%% TAKE HOME QUIZ (Quiz 2)

%  Name(s):

%% Question 1:

%  First, solve the exercise in class using Hebbian Learning (Widrow-Hoff
%  learning rule

X=[1 1 2  2 -1 -2 -1 -2
   1 2 -1 0  2  1 -1 -2];
T=[1 1 -1 -1 1 1 -1 -1;
   1 1 1 1 -1 -1 -1 -1]; 

alpha=0.04;

%Initialize W, b:
W=eye(2);
b=[1;1];

% Fill in the following for Question 1: (Hebbian Learning for W, b)
% You should do the update 200 times, and each time, choose one
% of the 8 data points at random.







% Leave this part- It plots the output using your W and b:
figure(1)
xx=linspace(-3,3);
yy=W*X+repmat(b,1,8);
plot(T(1,1),T(2,1),'r^',yy(1,1:2),yy(2,1:2),'r*');
hold on
plot(T(1,3),T(2,3),'go',yy(1,3:4),yy(2,3:4),'g*');
plot(T(1,5),T(2,5),'bp',yy(1,5:6),yy(2,5:6),'b*');
plot(T(1,7),T(2,7),'ms',yy(1,7:8),yy(2,7:8),'m.');

% And the decision boundaries:
L1=(-W(1,1)/(W(1,2)))*xx-(b(1)/W(1,2));
L2=(-W(2,1)/(W(2,2)))*xx-(b(2)/W(2,2));
plot(xx,L1,xx,L2);
axis([-2 2 -2 2]);
hold off

W

b

%% Question 2:  

% Solve the problem using linear algebra.







% Be sure to convert your answer above to a matrix W
% and a vector b for the graphic routines below (nothing
% past here needs to be edited)


% Leave this part- It plots the output using your new W and b:
figure(2)
xx=linspace(-3,3);
yy=W*X+repmat(b,1,8);
plot(T(1,1),T(2,1),'r^',yy(1,1:2),yy(2,1:2),'r*');
hold on
plot(T(1,3),T(2,3),'go',yy(1,3:4),yy(2,3:4),'g*');
plot(T(1,5),T(2,5),'bp',yy(1,5:6),yy(2,5:6),'b*');
plot(T(1,7),T(2,7),'ms',yy(1,7:8),yy(2,7:8),'m.');

% And the decision boundaries:
L1=(-W(1,1)/(W(1,2)))*xx-(b(1)/W(1,2));
L2=(-W(2,1)/(W(2,2)))*xx-(b(2)/W(2,2));
plot(xx,L1,xx,L2);
axis([-2 2 -2 2]);
hold off

W

b