Manual Artificial Higher Order Neural Networks for Economics and Business

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The temperature can have a greater influence in daily life than any other single element on a routine basis. Therefore, some great observation are needed to obtain accuracies for the temperature measurement Ibrahim, Temperature forecasting undoubtedly is the most challenging task in dealing with meteorological parameters. It represents not only a very complex nonlinear problem, but also extremely difficult to model.

These methods, however, constitutionally complex and are limited and restricted to that of numerical weather prediction products Paras et al. Considering the downside of those methods, Neural Networks have placed such sophisticated models within the reach of practitioners, and therefore have been successfully applied in many problems. The forecasting horizon for temperature prediction is a one-step-ahead, whereas the output variable represents the temperature measurement of one-day ahead of temperature data.

A univariate data of a 5-years daily temperature measurement in Batu Pahat Malaysia, ranging from to was used for the simulation please refer to Table 1. The properties of Batu Pahat Temperature signal www. Max-Min Normalization maps a value v of data A to v ' in In data normalization, the statistical distribution values for each input and output are roughly uniform. Therefore, removing the outliers should make the data more accurate. Figure 3 shows the daily temperature data of Batu Pahat region before normalization while Figure 4 shows the daily temperature data of Batu Pahat region after normalization.

Meanwhile, Figure 5 shows the frequency of temperature distribution data for 5-years after normalization process. From Figure 5, it can be seen that the histogram of the transformed data is symmetrical.

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Therefore, it can be said that the temperature data for Batu Pahat after normalization is relatively uniform, and closely follow the normal distribution, thus suitable as the network inputs. Training Validation Testing Table 2. As there is no rule of thumb for identifying the number of input, a trial-and-error procedure was determined. All networks were built considering 5 different number of input nodes ranging from 4 to 8. A single neuron was considered for the output layer.


Simulation results The temperature dataset collected from MMD was used to demonstrate the performance of JPSN by considering a few different network parameters. Generally, the factors affecting the network performance include the learning factors, the higher order terms, and the number of neurons in the input layer.

Two stopping criteria were used during the learning process; the maximum epoch and the minimum error, which were set to and 0. In order to assess the performance of all network models, four measurement criteria, namely the number of epoch, Mean Squared Error, Normalized Mean Squared Error, and Signal to Noise Ratio are used.

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  • Convergence is achieved when the output of the network meets the earlier mentioned stopping criteria. The above discussions have shown that some network parameters may affect the network performances. It demonstrates that the combination of 8 input nodes and PSNN of Order 2 shows the best performance for all measuring criteria.

    Same thing goes to the MLP, which signifies that MLP with 2 hidden nodes and 8 input nodes attained the best results for all measuring criteria except for SNR and number of epochs refer to Table 5. This indicates that the network is capable of representing nonlinear function better than the two benchmarked models.

    On the whole, the performance of JPSN gives a gigantic comparison when compared to the two benchmarked models. This by means shows that the predicted and the actual values which were obtained by the JPSN are better than both comparable network models in terms of bias and scatter. Consequently, it can be inferred that the JPSN yield more accurate results, providing the choice of network parameters are determined properly.

    The parsimonious representation of higher order terms in JPSN assists the network to model successfully. The plots depicted in Figures 7 to 9 present the temperature forecast on the out-of-sample dataset for all network models. As shown in the plots, the blue line represents the trend of the actual values, while the red line represents the predicted values. The predicted values of daily temperature measurement made by all network models almost fit the actual values with minimum error forecast. It is verified that JPSN has the ability to perform an input-output mapping of temperature data as well as better performance when compared to www.

    The better performance of temperature forecasting is allocated based on the vigour properties it contains. Hence, it can be seen that the thrifty representation of higher order terms in JPSN assists the network to model effectively.

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    NMSE 0. Conclusion There are many applications and techniques on temperature that was developed in the past. However, limitations such as the accuracy and complexity of the models make the existing system less enviable for some applications. Therefore, improvement on temperature forecasting requires continuous efforts in many fields, including NN. Several methods related to NN, particularly have been investigated and carried out.

    However, the ordinary feedforward NN, the MLP, is prone to overfitting and easily get stuck into local minima.

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    Thus, to overcome the drawbacks, a new model, called JPSN is proposed as an alternative mechanism to predict the temperature event. In this chapter, JPSN is used to learn the historical temperature data of Batu Pahat, and to predict the temperature measurements for the next-day ahead. Acknowledgment The work of R. References Baboo, S. Atmosphere, Weather, and Climate: Methuen.

    Artificial Higher Order Neural Networks for Economics and Business

    Chang, F. Assessing the effort of meteorological variables for evaporation estimation by self-organizing map neural network. Journal of Hydrology, , Cybenko, G. Approximation by Superpositions of a Sigmoidal Function. Signals Systems, 2 , pp. Ghazali, R. Dynamic Ridge Polynomial Neural Network: Forecasting the univariate non-stationary and stationary trading signals. Elsevier: Expert Systems with Applications.

    Hussain, A. Neurocomputing, 55, pp. Ibrahim, D. Temperature and its Measurement.

    Oxford: Newnes.