Complete the following:
Problem 1: Consider the example shown in the lecture of classifying an animal as cat (1) or kitten (0) using the proportion of day the animal was asleep, xS, and the proportion of day the animal was grumpy, xg. Four training examples are given in the table. The first two epochs were completed in the lecture and did not converge. The third epoch did not converge either and concluded with the weights (1, -1.1, - 1.8).
|
id
|
xs
|
xg
|
Class
|
|
1
|
0.2
|
0.1
|
Kitten
|
|
2
|
0.4
|
0.6
|
Kitten
|
|
3
|
0.5
|
0.2
|
Kitten
|
|
4
|
0.7
|
0.9
|
Cat
|
(a) Complete one more epoch and state whether it converged or not. To show your work you may use a table similar to the one used on the slides.
(b) What is the decision boundary? Write the equation and sketch it. Plot the four records on your graph.
Problem 2: Use the same problem as above but instead of the step activation, use the sigmoid function g(z). Since the sigmoid function returns the posterior probability of class 1 given a record, i.e., it returns a value between 0 and 1, classify a record as 1 only if the probability is 0.5 or greater. Run the algorithm for two epochs.
Problem 3: Again use cat-kitten classification data from above. Run a single epoch of an artificial neural network with one hidden layer consisting of the same notes as the input nodes. Use the sigmoid function for the activation and the same decision rule as in Problem 2.
Problem 4: For the two Boolean functions given below, state whether the problem is linearly separable. You must justify your answer to obtain credit.
(a) NOT A AND B
(b) (A XOR B) AND (A OR B)
Attachment:- Assignment File.rar