how to compute separate line 2 dimensional points

hi all i have set of points and class + -1 i want to calculate the line i want to use 1. direct linear algebra (inverse matrix , cross product) 2. use gradient descent i dont want to use the svm function or quadratic programming

x=[ 1 2 ; 3 3  ; 4 5;         45 17 ; 33 20];
label=[ 1 ;1 ;1;-1 ;-1];
gscatter(x(:,1),x(:,2),label)

so how to calculate the line wx+b , i need w,b

Answer 1

[David Sanchez]

Once you have the plot, go to tools -> Basic fitting

select the data (1 or -1 in your case), linear and click in the bottom arrow to get the values of your parameters. You will see you can save to workspace.

Answer 2

[Michael sch]

but it fits to one of the set of points and not the seperate line !! , also i dont have the process for compute the line

Answer 3

[Zikobrelli]

Given X and Y, this function will give you your 'w' and 'b'

function [a b] = droite_reg(X,Y)

% Linear fitting

% Y = a + bX

n = length (Y);

 sumY = sum(Y);

 sumX = sum(X);

X2 = X.^2;sumX2 = sum(X2);

Y2 = Y.^2; sumY2 = sum(Y2);

XY = X.*Y; sumXY = sum(XY);

%slope estimation

a = (sumXY - ((sumX * sumY)/n))/ (sumX2 - ((sumX^2)/n));

% b estimation

b = (sumY/n)-(a.*(sumX/n));

% r^2

r2 = ((sumXY - ((sumX.*sumY)/n)).^2)/((sumX2-((sumX.^2)/n)).*(sumY2 - ((sumY.^2)/n)));

end

[Zikobrelli]

To get your two sets of data differentiated, you can try something like:

plot(x(label==1,1),x(label==1,2))

[w,b]=droite_reg(x(label==1,1),x(label==1,2))

hold on

plot(x(label==-1,1),x(label==-1,2),'r')

[w1,b1]=droite_reg(x(label==-1,1),x(label==-1,2))

Answer 4

[Michael sch]

it seems you go in the correct answer but stil the line is not between alsow what is theory (article )

x=[ 1 2 ; 3 3  ; 4 5;         45 17 ; 33 20];
label=[ 1 ;1 ;1;-1 ;-1];
gscatter(x(:,1),x(:,2),label)

%w = label'*x;

   [a b] = droite_reg(x(:,1),x(:,2))

   xvec=[-1:0.5:30];
   yvec  = b*xvec+a;
   hold on;plot(xvec,yvec,'k-.');

    xvec=[-1:0.5:30];
   yvec  = a*xvec+b;
   hold on;plot(xvec,yvec,'k-.');

Answer 5

[Michael sch]

 i need to seperate plane like in svm  and not like in the figure 
 http://en.wikipedia.org/wiki/Support_vector_machine

[Zikobrelli]

You might want to look into nnd4pr or perceptron in the matlab help section.

There's a demo abt 2 inout classifiers

[Zikobrelli]

*input

Answer 6

[Michael sch]

as you see i need the black line and not the fit line