How to weighting to the number of observations in a regularized nonlinear least squares?

[hwdo...@gmail.com]

I want to solve a PCA based fitting problem and want to regularize the PCA parameters. 

I weighted the two terms for data fitting and parameter regularization. 

 Suppose the number of observations is m,the number of theta is n.  I use w1 and w2 to weight the two terms. the formula is:

     w1/(2m) *sum_i(||f(xi,yi, theta||^2) + w2/n *||theta||^2  

 Where these {(xi,yi)} are observations and theta are shape parameters

The weight w1 and w2 is fixed, so  we should divided by m. 

I chosed  w1 and w2 for m=50 by experiment, when I add more observations (some may be noisy),that is become larger, the result become bad and resulted shape is the mean shape although the theta are not zeros.

What's the problem? 

Another question:

I also used the  bounds constrained non-linear least squares without parameter regularization,it seems works. But it is very very slow compared to matlab's lsqlin.  Why ceres -solver so slow than matlab (matlab is 30X faster than ceres-solver)? 

[hwdo...@gmail.com]

The weight for data fitting is coded as :

         residuals[0] *= shape_weight;

residuals[1] *= shape_weight;

and the weight for regularization is coded as :

     residual[i] = prior_weight * x[i];

Where the  shape_weight = w1/(2m) and prior_weight = w2/n

[Sameer Agarwal]

you need to take the square root of the weights for one.

secondly can you share the execution log and the output of Summary::FullReport() ?

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[hwdo...@gmail.com]

Thank you. What do meannig by "...weights for one"?

Do you mean the code for weights should be:

      shape_weight = sqrt( w1/(2m) ) and prior_weight = sqrt( w2/n)

 or  

      shape_weight = sqrt( w1) /(2m)  and prior_weight = sqrt( w2) /n

Which should I use?

The the execution log is too log in cmd windows, should I log to a file ?

I think I should try  the square root of the weights?

[hwdo...@gmail.com]

I tried both ways but failed too. Do ceres-solver divided the number of observation internally?  

I want w1 and w2 independent of the  the number of observation.

[Sameer Agarwal]

no ceres does not do any sort of division. it takes the problem as you give it.

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[hwdo...@gmail.com]

Thank you. It seems it sometimes hard to converges ant the time is very very long.

[Sameer Agarwal]

can you share the output of Summary::FullReport ?

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