Approximation and Prediction of Wages Based on Granular Neural Network

1
Approximation and Prediction of Wages Based on
Granular Neural Network

• Milan Marcek1 and Duan Marcek2
• 1Faculty of Philosophy and Science, Silesian
  University, 746 01 0pava, Czech Republic MEDIS
  Nitra, Ltd., Pri Dobrotke 659/81, 949 01
  Nitra-Draovce, Slovak Republic
• marcek_at_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_at_fpf.slu.cz, dusan.marcek_at_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 B where 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
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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) et 0.90516e(t-1)
0.58768e(t-2) 0.36497e(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)
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Results
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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
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• Continued