smoothing with Gaussian Kernel for loop problem

im having a probelm with smoothing the data "ys" using gaussian kernel function everytime i run the for loop i recieve uhat = ys and kerf = 0 0 0 0 0 ... anyone can help me?

ns =length(ys);
nv =length(tv);
lambda = 0.05;
tv = (1:1:1000)';
for i = 1 : ns
    k=(tv-tv(i));
    kerf=exp(-k.*k/2*(lambda^2))/(sqrt(2*pi)*lambda);
    uhat(i)=sum(kerf.*ys(i))/sum(kerf);
end

Answer 1

[Mathieu NOE]

hello

try this

lambda = 0.05;
tv = (1:1:1000)';
nv =length(tv);

ys = sin(4*pi*tv./max(tv))+0.25*rand(nv,1);% dummy data

for i = 1 : nv
    k=(tv-tv(i));
    kerf=exp(-k.*k/2*(lambda^2))/(sqrt(2*pi)*lambda);
    uhat(i)=sum(kerf(:).*ys(:))/sum(kerf);
end

plot(tv,ys,tv,uhat);

[KHOULOUD DABOUSSI]

hello,i receive this error message "Arrays have incompatible sizes for this operation.",if you want this is the data im working on it and tv = (1:1:ts(end))';

[Mathieu NOE]

hello again

try this code :

load('test_b.mat')

lambda = cv;

for i = 1 : numel(ts)
    k=(ts-ts(i));
    kerf=exp(-k.*k/2*(lambda^2))/(sqrt(2*pi)*lambda);
    uhat(i)=sum(kerf(:).*ys(:))/sum(kerf);
end

plot(ts,ys,ts,uhat);

[Mathieu NOE]

FYI, I made a comparison with matlab smoothdata function

with a gaussian window (length = 10 samples) you get pretty much the same result (the two traces are quite perfectly overlaid)

load('test_b.mat')

lambda = cv;

for i = 1 : numel(ts)
    k=(ts-ts(i));
    kerf=exp(-k.*k/2*(lambda^2))/(sqrt(2*pi)*lambda);
    uhat(i)=sum(kerf(:).*ys(:))/sum(kerf);
end

% comparison with smoothdata function
ysm = smoothdata(ys,'gaussian',10);

plot(ts,ys,ts,uhat,ts,ysm);
legend('raw','exp smoothing','gaussian smoothing');

[Mathieu NOE]

well, this is no surprise as both codes implement a gausian window !! :)

[KHOULOUD DABOUSSI]

hi,thank you for your help!

[Mathieu NOE]

as always, my pleasure !

[KHOULOUD DABOUSSI]

by chance,do you have any idea how to select the optimal bandwidth (lambda)? not using ksdensity?

[Mathieu NOE]

hello again

well, statistics are not my field of expertise

there are some publications that describe some methods for optimal tuning of lambda

Kernel density estimation - Wikipedia

but then i's up to you to code that as a matlab function (would basically be your own version of ksdensity)