Paper:

# Predictor Using an Error-Convergence Neuron Network and its Application to Electrocardiograms

## Shunsuke Kobayakawa and Hirokazu Yokoi

Graduate School of Life Science and Systems Engineering, Kyushu Institute of Technology, 2-4 Hibikino, Wakamatsu-ku, Kitakyushu-shi, Fukuoka 808-0196, Japan

The output error of a neuron network cannot converge at zero, even if the training for a neuron network is iterated many times. “Error-convergence neuron network” in which the output error of a singleoutput system uses neuron networks with multiplestep convergence, has been designed to resolve this problem. The output error is converged at zero by setting infinite steps of the neuron network. Three types of neuron network systems also have been designed. They are “Error-convergence parallel neuron network,” “Error-convergence recurrent neuron network,” and “Error-convergence parallel recurrent neuron network.” A subsequent prediction can be obtained by recurring the prediction of a predictor to its input if the predictor is free of prediction error. An error-convergence neuron network can be applied to realize this predictor. “Error-convergence neuron network predictor” has been proposed as such a predictor. In this study, its feasibility is investigated by performing prediction training for the errorconvergence neuron network predictor constructed of second-order Volterra neuron networks with two steps, using the nonlinear time series signal of a normal sinus rhythm electrocardiogram. Predictions without any error were obtained.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.15, No.1, pp. 21-33, 2011.

