Neural Networks in Statistica

Transcription

1 Neural Networks in Statistica Agnieszka Nowak - Brzezińska

2 The basic element of each neural network is neuron. x1 x2 w1 w2 Dendrites Terminal Branches of Axon x3 w3 S Axon xn wn

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4 Types of neurons y S- aggregated input value Activation function

5 Activation function For linear neurons: Linear, sigmoidal, hiperbolic, exponential, sinusoidal, For radial: gauss. Linear is the aggregation. Output value can be taken from nonlinear activation function.

6 Neuron s learning y

7 Prediction Input: X 1 X 2 X 3 Output: Y Model: Y = f(x 1 X 2 X 3 ) X 1 =1 X 2 =-1 X 3 =2 0.2 = 0.5 * 1 0.1*(-1) 0.2 * f(x) = e x / (1 + e x ) f(0.2) = e 0.2 / (1 + e 0.2 ) = f (0.2) = f (0.9) = Prediction Y = f (-0.087) = If true id Y = 2 Then prediction error is = ( ) =1.522

8 Learning process 2. Calculate the value of Y 1. Randomly choose one observation 3. Compare Y with the actual value 4. Modify the weights by calculation the error

9 Backpropagation It is one of the most popular techniques of learning process for NN.

10 How to calculate the prediction error? where: Error i is the error ofr i-th node, Output i is the predicted by the network, Actual i is the real value which should be predicted

11 Weights modification L- is the learning factor from the range [0,1] The less the l values is the slowest the learning process is. Very often l is the highest in the begining and then reducted with the changing of the weights.

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13 Example

14 Zmiana wag L- is the learning factor from the range [0,1] The less the l values is the slowest the learning process is. Very often l is the highest in the begining and then reducted with the changing of the weights.

15 How many neurons? The number of neurons in the input layer depends on the number of input variables The number of neurons in output layer depends on the type of the problem to solve by the network The number of neurons in hidden layer depends on the users qualifications

16 Neural network tasks: clasification NN is to decide about the class of a given object (classes in nominal scale) regresion NN is to predict a value (numerical) of the attribute which is the output value.

17 Clasification 1. Dataset leukemia.sta 2. choose the type of NN

18 3. Choose the variables: 4. Automatic generation of NN

19 You may change the proportions of division of dataset in learning and testing probes

20 Automatic generation of NN Linears neurons(mlp) Minimal (3) maksimal (10) neurons in hidden layer 20 NN, 5 the best is displayed Error function: SSE The window presents the creation of model where 3 are neurons in input layer, 6 in hidden and 2 in output layer.

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23 3 best nets are saved

24 Predictions Graphs Details Liftcharts Custom predictions SUMMARY

25 Predictions

26 Details Summary Weights Confusion matrix

27 Details Ciekawe są opcje: Summary Weights Confusion matrix

28 Details Ciekawe są opcje: Summary Weights Confusion matrix

29 Results

30 Zakładka liftcharts Further read:

31 1 dataset tomatoes.sta Regression 2. type of the network:

32 3. Choose from the variables: 4. Automatic generation of NN

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36 2 best NN saved

37 Predictions Graphs Details Liftcharts Custom predictions SUMMARY

38 Predictions

39 Graphs

40 Details Ciekawe są opcje: Summary Weights Correlation coefficients Confusion matrix -

41 Results

42 read: