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Application of Back-Propagation neural network in data forecasting

Application of Back-Propagation neural network in data forecasting. Le Hai Khoi, Tran Duc Minh Institute Of Information Technology – VAST Ha Noi – Viet Nam. Acknowledgement . The authors want to Express our thankfulness to Prof. Junzo WATADA who read and gave us worthy comments.

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Application of Back-Propagation neural network in data forecasting

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  1. Application of Back-Propagation neural network in data forecasting Le Hai Khoi, Tran Duc Minh Institute Of Information Technology – VAST Ha Noi – Viet Nam

  2. Acknowledgement The authors want to Express ourthankfulness to Prof. Junzo WATADA who read and gave us worthy comments. Authors

  3. CONTENT • Introduction • Steps in data forecasting modeling using neural network • Determine network’s topology • Application • Concluding remarks

  4. Data collecting and analyzing Pre-processing Post-processing Neural Networks Figure 1: Data Processing. Introduction • Neural networks are “Universal Approximators” • To find a suitable model for the data forecasting problem is very difficult andin reality, it might be done only by trial-and-error • We may take the data forecasting problem for a kind of data processingproblem

  5. Steps in data forecasting modeling using neural network The works involved in are: * Data pre-processing: determining data interval: daily, weekly, monthly or quarterly; data type:technical index or basic index; method to normalize data: max/min ormean/standard deviation. * Training: determining the learning rate, momentum coefficient, stop condition, maximumcycles, weight randomizing, and size of training set, test set and verificationset. * Network’s topology: determining number of inputs, hidden layers, number of neurons in each layer,number of neurons in output layer, transformation functions for the layers anderror function

  6. Steps in data forecasting modeling using neural network The major steps in design the data forecasting model is as follow: １.Choosing variables ２．Data collection ３．Data pre-processing ４．Dividing the data set into smaller sets: training, test and verification ５．Determining network’s topology: number of hidden layers, number ofneurons in each layer, number of neurons in output layer and thetransformation function. ６．Determining the error function ７．Training ８．Implementation. In performing the above steps, it is not necessary to perform steps sequentially. We could be back to the previous steps, especially in training and choosing variables steps. The reason is because in the designing period, if the variables chosen gave us unexpected results then we need to choose another set of variables and bring about the training step

  7. Choosing variables and Data collection • Determining which variable is related directly or indirectly to the data that we need to forecast. • If the variable does not have any affect to the value of data that we need to forecast then we should wipe it out of consider. • Beside it, if the variable is concerned directly or indirectly then we should take it on consider. Collecting data involved with the variables that are chosen

  8. Data pre-processing Analysis and transform values of input and output data to emphasize the important features, detect the trends and the distribution of data. Normalize the input and output real values into the interval between max and min of transformation function (usually in [0, 1] or [-1, 1] intervals). The most popular methods are following: SV = ((0.9 - 0.1) / (MAX_VAL - MIN_VAL)) * (OV - MIN_VAL) Or: SV = TFmin + ((TFmax - TFmin) / (MAX_VAL - MIN_VAL)) * (OV - MIN_VAL) where: SV: Scaled Value MAX_VAL: Max value of data MIN_VAL: Min value of data TFmax: Max of transformation function TFmin: Min of transformation function OV: Original Value

  9. Dividing patterns set • Divide the whole patterns set into the smaller sets: • Training set • Test set • Verification set. • The training set is usually the biggest set employed in training the network. The test set, often includes 10% to 30% of training set, is used in testing the generalization. And the verification set is set balance between the needs of enough patterns for verification, training, and testing.

  10. Determining network’s topology This step determines links between neurons, number of hidden layers, number of neurons in each layer. 1. How neurons in network are connected to each other. 2. The number of hidden layers should not exceed two 3. There is no method to find the most optimum number of neurons used in　　hidden layers. => Issue 2 and 3 can only be done by trial and error since it is depended on the problem that we are dealing with.

