PCA for confidence ellipses

Question

david nickerson 2011-12-19

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https://ww2.mathworks.cn/matlabcentral/answers/24312-pca-for-confidence-ellipses

回答： Mohammad Abdolrahmani 2017-6-8

        I have a cloud of two dimensional data (catesian or polar coordinates, don't mind which) and want to plot a confidence ellipse based on a principle components analysis. i have some code to do this (see below), but i also want to get out all the information i can about the orientation of the elipses/ relative sizes of the principle axes. any explanation would be very helpful, as part of this code was given to me and i don't really understand it, though i have done my best to comment it appropriately.
    function hh = confellipse2(xy,conf)
  %CONFELLIPSE2 Draws a confidence ellipse.
  % CONFELLIPSE2(XY,CONF) draws a confidence ellipse on the current axes
  % which is calculated from the n-by-2 matrix XY and encloses the
  % fraction CONF (e.g., 0.95 for a 95% confidence ellipse).
  % H = CONFELLIPSE2(...) returns a handle to the line.
n = size(xy,1);
mxy = mean(xy);
numPts = 200; % The number of points in the ellipse.
th = linspace(0,2*pi,numPts)';
%dimensionality of the data
p = 2; 
%convert confidence rating (eg 0.95) into z score - relative to size of
%sample(n) and the dimensionality of the data, n-p is therefore the degrees
%of freedom.
k = finv(conf,p,n-p)*p*(n-1)/(n-p);
% principle components analysis, lat gives eigenvalues
[pc,score,lat] = princomp(xy);
ab = diag(sqrt(k*lat));
exy = [cos(th),sin(th)]*ab*pc' + repmat(mxy,numPts,1);
% Add ellipse to current plot
%plot(x,y)
hold on
h = line(exy(:,1),exy(:,2),'Clipping','off');
if nargout > 0
    hh = h;
end

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bym 2011-12-20

I would say, if you don't understand it - don't use it

david nickerson 2011-12-20

ok, in that case proecsm could you please suggest an alternative method? how would you go about solving the problem? any help would be much appreciated.

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