locally weighted least square regresion

Dear all

I have a curve that I would like to apply locally weighted polynominal regresion on them. I do not how how define the span and the weight for this type of regresion.

Thanks for your help in advance

Answer 1

[KSSV]

t = linspace(0,2*pi) ;
y = sin(t) ;
p = polyfit(t,y,3) ;
xi = linspace(t(1),t(end)) ;
yi = polyval(p,xi) ;
plot(t,y,'r',xi,yi,'.b')

[Fahime Sokhangou]

@KSSV thanks but this is not weighted. I am searching for doing weighted and also implement of span.

[KSSV]

Least square regression:

A*x = b ;   % A is m*n matrix, b is column matrix m*1 
x = A\b ;   % solve for unknow x 

Weighted least square regression:

W = diag(W);  % where W is column matrix of weights 
x = (W*A)\(w.*y);

[Fahime Sokhangou]

@KSSV thank you so much. so you mean that if I have curve with 68 points and I want to do local regresion smoothing with polynominal for this curve, I should define the weight myself and put them in the matrix. But in the paper that I am following, it is written 10 persent of data points and I do not know how to consider this span?

I do not know how to define the span...

also they used following weight function.

should I have (10%*68 points=7 weights) for each point?

I found the following link very helpful.

https://www.mathworks.com/matlabcentral/fileexchange/55407-loess-regression-smoothing?s_tid=srchtitle

Thanks in advance