# gaussian kernel smoothing, how to optimize parameter sigma?

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cyril on 5 May 2014
Answered: Junpeng Lao on 9 Oct 2015
Hi, my question is how to find an optimal standard deviation for the gaussian kernel filter smoothing?
too large, we are losing amplitude, too small, it can be still noisy
Are there standard methods to optimize this choice? on which metrics?
x= (0:0.1:7)';
y = sin(x);
y_=y + 0.3*randn(size(y)); %noisy signal
y__ = zeros(length(x), 3); % reconstructs
for i=1:length(x)
%test different gaussian sigmas
k = exp( -(x-repmat(x(i),length(x),1)).^2 / (2*.2^2) ) ;
y__(i,1) = k'*y_ / sum(k);
k = exp( -(x-repmat(x(i),length(x),1)).^2 / (2*.5^2) ) ;
y__(i,2) = k'*y_ / sum(k);
k = exp( -(x-repmat(x(i),length(x),1)).^2 / (2*.8^2) ) ;
y__(i,3) = k'*y_ / sum(k);
end
plot([y y_ y__])

Junpeng Lao on 9 Oct 2015
Hey Cyril, I come across this paper might be related to your question: http://www.princeton.edu/~samory/Papers/adaptiveKR.pdf

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