locally weighted least square regresion

Question

Fahime Sokhangou 2022-8-3

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https://ww2.mathworks.cn/matlabcentral/answers/1773015-locally-weighted-least-square-regresion

编辑： Fahime Sokhangou 2022-8-3

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

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Answer 1

KSSV 2022-8-3

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https://ww2.mathworks.cn/matlabcentral/answers/1773015-locally-weighted-least-square-regresion#answer_1020240

在 MATLAB Online 中打开

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')

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KSSV 2022-8-3

在 MATLAB Online 中打开

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 2022-8-3

编辑：Fahime Sokhangou 2022-8-3

Screenshot 2022-08-03 091505.png

@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

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