×

On the global convergence of the Parzen-based generalized regression neural networks applied to streaming data. (English) Zbl 1508.68314

Rutkowski, Leszek (ed.) et al., Artificial intelligence and soft computing. 17th international conference, ICAISC 2018, Zakopane, Poland, June 3–7, 2018. Proceedings. Part I. Cham: Springer. Lect. Notes Comput. Sci. 10841, 25-34 (2018).
Summary: 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.
For the entire collection see [Zbl 1387.68028].

MSC:

68T09 Computational aspects of data analysis and big data
68T05 Learning and adaptive systems in artificial intelligence
68W27 Online algorithms; streaming algorithms
Full Text: DOI

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) · doi:10.1515/jaiscr-2017-0019
[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) · Zbl 1368.34084 · doi:10.1109/TCSI.2002.807494
[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) · Zbl 1374.93285 · doi:10.1109/TCSI.2004.841574
[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) · doi:10.1515/jaiscr-2017-0009
[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) · doi:10.1515/jaiscr-2017-0011
[6] Devroye, L., Krzyżak, A.: On the hilbert kernel density estimate. Stat. Probab. Lett. 44(3), 299-308 (1999) · Zbl 0947.62025 · doi:10.1016/S0167-7152(99)00021-8
[7] Devroye, L., Krzyżak, A.: New multivariate product density estimators. J. Multivar. Anal. 82(1), 88-110 (2002) · Zbl 0995.62034 · doi:10.1006/jmva.2001.2021
[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 · doi:10.1002/widm.51
[9] Ditzler, G., Roveri, M., Alippi, C., Polikar, R.: Learning in nonstationary environments: a survey. IEEE Comput. Intell. Mag. 10(4), 12-25 (2015) · doi:10.1109/MCI.2015.2471196
[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)
[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)
[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 · Zbl 1440.68207 · doi:10.1016/j.ins.2017.07.013
[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) · doi:10.1142/S0129065717500484
[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 · Zbl 1358.68234 · doi:10.1007/978-3-319-39384-1_4
[15] Ellis, P.: The time-dependent mean and variance of the non-stationary Markovian infinite server system. J. Math. Stat. 6, 68-71 (2010) · Zbl 1202.60143 · doi:10.3844/jmssp.2010.68.71
[16] Greblicki, W., Pawlak, M.: Nonparametric System Identification. Cambridge University Press, Cambridge (2008) · Zbl 1172.93001 · doi:10.1017/CBO9780511536687
[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)
[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 · doi:10.1007/978-3-319-59060-8_65
[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 · doi:10.1109/TNNLS.2017.2698204
[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) · doi:10.1016/j.inffus.2017.02.004
[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) · Zbl 1426.92003 · doi:10.1016/j.cam.2016.10.002
[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) · Zbl 1445.34105 · doi:10.1186/s13662-018-1509-y
[23] Phillips, P.C.: Impulse response and forecast error variance asymptotics in nonstationary VARs. J. Econom. 83(1), 21-56 (1998) · Zbl 0919.62131 · doi:10.1016/S0304-4076(97)00064-X
[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)
[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) · Zbl 1429.68237 · doi:10.1016/j.ins.2016.10.028
[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) · doi:10.1515/jaiscr-2017-0010
[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 · Zbl 1054.68127 · doi:10.1007/978-3-540-40046-2
[28] Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: The CART decision tree for mining data streams. Inf. Sci. 266, 1-15 (2014) · Zbl 1339.68229 · doi:10.1016/j.ins.2013.12.060
[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) · doi:10.1109/TKDE.2013.34
[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) · doi:10.1109/TNNLS.2014.2333557
[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) · doi:10.1109/TKDE.2012.66
[32] Specht, D.F.: A general regression neural network. IEEE Trans. Neural Netw. 2(6), 568-576 (1991) · doi:10.1109/72.97934
[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)
[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 · doi:10.1515/jaiscr-2017-0005
[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) · doi:10.1016/j.compbiomed.2005.10.001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.