Approximation and Prediction of Wages Based on Granular Neural Network

1. Approximation and Prediction of Wages Based on Granular Neural Network Milan Marček1 and Dušan Marček2 1Faculty of Philosophy and Science, Silesian University, 746 01 0pava, Czech Republic & MEDIS Nitra, Ltd., Pri Dobrotke 659/81, 949 01 Nitra-Dražovce, Slovak Republic marcek@fria.utc.sk 2Faculty of Philosophy and Science, Silesian University, 746 01 0pava, Czech Republic & Faculty of Management Science and Informatics, University of Zilina 010 26 Zilina, Slovak Republic dusan.marcek@fpf.slu.cz, dusan.marcek@fri.uniza.sk

2. Outlines • Basic principles of identifying input-output functions of systems and forecasting • RBF and soft RBF NNs for approximation of input - output functions • Additive fuzzy system • Granular RBF network based on cloud concept • An application (experimenting with statistical and eonometric models vs. RBF networks) • Results • Conclusions

3. Basic principles of identifying input-output functions of systems and forecasting There are two major approaches to forecasting – explanatory and time series. Explanatory forecasting Time series forecasting (ANN)

4. RBF and soft RBF NNs for approximation of input - output functions and forecasting a) b)

5. Additive fuzzy system The fuzzy system consists of series of separate fuzzy rules (relations) each of the type of if Ai then Bi. Centroidal output converts fuzzy sets vector B to a scalar. The most popular centroidal defuzzification technique uses all the information in the fuzzy distribution B to compute the crisp y value as the centroid or centre of mass of Bwhere y stands for the centre of gravidity of the jth output singleton.

6. Granular RBF network based on cloud concept Cloud models are described by three numerical characteristics : Expectation (Ex) as most typical sample which represents a qualitative concept, Entropy (En) as the uncertainty measurement of the qualitative concept and Hyper Entropy (He) which represents the uncertain degree of entropy. En and He represent the granularity of the concept, because both the En and He not only represent fuzziness of the concept, but also randomness and their relations. Then, in the case of soft RBF network, the Gaussian membership function

7. An application (experimenting with statistical and eonometric models vs. RBF networks) a) b) B-J methodology – ARMA(1, 3) process yt = -0.0016557 -0.4567y(t-1) + εt + 0.90516ε(t-1) + 0.58768ε(t-2) + 0.36497ε(t-3); MSEA = 0.014, MSEE = 0.048 Ekonometric model (transfer functions model) yt = 0.239347 + 1.04044 yt-4 MSEA = 0.0026, MSEE = 0.0033 (7)

8. Results

9. Conclusions The estimated parameters, in contrast with statistical models, have no economic interpretation to structural model, all parameters in the model are fixed, and there is no possibility to test the stability of the parameters The econometric model in (7) gives best predictions outside the estimation period and clearly dominates the other models. We have shown that too many model parameters results in overfitting, i.e. a curve fitted with too many parameters follows all the small fluctuations, but is poor for generalisation

10. Algoritm for updating weights in the granular neural network

11. Continued