2D fitting with LASSO?
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I have a problem where I need to fit two-dimensional data. The matrix is of size 10x1000, where the rows correspond to discretely measured time points, and the columns correspond to measured spectra at each of those discrete time points. The model I need to fit the data to in the row dimension is semi-known and given by some physics, it is:
where 
are the amplitudes which I am trying to obtain, and 
are time constants associated with those amplitudes and tt is the discretely measured time points (known values of course). The value of N is not known, I would like it to be as small as possible while adequately describing the data, thus where I came across LASSO which appears to do exactly this. The value ff is a known frequency component. In essence I expect 
to be a vector of size 1000, 
to be of the same size, etc,. The values for 
, 
, etc should also be of the same size. I have one other very important condition which is that within a single row both 
and 
are smoothly varying functions. I believe this is a very strong constraint which will help deal with the fact that the data obviously has noise. What I am not sure is 1) is LASSO the best method to use for this problem, 2) how to do a 2D fit with LASSO where the model is semi-known, and 3) how to impose this constraint into the 2D fit. I will be using MATLAB for the analysis. Does anybody have any ideas to help me with this problem? Thanks very much
are the amplitudes which I am trying to obtain, and are time constants associated with those amplitudes and tt is the discretely measured time points (known values of course). The value of N is not known, I would like it to be as small as possible while adequately describing the data, thus where I came across LASSO which appears to do exactly this. The value ff is a known frequency component. In essence I expect to be a vector of size 1000, to be of the same size, etc,. The values for , , etc should also be of the same size. I have one other very important condition which is that within a single row both and are smoothly varying functions. I believe this is a very strong constraint which will help deal with the fact that the data obviously has noise. What I am not sure is 1) is LASSO the best method to use for this problem, 2) how to do a 2D fit with LASSO where the model is semi-known, and 3) how to impose this constraint into the 2D fit. I will be using MATLAB for the analysis. Does anybody have any ideas to help me with this problem? Thanks very muchAnswers (1)
Kman
on 18 Jan 2019
0 votes
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