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covariance of weighted multidimensional samples

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PChoppala
PChoppala on 24 Jun 2016
Edited: PChoppala on 24 Jun 2016
I have a multidimensional weighted sample set, e.g.
D=2; % dimension
N=100; % number of samples
x=randn(D,N); % samples
w=ones(1,N)/N; % corresponding weights
I would like to find the weighted covariance of this sample set. To obtain this, I first computed the weighted mean using the formula \mu = \sum_{i=1}^{N} w_{i} x_{i} as
mu=sum(bsxfun(@times,w,x),2);
Then I need to find the covariance according to the formula \Sigma = \sum_{i=1}^{N} w_{i} (x_{i} - \mu)*(x_{i} - \mu)'. My current code is this:
ct=bsxfun(@minus,particles,mu);
P=zeros(Dx,Dx,N);
for n=1:N,
P(:,:,n)=w(n)*(ct(:,n)*ct(:,n)');
end
Sigma=sum(P,3);
What is the computationally best coding procedure to calculate this covariance? Suggestions appreciated, thanks.

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