## Control Systems and Computers, N2, 2016, Article 4

##### DOI: https://doi.org/10.15407/usim.2016.02.034

*Upr. sist. maš., 2016, Issue 2 (262), pp. 34-40.*

UDC 004.032.26

**Bodyanskiy** Yevgeniy V., Doctor (Eng.), Prof., Professor of the Department of Artificial Intelligence, Scientific Director of the Problem Research Laboratory of Automated Control Systems, Kharkiv National University of Radio Electronics, E-mail: yevgeniy.bodyanskiy@nure.ua,

**Vynokurova** Olena А., Doctor (Eng.), Prof., Chief Scientist of the Problem Research Laboratory of Automated Control Systems, Professor of the Department of Information Technology Security, Kharkiv National University of Radio Electronics, E-mail: olena.vynokurova@nure.ua,

**Mulesa** Pavlo P., PhD (Eng.), Associate Professor, Department of Cybernetics and Applied Mathematics, State University “Uzhgorod National University”, E-mail: ppmulesa@gmail.com

### Diagnosis Wavelet-Neuro-Fuzzy System with Adaptive Wavelet Membership Function for Big Data Analysis Tasks

**Introduction.** The synthesis of the diagnostic wavelet-neuro-fuzzy system (WNFS) is used for the case, when training set volume is comparable with input patterns dimension. These patterns are fed for processing in on-line mode. An architecture of considered NFS consists of the six sequentially-connected layers.

**Method.** In the input (zero, receptive) layer of NFS *(nх1)*-dimensional vector of input signals-patterns *x(k)* is fed, where *k* is observation number in initial data set. In this case, it is supposed that all components *xi(k)* preliminary are modified so that *0<xi(k)<1, *and the binary input features have value 0 or 1. The first hidden layer consists of *nh* membership function and provides fuzzyfication of input variables, the larger the number *h* , the better approximating properties of WNFS, although it is enough to have *h=2* for the binary features.

The second hidden layer realizes an aggregation of the membership levels, which are computed in the first layer, and consists of* h* multiplication units. The third hidden layer is one of the synaptic weights, which are adjusted during the learning process. The proposed WNFS consists of mh tuning weights, where m is a number of the potential classes, one for each system output.

The fourth hidden layer consists of *m+1* summators, which compute sum of output signal of the second and the third hidden layers. In fifth hidden layer, that consists of *m* division unit normalization of fourth layer output signals is realized. And finally output (sixth) layer consists of m non-linear activation functions, in diagnosis tasks it is reasonable to use the simplest signum-functions, which takes +1 value in case of right diagnosis, and -1 – otherwise. Therefore output system signals* yj(k)* can take only two values +1 or -1. Thus, if vector signal *x(k)* is fed on NFS input, the first layer elements compute membership levels, at that usually the bell-shaped (kernel) construction with as membership function nonstrictly local receptive field is used as membership functions. It allows to avoid the appearing of “gaps” in fuzzyficated space.

**Results and Conclusion. **The diagnostic wavelet neuro-fuzzy system and its adaptive learning algorithm are introduced for solving the pattern recognition, classification, diagnostics tasks etc., under condition when training set value is comparable with input patterns dimension, and these patterns are fed for processing in on-line mode. The feature of proposed systems is significant smaller number of the tuning parameters comparing with the artificial neural networks that solve the same task. The system is characterized by simplicity of the computational implementation, the high speed of learning process, possibility of processing information, which is described in the different scales (interval, ordinal, binary).

Download full text! (Russian).

**Keywords**: diagnosis, wavelet-neuro-fuzzy-system, computational intelligence, online learning.

- Bifet, A., 2010. Adaptive Stream Mining: Pattern Learning and Mining from Evolving Data Streams. Amsterdam: IOS Press, 218 p.
- Springer Handbook of Computational Intelligence. Eds. J. Kacprzyk, W. Pedrycz. Berlin–Heidelberg: Springer-Verlag, 2015, 1634 p.
- Computational Intelligence: A Methodological Introduction. R. Kruse, C. Borgelt, F. Klawonn et al. Berlin: Springer-Verlag, 2013, 488 p.
- Haykin, S., 1999. Neural Networks. A Comprehensive Foundation. N.J., Upper Saddle River: Prentice Hall, Inc, 842 p.
- Rizzo, R., 2011. “Computational Intelligence Methods for Bioinformatics and Biostatistics. Lecture Notes in Bioinformatics”. (7th Int. Meeting, CIBIB 2010, Palermo, Italy, Sept. 16–18, 2010). Springer-Verlag, 301 p.
- Kountchev, R., Iantovics, B., 2013. Advances in Intelligent Analysis of Medical Data and Decision Support Systems (Studies in Computational Intelligence). Switzerland: Springer-Verlag, 246 p.
- Ljung, L., 1999. System Identification: Theory for the User. N.J., Upper Saddle River: PTR Prentice Hall, 672 p.
- Shynk, J.J., 1990. “Performance surfaces of a single-layer perceptron”. IEEE Trans. on Neural Networks, 1 (3), pp. 268–274.

https://doi.org/10.1109/72.80252 - Bodyanskiy, Ye.V., Kucherenko, Ye.I., Chaplanov, A.P., 2002. Diagnostika i prognozirovaniye vremennykh ryadov s pomoshch’yu mnogosloynoy radial’no-bazisnoy neyronnoy seti. Trudy 8 Vseros. konf. s mezhdunar. uchastiyem «Neyrokomp’yutery i ikh primeneniye». M.: In-t problem upravl. im. V.A. Trapeznikova RAN (21–22 marta 2002), pp. 209–213. (In Russian).
- Bodyanskiy, Ye.V., Kucherenko, Ye.I., Mikhalev, A.I., 2005. Neyro-fazzi seti Petri v zadachakh modelirovaniya slozhnykh sistem. Dnepropetrovsk: Sistemnyye tekhnologii, 311 p. (In Russian).
- Bodyanskiy, Ye., Vynokurova, O., 2013. Hybrid adaptive wavelet-neuro-fuzzy system for chaotic time series identification. Inform. sci., 220, pp. 170–179.

https://doi.org/10.1016/j.ins.2012.07.044 - Wang, L.-X., 1994. Adaptive Fuzzy Systems and Control: Design and Stability Analysis. N.J.: Prentice Hall, 256 p.
- Shepherd, A.J., 1997. Second-Order Methods for Neural Networks. London: Springer-Verlag, 145 p.

https://doi.org/10.1007/978-1-4471-0953-2 - Tsypkin, YA.Z., 1970. Osnovy teorii obuchayushchikhsya sistem. M.: Nauka, 252 p. (In Russian).
- Murphy, P.M., Aha, D.W., 1994. UCI Repository of machine learning databases. URL: http://www.ics.uci.edu/mlearn/MLRepository.html. CA: University of California, Depart. of Inform. and Comp. Sci.

**Received** 30.12.2015