integer parameter in lsqcurvefit
11 次查看(过去 30 天)
显示 更早的评论
Hi, I am trying perhaps something foolish but let me pose the question anyway. I am trying to fit a data whose model is an unknown sum of gaussians. I would like to try starting with one Gaussian term and increase the number of terms up until lsqcurvefit provides the best fit i.e., let lsqcurvefit decide for me the number of terms to be used and then let it fit its parameters too.
I do the following:
p0=[n zeros(1,100)]
G=lsqcurvefit(@FUN,p0,x,y)
function FUN(p0,x)
for i=1:round(p0(1))
build the expression f=[f 'f1(i)+f2(i)...']
eval(string expression f)
return
Note that I have to provide some large number of zero initial parmeters even though number of parameters may be much small i.e., 20 or so (3 parameters per Gaussian term for say 7 Gaussian terms). I realize I cannot vary the number of initial parameters when it is lsqcurvefit which decides that. So I am helpless here..but it works so far.
I expect the lsqcurvefit to search for most effective 'n' i.e., number of Gassian terms which describe my data and then fit it to get the 20 parameters even though their start value is initialized to zero.
However, I see that 'n' always remains at 1 or whatever lowerbound I give to that parameter. I realized that lsqcurvefit may not be searching the integer parameter space. And moreover not sure how xtol would now behave. I am quite perplexed.
I could try comparing residual after each term and decide with my own logic to arrive at the number of terms rather than let lsqcurvefit do it for me. But I was looking at easier route and moreover I wasn't sure if my brute force idea is good or efficient.
Any suggestions here would be welcome, Thank you
0 个评论
采纳的回答
Matt J
2013-1-13
编辑:Matt J
2013-1-13
Only solvers in the Global Optimization Toolbox have discrete parameter estimation capabilities.
Why not express FUN in terms of a fixed n and repeat the estimation, i.e., the calls to lsqcurvefit, within a loop over n until the estimate satisfies a performance criterion that you like?
3 个评论
Matt J
2013-1-13
编辑:Matt J
2013-1-13
Therefore, why burden the algorithm with so many terms when there may not be so many for certain experiments.
I still don't have a clear picturea of what other parameters, if any, there are in your system. However, if the Gaussians are all of the same known width, you may as well view ydata as the output of a Gaussian filter. The inverse filter can be implemented in closed form, with something more efficient than lsqcurvefit.
If nothing else, this would at least give you an approximate initial solution, which would help you decide which Gaussians make an important contribution and which can be discarded. It would also give you an initial guess to use in LSQCURVEFIT.
更多回答(0 个)
另请参阅
类别
在 Help Center 和 File Exchange 中查找有关 Least Squares 的更多信息
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!