential and fixed-time synchronization of cohen-grossberg neural networks with time-varying delays and reaction-diffusion terms. Appl. Math. Comput. 313, 37–51 (2017)

    Article  MathSciNet  Google Scholar 

  22. Manivannan, R., Samidurai, R., Cao, J., Alsaedi, A., Alsaadi, F.E.: Delay-dependent stability criteria for neutral-type neural networks with interval time-varying delay signals under the effects of leakage delay. Adv. Differ. Equ. 2018(1), 53 (2018)

    Article  MathSciNet  Google Scholar 

  23. Phillips, P.C.: Impulse response and forecast error variance asymptotics in nonstationary VARs. J. Econom. 83(1), 21–56 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  24. Pietruczuk, L., Rutkowski, L., Jaworski, M., Duda, P.: The Parzen kernel approach to learning in non-stationary environment. In: 2014 International Joint Conference on Neural Networks (IJCNN), pp. 3319–3323. IEEE (2014)

    Google Scholar 

  25. Pietruczuk, L., Rutkowski, L., Jaworski, M., Duda, P.: How to adjust an ensemble size in stream data mining? Inf. Sci. 381, 46–54 (2017)

    Article  MathSciNet  Google Scholar 

  26. Riid, A., Preden, J.S.: Design of fuzzy rule-based classifiers through granulation and consolidation. J. Artif. Intell. Soft Comput. Res. 7(2), 137–147 (2017)

    Article  Google Scholar 

  27. Rutkowski, L.: New Soft Computing Techniques for System Modeling, Pattern Classication and Image Processing. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-40046-2

    Book  MATH  Google Scholar 

  28. Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: The CART decision tree for mining data streams. Inf. Sci. 266, 1–15 (2014)

    Article  MATH  Google Scholar 

  29. Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: Decision trees for mining data streams based on the Gaussian approximation. IEEE Trans. Knowl. Data Eng. 26(1), 108–119 (2014)

    Article  MATH  Google Scholar 

  30. Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: A new method for data stream mining based on the misclassification error. IEEE Trans. Neural Netw. Learn. Syst, 26(5), 1048–1059 (2015)

    Article  MathSciNet  Google Scholar 

  31. Rutkowski, L., Pietruczuk, L., Duda, P., Jaworski, M.: Decision trees for mining data streams based on the McDiarmid’s bound. IEEE Trans. Knowl. Data Eng. 25(6), 1272–1279 (2013)

    Article  Google Scholar 

  32. Specht, D.F.: A general regression neural network. IEEE Trans. Neural Netw. 2(6), 568–576 (1991)

    Article  Google Scholar 

  33. Street, W.N., Kim, Y.: A streaming ensemble algorithm (SEA) for large-scale classification. In: Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 377–382. ACM (2001)

    Google Scholar 

  34. Villmann, T., Bohnsack, A., Kaden, M.: Can learning vector quantization be an alternative to SVM and deep learning? - recent trends and advanced variants of learning vector quantization for classification learning. J. Artif. Intell. Soft Comput. Res. 7(1), 65–81 (2017). https://doi.org/10.1515/jaiscr-2017-0005

    Article  Google Scholar 

  35. Wong, K.F.K., Galka, A., Yamashita, O., Ozaki, T.: Modelling non-stationary variance in EEG time series by state space garch model. Comput. Biol. Med. 36(12), 1327–1335 (2006)

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the Polish National Science Center under Grant No. 2014/15/B/ST7/05264.

Author information

Authors and Affiliations

  1. School of Mathematics, Southeast University, Nanjing, 211189, China

    Jinde Cao

  2. Institute of Computational Intelligence, Czestochowa University of Technology, Al. Armii Krajowej 36, 42-200, Czestochowa, Poland

    Leszek Rutkowski

  3. Information Technology Institute, Academy of Social Sciences, 90-113, Łódź, Poland

    Leszek Rutkowski

Authors
  1. Jinde Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leszek Rutkowski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Leszek Rutkowski .

Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Częstochowa, Poland

    Leszek Rutkowski

  2. Częstochowa University of Technology, Częstochowa, Poland

    Rafał Scherer

  3. Częstochowa University of Technology, Częstochowa, Poland

    Marcin Korytkowski

  4. University of Alberta, Edmonton, AB, Canada

    Witold Pedrycz

  5. AGH University of Science and Technology, Kraków, Poland

    Ryszard Tadeusiewicz

  6. University of Louisville, Louisville, KY, USA

    Jacek M. Zurada

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Cao, J., Rutkowski, L. (2018). On the Global Convergence of the Parzen-Based Generalized Regression Neural Networks Applied to Streaming Data. In: Rutkowski, L., Scherer, R., Korytkowski, M., Pedrycz, W., Tadeusiewicz, R., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2018. Lecture Notes in Computer Science(), vol 10841. Springer, Cham. https://doi.org/10.1007/978-3-319-91253-0_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-91253-0_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91252-3

  • Online ISBN: 978-3-319-91253-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation