Intelligent Systems

Take Home Quiz 1 - Due Feb 11, 1998

 

 

1. Use a modified version of the Matlab Neural Network Toolbox program DEMOP1 to correctly classify the Bongard data. The data as measured in class is given in the previous course notes. You must modify the target vector, T, to make a two parallel perceptron classifier that can accomplish the XOR classification. A sample program segment is shown below.

 

% A row vector T defines the vector's target categories.

% A two-row target vector defines the two

% parallel perceptron neural net that performs the XOR classification

T = [1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 ;

0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 ];

 

 

2. Determine whether either of the following two points:

 

P1 = [3/4 7/4 5/4 7/4]T

and

P2 = [5/4 9/4 7/4 7/4] T

is on the line through

 

Q1 = [1 2 1 2] T and Q2 = [2 3 4 1] T

 

 

3. Determine whether the following two lines are parallel, where

 

L1 = { x: x = [2 3 1] T + a [1 4 -1] T }

and L2 = {x: x = [5 7 2] T + a [ -3 -12 3] T}

 


4. Let L be the line through

P1 = [1 2 1 3] T and P2 = [ 2 3 4 1] T

Find the equation of a line L2 through P1 and perpendicular to L1.

 


      5. Determine if the hyperplanes H1 and H2 are parallel, where

      H1 = { x: [4 2 7 8 ] x = 4} and H2 = { x : [1 1/2 7/4 2] x = 19}

       


      6. Given a point, z, and a hyperplane, H, where H = {x : aTx = b} ,

      determine the point y on H closest to z.


      7. The following 10 samples have measured experimentally. Determine a neural net classification of the samples.

    Sample number

    Measurement

    Class

    1

    0.608

    2

    2

    -1.590

    1

    3

    0.235

    2

    4

    3.949

    2

    5

    -2.249

    1

    6

    2.704

    2

    7

    -2.473

    1

    8

    0.672

    2

    9

    0.262

    2

    10

    1.072

    2

     


    8.The following data was collected by Shawn Mill for Hasbro for the period 9/3/96 - 12/30/96. Use a function approximation neural network such as DEMOBP4 to fit the data.

Week

Stock Price

1

37.25

2

36.875

3

36.625

4

37.625

5

39.75

6

38.75

7

39.125

8

38.875

9

39.375

10

42.25

11

43.125

12

41.375

13

41.125

14

40.25

15

39.0

16

38.375

17

38.25

18

39.25

 

 

PLEASE TURN IN YOUR SOLUTIONS IN SUFFICIENT DETAIL TO PERMIT A VERIFICATION OF YOUR WORK. A TYPED SOLUTION IS PREFERRED. A CAREFULLY PRINTED HANDWRITTEN SOLUTION IS ACCEPTABLE. PROGRAM LISTINGS FOR PROBLEMS 1,7 AND 8 ARE NECESSARY AS WELL