Can't plot all the four points among the inputs given in an OR Gate.

Here's my code for plotting the inputs in an OR Gate but among the four inputs only three gets plotted.Can anyone provide me solution to this??

CODE:

x=[1 0;0 1;0 0;1 1];
y=[1;1;0;1];
plot(x,y,'o')

Here is the output showing only three points rather it should have showen four.

Can anyone please provide me the reason behind this and the solution to overcome this.

[James Tursa]

It is not clear to me what result you want for the plot. Can you describe what your desired plot would look like?

[Saptarshee Sarkar]

My desired plot should contain a forth point at x-coordinate (1,0) as it skipping that point and showing all the other 3 points.

Answer 1

[Ameer Hamza]

The way you are using plot() does not make much sense here. Using scatter() with y as the color value will show the difference f true and false values.

x=[1 0;0 1;0 0;1 1];
y=[1;1;0;1];
scatter(x(:,1),x(:,2),[],y,'filled')
colormap(cool)

[Saptarshee Sarkar]

Why the use plot() doesn't gives the desired output.What's wrong in its use?

[Ameer Hamza]

plot() is mainly used to draw lines. plot() can also be used in this case, but the code will be a bit more complicated

x=[1 0;0 1;0 0;1 1];
y=[1;1;0;1];

mask = y==1;
hold on
plot(x(mask,1),x(mask,2), 'r.', 'MarkerSize', 20)
plot(x(~mask,1),x(~mask,2), 'b.', 'MarkerSize', 20)
colormap(cool)

[Saptarshee Sarkar]

Then why didn't it showed the point x(1,0) rather only showed 3 points among the mentioned 4 points.

Basically the above mentioned code is a part of logistic regression where I am treating the equation " y = w0+w1*x1+w2*x2 " as an Or gate to verify my output is same as the ground truth (y) where the two values of x1 and x2 are the columns of the matrix x and y is the ground truth values.

If you want I can show you the code.

[Ameer Hamza]

The plot() command in the code in your question is not written correctly. If you run the plot command in my code, you will get 4 dots

Also, If you want to find w0, w1 and w2 in this equation, following code shows how to do that

x=[1 0;0 1;0 0;1 1];
y=[1;1;0;1];

X = [ones(size(x,1), 1) x];
W = X\y;
w0 = W(1);
w1 = W(2);
w2 = W(3);

[Saptarshee Sarkar]

x=[0 0;0 1;1 0;1 1]; %input for the OR logic gate
y=[1;0;0;0];         %output for the logic gate
alp=1;ep=1.e-3;      % "alp" is the constant "a" in the equation "w=w-a*d(J)/d(w)" and "ep" is upto which error we would be running the function

w=LogisticModel(x,y,alp,ep); % calling the respective function

% here d(J)/d(w) refers partial differentiation of J(cost funtion) with "w" weight
%---------------------------------------------------------------------------------------%

function w= LogisticModel(x,y,alp,ep)
[m,n]=size(x); 
w = rand(n+1,1);  %make initial guess of the w vector

sigmoid = @(z) 1./(1+exp(-z));   %defining the sigmoid function 
 for i=1:m 
     z=[1 x(i,:)]*w;       % optimization function would be of the form "z=w0+w1*x1+w2*x2"
     yh(i,1)=sigmoid(z);   % scaling and reducing the values between  [0,1] where "yh" is in the form of probability & "y" is the ground truth
                           %[1 x] is augmenting x with x0=1 to achieve the multiplication
 end
 
 J(1)=-1*sum(y.*log(yh)+(1.-y).*log(1-yh));   %cost function "J=-(y*ln(yh)+(1-y)*ln(1-yh))
 
 err=1;
 iter=1; %iteration
 
 % d(J)/d(w) = 
 
 
 while(err>ep)
     pred_err=yh-y;
     DJ(1,1)=sum(pred_err)/m;    
     for j=2:n+1
         DJ(j,1)=sum(pred_err.*x(:,j-1))/m;
     end
     
     w=w-alp*DJ;
     for i=1:m
        z=[1 x(i,:)]*w;
        yh(i,1)=sigmoid(z);
     end
     iter=iter+1;
     J(iter)=-1*sum(y.*log(yh)+(1.-y).*log(1-yh));
     err=abs(J(iter)-J(iter-1));
     
    subplot(2,1,1)
    plot(x(:,1),y,'o',x(:,1),yh,'r');
    xlabel('x')
    ylabel('y')
    legend({'Data','Linear Fit'},'Location','NorthWest')
    drawnow;
    
    subplot(2,1,2)
    plot([1:iter],J([1:iter]),'-o');
    xlabel('iterations');
    ylabel('J');
    drawnow;
 end
end

This is the above code for logistic regression and used for representing as an OR Gate

The output I am getting is:

And the output I should get:

[Ameer Hamza]

Can you write the equation in mathematical form? It isn't easy to understand it from the code. What is the equation of the classifying line using logistic regression? What is the optimization function?

[Saptarshee Sarkar]

I have explain the lines of the code by commenting you could refer them.

The optimization ffunction "y=w0+w1*x1+w2*x2"

For the

DJ(1,1)=sum(pred_err)/m;

for j=2:n+1

DJ(j,1)=sum(pred_err.*x(:,j-1))/m;

end

here's the part which would probably explain ,I didn't mebtioned it there because of subscript and superscript.

The red line in the graph is the classiication line which would of the form or near to " x1+x2=1/2 " with assuming the values of w0 = -1 ; w1= 2 ; w3=2 for the case of OR gate.

[Saptarshee Sarkar]

I am also attaching few links below so that you could refer for better understanding:

OR gate

Gradient for logistic regression

Code for the logistic regression OR gate (I have copied the above written code from this video)

I would be very thankful if you kindly go through these and help me out for my issue.