I am trying to work out how to generate confidence ellipses for datasets.
I have tried the following code:
%# generate data
num = 50;
X = [ mvnrnd([0.5 1.5], [0.025 0.03 ; 0.03 0.16], num) ; ...
mvnrnd([1 1], [0.09 -0.01 ; -0.01 0.08], num) ];
G = [1*ones(num,1) ; 2*ones(num,1)];
gscatter(X(:,1), X(:,2), G)
%# indices of points in this group
idx = ( G == k );
%# substract mean
Mu = mean( X(idx,:) );
X0 = bsxfun(@minus, X(idx,:), Mu);
%# eigen decomposition [sorted by eigen values]
[V D] = eig( X0'*X0 ./ (sum(idx)-1) ); %#' cov(X0)
[D order] = sort(diag(D), 'descend');
D = diag(D);
V = V(:, order);
t = linspace(0,2*pi,100);
e = [cos(t) ; sin(t)]; %# unit circle
VV = V*sqrt(D); %# scale eigenvectors
e = bsxfun(@plus, VV*e, Mu'); %#' project circle back to orig space
%# plot cov and major/minor axes
plot(e(1,:), e(2,:), 'Color','k');
%quiver(Mu(1),Mu(2), VV(1,1),VV(2,1), 'Color','k')
%quiver(Mu(1),Mu(2), VV(1,2),VV(2,2), 'Color','k')
However this seems to drastically underestimate the confidence ellipse. I also tried this function I found in the file exchange:
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.
% written by Douglas M. Schwarz
% last modified: 12 June 1998
n = size(xy,1);
mxy = mean(xy);
numPts = 181; % The number of points in the ellipse.
th = linspace(0,2*pi,numPts)';
p = 2; % Dimensionality of the data, 2-D in this case.
k = finv(conf,p,n-p)*p*(n-1)/(n-p);
% Comment out line above and uncomment line below to use ftest toolbox.
% k = fdistinv(p,n-p,1-conf)*p*(n-1)/(n-p);
[pc,score,lat] = princomp(xy);
% Comment out line above and uncomment 3 lines below to use ftest toolbox.
% xyp = (xy - repmat(mxy,n,1))/sqrt(n - 1);
% [u,lat,pc] = svd(xyp,0);
% lat = diag(lat).^2;
ab = diag(sqrt(k*lat));
exy = [cos(th),sin(th)]*ab*pc' + repmat(mxy,numPts,1);
% Add ellipse to current plot
h = line(exy(:,1),exy(:,2),'Clipping','off');
if nargout > 0
hh = h;
However this seems to drastically over estimate the ellipse.
Can anyone help me work out which code is nearer to being correct and how to amend the code?
Thanks in advance
You can think of your watch list as threads that you have bookmarked.
You can add tags, authors, threads, and even search results to your watch list. This way you can easily keep track of topics that you're interested in. To view your watch list, click on the "My Newsreader" link.
To add items to your watch list, click the "add to watch list" link at the bottom of any page.
To add search criteria to your watch list, search for the desired term in the search box. Click on the "Add this search to my watch list" link on the search results page.
You can also add a tag to your watch list by searching for the tag with the directive "tag:tag_name" where tag_name is the name of the tag you would like to watch.
To add an author to your watch list, go to the author's profile page and click on the "Add this author to my watch list" link at the top of the page. You can also add an author to your watch list by going to a thread that the author has posted to and clicking on the "Add this author to my watch list" link. You will be notified whenever the author makes a post.
To add a thread to your watch list, go to the thread page and click the "Add this thread to my watch list" link at the top of the page.
The newsgroups are a worldwide forum that is open to everyone. Newsgroups are used to discuss a huge range of topics, make announcements, and trade files.
Discussions are threaded, or grouped in a way that allows you to read a posted message and all of its replies in chronological order. This makes it easy to follow the thread of the conversation, and to see what’s already been said before you post your own reply or make a new posting.
Newsgroup content is distributed by servers hosted by various organizations on the Internet. Messages are exchanged and managed using open-standard protocols. No single entity “owns” the newsgroups.
There are thousands of newsgroups, each addressing a single topic or area of interest. The MATLAB Central Newsreader posts and displays messages in the comp.soft-sys.matlab newsgroup.
You can use the integrated newsreader at the MATLAB Central website to read and post messages in this newsgroup. MATLAB Central is hosted by MathWorks.
Messages posted through the MATLAB Central Newsreader are seen by everyone using the newsgroups, regardless of how they access the newsgroups. There are several advantages to using MATLAB Central.
Your MATLAB Central account is tied to your MathWorks Account for easy access.
Use the Email Address of Your Choice
The MATLAB Central Newsreader allows you to define an alternative email address as your posting address, avoiding clutter in your primary mailbox and reducing spam.
Most newsgroup spam is filtered out by the MATLAB Central Newsreader.
Messages can be tagged with a relevant label by any signed-in user. Tags can be used as keywords to find particular files of interest, or as a way to categorize your bookmarked postings. You may choose to allow others to view your tags, and you can view or search others’ tags as well as those of the community at large. Tagging provides a way to see both the big trends and the smaller, more obscure ideas and applications.
Setting up watch lists allows you to be notified of updates made to postings selected by author, thread, or any search variable. Your watch list notifications can be sent by email (daily digest or immediate), displayed in My Newsreader, or sent via RSS feed.