Fminsearch for fitting models (unconstrained nonlinear minimization of rmse)

Hi all, I'm trying to use the fminsearch function to fit a double sigmoidal models to my data. And the conditions is minimization of the root mean squared error(RMSE). I have seven parameters. At the moment, I'm using the following code.

load data

%xdata=Limb1_x; % 2424*1 vector
%ydata=Limb1_y; % 2424*1 vector

%type rmseval.mat


fun = @(v)rmseval(v,xdata,ydata);
v0= rand(1,7);
bestv = fminsearch(fun,v0);

Unable to perform assignment because the size of the left side is 1-by-1 and the size of the right side is 1-by-2424.

Error in fminsearch (line 201)
fv(:,1) = funfcn(x,varargin{:});

a1=bestv(1);
a2=bestv(2);
b1=bestv(3);
b2=bestv(4);
c1=bestv(5);
c2=bestv(6);
d=bestv(7);
yfit=c1/(1+exp(-a1-b1*xdata))+c2/(1+exp(-a2-b2*xdata))+d;
figure;
plot(Limb1_x, Limb1_y, '+', 'MarkerSize', 10, 'LineWidth', 2)
hold on
plot(Limb1_x, yfit, '-')

function rmse = rmseval(v,xdata,ydata)
a1=v(1);
a2=v(2);
b1=v(3);
b2=v(4);
c1=v(5);
c2=v(6);
d=v(7);
rmse= sqrt(sum((ydata-(c1/(1+exp(-a1-b1.*xdata))+c2/(1+exp(-a2-b2.*xdata))+d).^2))/numel(xdata));
end

I don't have a good startpunkt. And the error is "Unable to perform assignment because the size of the left side is 1-by-1 and the size of the right sideis 1-by-2424." I'm quite a newbie in optimization. There is something I'm missing? And the data is in attachments.

Thank you in advance

Answer 1

[Matt J]

rmse= sqrt(sum((ydata-(c1./(1+exp(-a1-b1.*xdata))+c2./(1+exp(-a2-b2.*xdata))+d).^2))./numel(xdata));

[Matt J]

I have seven parameters.

That is getting to be a bit much for fminsearch. I would instead use fminspleas from this FEX download

https://www.mathworks.com/matlabcentral/fileexchange/10093-fminspleas

load data

[xdata,is]=sort(xdata);
ydata=ydata(is);

funlist = {  @(p,xdata)1./(1+exp(-p(1)-p(3)*xdata))  ,  @(p,xdata)1./( 1+exp(-p(2)-p(4)*xdata) ) ,1};
p0=[-0.6123  -14.4415    0.5858   22.4340];
[p ,lp]= fminspleas(funlist,p0,xdata,ydata);

a1=p(1);
a2=p(2);
b1=p(3);
b2=p(4);
c1=lp(1);
c2=lp(2);
d=lp(3);

yfit=c1./(1+exp(-a1-b1*xdata))+c2./(1+exp(-a2-b2*xdata))+d;
Limb1_x=xdata;
Limb1_y=ydata;
plot(Limb1_x, Limb1_y, '+', 'MarkerSize', 10, 'LineWidth', 2)
hold on
plot(Limb1_x, yfit, '-')

[Wenquan]

Thank you so much! I have one more question, how is p0 determined?

[Wenquan]

When using the fminsearch, I also don't know how to determine the starting value.

[Matt J]

I used trial and error. One of the advantages of fminspleas, however, if that you only need guesses for four of the parameters a1,b1,a2,b2. So, if you have any prior knowledge that can inform your guess of those, that might make things easier in future curve fittings.

[Wenquan]

Thank you very much! Your answer is very helpful for me!