  11. Determining the error function • To estimate the network’s performance before and after training process. • Function used in evaluation is usually a mean squared errors. Other functions may be: least absolute deviation, percentage differences, asymmetric least squares etc. • Performance index • F(x) = E[eTe]= E [ (t - a)T(t - a) ] • Approximate Performance index • F(x) = eT(k)e(k)]= (t(k) - a(k) )T(t(k) - a(k)) • The lastest quality determination function is usually the Mean Absolute Percentage Error - MAPE.

  12. Training • Training tunes a neural network by adjusting the weights and biases that is expected to give us the global minimum of performance index or error function. • When to stop the training process ? • It should stop only when there is no noticeable progress of the error function against data based on a randomly chosen parameters set? • It should regularly examine the generalization ability of the network by checking the network after a pre-determined number of cycles? • Hybrid solution is having a monitoring tool so we can stop the training process or let it run until there is no noticeable progress. • The result after examining of verification set of a neural network is most persuadable since it is a directly obtained result of the network after training.

  13. Implementation This is the last step after we determined the factors related to network’s topology, variables choosing, etc. 1. Which environment: Electronic circuits or PC 2. The interval to re-train the network: might be depended on the times and also other factors related to our problem.

  14. Determine network’s topology Multi-layer feed-forward neural networks a1 a2 W1 W2 f1 f2 R1 x1 S1x1 S2x1 n1 n2 S1xR1 S2xS1   S1x1 S2x1 1 1 b1 b2 P S1x1 S2x1 a2 = f2( W2 f1 (W1p + b1) + b2) Figure 2: Multi-layer feed-forward neural networks where: P: input vector (column vector) Wi: Weight matrix of neurons in layer i. (SixRi: Si rows (neurons), Ri columns (number of inputs)) bi: bias vector of layer i (Six1: for Si neurons) ni: net input (Six1) fi: transformation function (activate function) ai: net output(Six1) : SUM function i = 1 .. N, N is the total number of layers.

  15. bias x１ x2 … xn wij wjk bias wkl Output … … … Input layer Hidden layers Output layer 1 ƒ(x) = and ƒ’(x) = ƒ(x) { 1 - ƒ(x) } 1 + e-δx Determine training algorithm and network’s topology 1 1 Figure 3: Multi-layered Feed-forward neural network layout Transfer function is a sigmoid or any squashing function that is differentiable

  16. Back-propagation algorithm Step 1: Feed forward the inputs through networks: a0 = p am+1 = fm+1 (Wm+1am + bm+1), where m = 0, 1, ..., M– 1. a = aM Step 2: Back-propagate the sensitive (error): at the output layer at the hidden layers where m = M– 1, ..., 2, 1. Step 3: Finally, weights and biases are updated by following formulas: . (Details on constructing the algorithm and other related issues should be found on text book Neural Network Design)

  17. Using Momentum This is a heuristic method based on the observation of training results. The standard back-propagation algorithm will add following item to the weight as the weight changes: ∆Wm(k) = - sm (am – 1)T, ∆bm(k) = - sm . When using momentum coefficient, this equation will be changed as follow: ∆Wm(k) = ∆Wm(k – 1) – (1 – ) sm (am – 1)T, ∆bm(k) = ∆bm(k – 1) – (1 – ) sm .

  18. LAYERclass NEURAL NETclass friend Arrow: inheritance relation Rhombic antanna arrow: Aggregate relation NEURAL NET class includes the components that are the instances of Output Layer and Hidden Layer. Input Layer is not implemented here since it does not do any calculation on the input data. Output layer Hidden layer Application

  19. Application

  20. Application

  21. Application

  22. Concluding remarks • The determination of the major works is important and realistic. It will help develop more accuracy data forecasting systems and also give the researchers the deeper look in implementing the solution using neural networks • In fact, to successfully apply a neural network, it is depended on three major factors: • First, the time to choose the variables from a numerous quantity of data as well as performpre-processing those data; • Second, the software should provide the functions to examine the generalization ability,help find the optimal number of neurons for the hidden layer and verify with many input sets; • Third, the developers need to consider, examine all the possible abilities in each timechecking network’s operation with various input sets as well as the network’s topologies so that the chosen solution will exactly described the problem as well as give us the mostaccuracy forecasted data.

  23. THANK YOU FOR ATTENDING! Authors Kytakyushu 03/2004

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