Assignment: Artificial Intelligence

All the perceptron questions below must be answered by writing a program in the language of your choice that implements the perceptron algorithm given in class. The program should take as input a FILE in this format:

sample_vector class

for the example below the first class should appear as:

0 0 0

0 1 0

---> the class is 0 

Notice that the vectors are NOT augmented in the file.                                              

Unless instructed by the problem, all weight vectors must start a 0 

This code must be submitted with your answers and I will carefully check each submission

1.  Take the original perceptron problem done in class: 

class 1:  (0,0)  and (0,1)

class 2. (1,0) and (1,1)

however: instead of starting the weight vector at  (0, 0) start it at (3,-1). So we all get the same answer, the AUGMENTED weight vector should be (3,-1,0)

ANSWER THE FOLLOWING QUESTIONS

(A) what is the final weight vector?  

(b) graph the final weight vector

Absolutely no credit given with all the supporting work - all calculations for 1(a) above

2.  consider the following points:

class 1:  (0 0 -4 1), (2 3 -4 1), (12 14 -4 1)

class 2: (0 0 5 1) , (2 3 5 1), (12 14 5 1)

(a) what is the final weight vector?

(b) write the final weight vector as an equation

3. on page 765 of the text , (Norvig 3rd ed) problem 18.12 asked you to make a decision list and gives you some data. Forget that!

(a) Instead , use Weka to make a decision tree (the easiest thing to do is simply look at an existing ARF file , see the format, and make your own ARF file in the Weka data folder.  Dump the decision tree and submit it.

(b) run the perceptron algorithm on the same data. 

   (1) does the algorithm converge? If so, what is the final weight vector?

   (2) if it does not converge, give at least one data point that causes the non convergence of the algorithm

Absolutely no credit given with all the supporting work - all calculations for 2(a) above

4. By hand calculation determine the entropies of the weather NOMINAL dataset included with Weka 

(a) give the initial value of the entropy calculation of the Windy Attribute

(b) after the root OUTLOOK is selected, give the value of the value of the remaining attributes under the sunny SUBTREE. 

-> Take problem 1 but change the perceptron algorithm to start over again from the first point whenever a misclassification occurs. (The original Algorithm states we go through all the examples in order regardless of whether misclassify or not).

What is the final weight vector using the modified perception algorithm?