1. 1 st Neural Network: AND function Threshold(Y) = 2 X1 Y X2 1 1 1 2 Y

2. 1 st Neural Network: OR function X1 Y X2 2 2 Threshold(Y) = 2 1 2 Y

3. 1 st Neural Network: AND not function Threshold(Y) = 2 1 2 Y X1 Y X2 2

4. 1 st Neural Network: XOR function X1 Y X2 2 Z2 Z1 2 2 2 Threshold(Y) = 2 1 2 Y

5. Modeling a neuron a j :Activation value of unit j a j :Activation value of unit j w j,I :Weight on the link from unit j to unit i w j,I :Weight on the link from unit j to unit i in I :Weighted sum of inputs to unit i in I :Weighted sum of inputs to unit i a I :Activation value of unit i a I :Activation value of unit i g:Activation function g:Activation function

6. Activation Function Step t (x)=1 if x >= t, else 0 Step t (x)=1 if x >= t, else 0 Sign(x)=+1 if x >= 0, else –1 Sign(x)=+1 if x >= 0, else –1 Sigmoid(x)=1/(1+e -x ) Sigmoid(x)=1/(1+e -x )

7. Simple Network

8. Learning (training) Learning in ANN is adjusting the connection weight between neurons. Knowledge is stored in this weight matrices.

9. Training Methods Unsupervised Learning (learning without teacher or learning by doing) Supervised Learning (learning with teacher) Back propagation It’s similar to Supervised Learning but the error signal is used to adjust the weight.

10. Simple Training While (epoch produces an error) { // give the next input Error = Target – Output; If (Error <> 0) Weight j+1 = Weight j + LearningRate * Input j * Error; } Epoch : Presentation of the entire training set to the neural network.

11. Example

12. ANN Design: How to arrange neurons in various layers How to connect neuron from different layer How the neurons get input(s) and give result(s) Learning rate value Using bias or not How to train the ANN

13. Applications: Prediction Currency, stock exchange, weather, etc. Classification Pattern, shape, etc.