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					                               Alexandria University

Fourth Year/Second term                                              Subject : AI
Instructor: Dr. Yasser Fouad                                         Time    : 2008

                               Neural Networks Sheet
   1. Solve the three classification problems shown blew by drawing the decision
      boundary. Find weights and bias values that result in single-neuron perceptrons with
      the chosen decision boundaries.




2. Consider the classification problem defined below

       1                 1                0                  1 
p i   , t 1  1 & p 2   , t 2  1 & p 3   , t 3  0 & p 4   , t 4  0
      1                   1                0                  0

   i)       Design a single neuron perceptron to solve this problem with initial weights W =
            [0 0] and b = 0?
   ii)      Classify the following inputs

   3. Covert the classification problem into perceptron neural network model (b=3 and
         start w1=1 and w2=2 or any other values).
         X1 = [0 2], t1=1 & x2 = [1 0], t2=1 & x3 = [0 –2] , t3=0 & x4=[2 0], t4=0
   4. The following multilayer network has three neurons. All neurons have negative
                           1
      sigmoid function 1  e . The equation for the derivative of f ' (n)  f (n)(1  f (n)) .
                             n


                                                                          1
                                                                            (2t  2 y ) 2
      Additionally, this network uses a non-standard error function E = 2                 using
      the initial weights [b1= - 0.5, w11=2, w12=2, w13=0.5, b2= 0.5, w21= 1, w22 = 2,
      w23 = 0.25, and b3= 0.5] and input vector [2, 2.5] and t = 8. Process Three iterations
      of backpropagation algorithm.
                                                 W11
                                      X1                             W13

                                           W12
                                                        b1

                                                W21
                                      X2                          W23
                                                                              b3
                                                 W2 2

                                                             b2


    5.    For the network shown below with initial weights and biases are chosen to be
                                                                                       1
                                                                      f 1  n2 , f 2 
         W  1, b  2, W  1, b  1 the transfer functions are
            1      1          2      2
                                                                                       n and an
         input / target pair is given to be ((p=1), (t=1)) perform three iterations of
         backpropagation with   1


          W1                          W2
p                                                                   Y


               b1                          b2

				
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Description: Artificial intelligence Academic lecture