- [1] S. Grossberg, “Adaptive Pattern Classification and Universal Recoding: I. Parallel Development and Coding of Neural Feature Detectors,” Biological Cybernetics, Vol.23, No.3, pp. 121-134, 1976.
- [2] T. Kohonen, “Self-Organization and Associative Memory,” Springer-Verlag, Berlin etc., 1984.
- [3] E. Levin, N. Tishby, and S. Solla, “A statistical approach to learning and generalization in layered neural networks,” Proc. of the IEEE, Vol.78, Issue 10, pp. 1568-1574, 1990.
- [4] C. L. Giles and T. Maxwell, “Learning, Invariance and Generalization in High Order Neural Networks,” Applied Optics, Vol.26, No.23, pp. 4972-4978, 1987.
- [5] K. J. Lang and G. E. Hinton, “A Time-Delay Neural Network Architecture for Speech Recognition,” Carnegie Mellon University Computer Science Technical Report, CMU-CS-88-152, pp. 1-37, 1988.
- [6] S. Kobayakawa, T. Fujii, and H. Yokoi, “Evaluation of Prediction Capabilities of Neuron Networks Used for Electrocardiogram,” Proc. of the 5th Int. Symp. on Management Engineering, Kitakyushu, Japan, pp. 156-161, 2008.
- [7] T. Possio and F. Girosi, “Networks for Approximation and Learning,” Proc. of the IEEE, Vol.78, No.9, pp. 1481-1497, 1990.
- [8] S. Iwamoto, T. Yoshida, and H. Yokoi, “Basic Investigation Associated with Neural Control of Biped Walking Robot,” Technical Report of IEICE, MBE93-106, pp. 23-30, 1994.
- [9] Y. Fujisue, E. Inohira, and H. Yokoi, “Robotic Control by Volterra Network,” Technical Report of IEICE, NC2003-78, pp. 39-43, 2003.
- [10] S. Uota and H. Yokoi, “A Realization of Motion Diversity of the Robotic Hand by the Hierarchical Motion Schema,” Technical Report of IEICE, NC2003-75, pp. 25-28, 2003.
- [11] J. Miyoshi and H. Yokoi, “An Improvement of a Neural Network for Learning a Slip Angle of a Four-Wheel Steering Car,” Technical Report of IEICE, NC2004-107, pp. 87-90, 2004.
- [12] S. Shigemura, T. Nishimura, and H. Yokoi, “A Method of Removing Blink Artifacts from EEG Signals Using Neural Networks with Volterra Filters,” Technical Report of IEICE, MBE2004-87, pp. 57-60, 2005.
- [13] S. Suematsu and H. Yokoi, “A Motion Generating System for Multi-Fingered Myoelectric Hand,” Int. Congress Series 1291, pp. 257-260, 2006.
- [14] S. Kobayakawa, T. Fujii, and H. Yokoi, “Evaluation of Nonlinear Prediction Capabilities of Neuron Networks for Electrocardiogram,” Proc. of the 20th Annual Meeting of Biomedical Fuzzy Systems Association, pp. 9-12, 2007.
- [15] S. Kobayakawa and H. Yokoi, “The Volterra Filter Built-in Neural Network for the Aircraft Pitch Attitude Control,” The Lecture Proc. of the 2005 Fiscal Year Electricity Relation Institute Kyushu Branch Association Convention, Fukuoka, Japan, p. 429, 2005.
- [16] A. G. Ivakhnenko, “The Group Method of Data Handling-A Rival of the Method of Stochastic Approximation,” Soviet Automatic Control, Vol.13 c/c of Avtomatika, 1, 3, pp. 43-55. 1968.
- [17] A. D. Back and A. C. Tsoi, “FIR and IIR Synapses, A New Neural Network Architecture for Time Series Modeling,” Neural Computations, Vol.3, pp. 375-385, 1991.
- [18] M. Hoshino, T. Kitamura, T. Masuda, M. Suzuki, and J. Chao, “On Multilayer RBF Networks and a Novel Pyramid Network,” Proc. of the Society Conf. of IEICE, Nagoya, Japan, p. 28, 2000.
- [19] N. Kinoshita and K. Nakamura, “Two-D Spreading Associative Neural Network Recognizes the Shape and Position of An Object Presented in the Two-D Space,” Technical Report of IEICE, NC97-166, Vol.97, No.623-624, pp. 209-216, 1998.
- [20] S. Kobayakawa and H. Yokoi, “Application to Prediction Problem of Parallelized Neuron Networks in the Aircraft,” Technical Report of IEICE, SANE2006-119-133, Vol.106, No.471, pp. 43-45, 2007.
- [21] S. Kobayakawa and H. Yokoi, “Evaluation for Prediction Capability of Parallelized Neuron Networks,” Proc. of the 8th SOFT Kyushu Chapter Annual Conf., Kitakyushu, Japan, pp. 3-6, 2006.
- [22] S. Kobayakawa and H. Yokoi, “Evaluation of the Learning Capability of a Parallel-type Neuron Network,” Proc. of the First Int. Symp. on Information and Computer Elements 2007, Kitakyushu, Japan, pp. 43-47, 2007.
- [23] S. Kobayakawa and H. Yokoi, “Experimental Study for Dominance to Accuracy of Prediction Output of Parallel-type Neuron Network,” Technical Report of IEICE, NC2008-1-10, Vol.108, No.54, pp. 29-34, 2008.
- [24] S. Kobayakawa and H. Yokoi, “Evaluation for Prediction Accuracies of Parallel-type Neuron Network,” Int. MultiConf. of Engineers and Computer Scientists 2009 Proc., Hong Kong, China, Vol.I, pp. 156-161, 2009.
- [25] H. Yokoi and T. Kimoto, “Multilayered Neural Networks with Intermediate Elements,” J. of Biomedical Fuzzy Systems Association, Vol.1, No.1, pp. 87-97, 1999.
- [26] H. Sori and T. Yasuno, “Several-Hours-Ahead Wind Speed Prediction System Using Hierarchical Neural Network,” J. of Signal Processing, Vol.12, No.6, pp. 507-514, 2008.
- [27] A. Cichocki and A. Bargiela, “Neural Networks for Solving Linear Inequality Systems,” Parallel Computing, Vol.22, No.11, pp.1455-1475, 1997.
- [28] A. Cichocki and R. Unbehauen “Neural Networks for Optimisation and Signal Processing,” Wiley-Teubner, Chichester etc., 1993.
- [29] S. Kobayakawa, T. Fujii, and H. Yokoi, “Nonlinear Prediction for ECG by 2
^{nd}-order Volterra Neuron Network,” J. of Biomedical Fuzzy Systems Association, Vol.11, No.2, pp. 101-111, 2009. - [30] S. Kobayakawa and H. Yokoi, “Proposal of Error Convergence-type Neuron Network System,” Presented Proc. to 2008 Int. Symp. on Intelligent Informatics, Kumamoto, Japan, pp. 1-10, 2008.
- [31] D. E. Rumelhart, G. E. Hinton and R. J. Williams, “Learning Representations by Back-propagating Errors,” Nature, Vol.323, No.6088, pp. 533-536, 1986.
- [32] A. Chatterjee, A. Nait-Ali, and P. Siarry, “An Input-delay Neural-Network-Based Approach for Piecewise ECG Signal Compression,” IEEE Trans. on Biomedical Engineering, Vol.52, No.5, pp. 945-947, 2005.
- [33] S. Kobayakawa and H. Yokoi, “Proposal of Predictive Coding Using Error Convergence-type Neuron Network System,” The Proc. of the ISCA 22nd Int. Conf. on Computers and Their Applications in Industry and Engineering, San Francisco, USA, pp. 169-174, 2009.
- [34] S. Kobayakawa and H. Yokoi, “Evaluation of Learning Capabilities of BP Networks to Number of Input Signals,” Technical Report of IEICE, SANE2007-102-124, Vol.107, No.442, pp. 83-86, 2008.
- [35] “A Normal Sinus Rhythm ECG,” Yokoi Lab. Kyushu Institute of Technology, 1999.http://www.life.kyutech.ac.jp/˜yokoi/yokoi_lab_ecg.dat
- [36] M. Onodera, Y. Isu, U. Nagashima, H. Yoshida, H. Hosoya, and Y. Nagakawa, “Noise Filtering Using FFT, Bayesian Model and Trend Model for Time Series Data,” The J. of Chemical Software, Vol.5, No.3, pp. 113-127, 1999.