Plotting axis of greatest variance

Hi Guys,

I am trying to plot the axis that has the greatest variance ontop of a graph i have previously coded for (eg from figure 1) as a new graph (eg figure 2). How do i do this?

And to plot an axis that is perpendicular to this axis ive just added?

TIA

Answer 1

[William Rose]

I am changing my comment to an answer, which is what i had intended.

Let's start by generating some data.

N=100;
theta=pi/6;
x0=3*randn(1,N)+2;
y0=randn(1,N);
x=cos(theta)*x0-sin(theta)*y0;
y=sin(theta)*x0+cos(theta)*y0;
figure;
subplot(2,1,1), plot(x,y,'rx'); axis equal; grid on; hold on

Now find principal axes and plot them.

[V,D]=eig(cov([x',y']));    %columns of V are directions of principal axes
%they are guaranteed to be perpendcular
m1=V(2,1)/V(1,1);           %slope of axis 1
b1=mean(y)-m1*mean(x);      %intercept of axis 1
m2=V(2,2)/V(1,2);
b2=mean(y)-m2*mean(x);
axisx=[min(x),max(x)];      %x values, for plotting the axes
axis1y=m1*axisx+b1;         %y values of axis 1
axis2y=m2*axisx+b2;
plot(axisx,axis1y,'-r',axisx,axis2y,'-r');
xlim(axisx);ylim([min(y),max(y)]);

Next, plot the data in the new coordinate system defined by the axes shown above.

x1=x-mean(x);
y1=y-mean(y); 
if D(1,1)>D(2,2)    %if column 1 of V is axis of max variation
    theta2=atan(V(2,1)/V(1,1));
else                %else column 2 of V is axis of max variation
    theta2=atan(V(2,2)/V(1,2));
end
x2=cos(theta2)*x1+sin(theta2)*y1;
y2=-sin(theta2)*x1+cos(theta2)*y1;
subplot(2,1,2), plot(x2,y2,'bx');
axis equal; grid on

Good luck.