R help - Jul 2006 - least square fit with non-negativity constraints for absorption spectra fitting

I would really appreciate it if someone can give suggestions on how to
do spectra fitting in R using ordinary least square fitting and
non-negativity constraints. The lm() function works well for ordinary
least square fitting, but how to specify non-negativity constraints? It
wouldn't make sense if the fitting coefficients coming out as negative
in absorption spectra deconvolution.

Thanks. 

Xiuli

Xu, Xiuli (NIH/NHLBI) [E] <xux3 <at> nhlbi.nih.gov> writes:
> 
> I would really appreciate it if someone can give suggestions on how to
> do spectra fitting in R using ordinary least square fitting and
> non-negativity constraints. The lm() function works well for ordinary
> least square fitting, but how to specify non-negativity constraints? It
> wouldn't make sense if the fitting coefficients coming out as negative
> in absorption spectra deconvolution.
I don't see much reasons to use lm() to fit a spectrum, but if you want to
do
that,  negative coefficients simply mean a shift by pi, sothe sign can be
discarded for most practical purposed. 

But better look at one of the specialized packages like spectrino.

Dieter

Xu, Xiuli (NIH/NHLBI) [E] wrote:
> I would really appreciate it if someone can give suggestions on how to
> do spectra fitting in R using ordinary least square fitting and
> non-negativity constraints. The lm() function works well for ordinary
> least square fitting, but how to specify non-negativity constraints? It
> wouldn't make sense if the fitting coefficients coming out as negative
> in absorption spectra deconvolution.
> 
> Thanks. 
> 
> Xiuli
> 
I'm not sure, but would presume that constraints could not be imposed on 
a linear least squares fit. maybe someone can correct me.

if you move to `nls', i.e. non-linear least squares fitting, you should 
be able to transform your model function. say, you want some parameter 
`a' to stay positive. then you could e.g. substitute

`a = exp(b)' in the model function and fit `b' without constraints in 
the "new" model and calculate `a' afterwards (which obviously is 
guaranteed now to be positive). note that error estimates would than 
have to be computed by gaussian error propagation from `b' to `a'.


joerg

Were you doing blind deconvolution or the spectrum basis are assummed to be
known?

As for blind deconvolution, alternatively you might consider alternating
least square, non-negative matrix factorization, or independent component
analysis + alternating least square as the post-processing.

yfl

On 7/11/06, Xu, Xiuli (NIH/NHLBI) [E] <xux3@nhlbi.nih.gov>
wrote:
>
> I would really appreciate it if someone can give suggestions on how to
> do spectra fitting in R using ordinary least square fitting and
> non-negativity constraints. The lm() function works well for ordinary
> least square fitting, but how to specify non-negativity constraints? It
> wouldn't make sense if the fitting coefficients coming out as negative
> in absorption spectra deconvolution.
>
> Thanks.
>
> Xiuli
>
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