Fitting to 4D data

The fit() function allows fitting a surface to 3D data, where regularly spaced x,y data values specify a "grid" location and the z value specifies a surface "height". The fitted surface can be expressed as a polynomial of up to degree 5 in x and y.

Is there a means of fitting a model (polynomial or otherwise) to 4D data? In this case, the x,y,z data values specify a location (regularly spaced, within a unit cube for example), and w specifies a value at that location. Such data expresses a 3D "field" rather than a surface.

Thanks, mitch

Answer 1

[Matt J]

Yes, you can use lsqcurvefit.

[Mitch]

Thanks Matt!

Looking at the documentation for lsqcurvefit(), I see only 1D curve fitting examples. Do you know of any multi-dimensional fitting examples I can look at? I'm new to Matlab, and it's hard to know exactly how to write the necessary commands without a simple/clear example.

Thanks, mitch

[Matt J]

Do you know of any multi-dimensional fitting examples I can look at?

Here's an example I just made up. The unknown parameter vector to be recovered is w:

xyz=rand(100,3);  %fake x,y,z data
w=[1,2,3];        %ground truth parameters
F=vecnorm(xyz.*w,2,2); %fake dependent data
 F=F+randn(size(F))*0.05; %add noise

wfit=lsqcurvefit(@modelFcn,[1,1,1], xyz,F)

Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.

wfit = 1×3

1.0162 1.9904 2.9886

function Fpred=modelFcn(w,xyz)

    Fpred=vecnorm(xyz.*w,2,2);

end

Anyway, the point is that lsqcurvefit doesn't care about the dimensions of the data xyz and F. It only cares that your modelFcn returns a prediction Fpred of F as an array the same size as F.

[Mitch]

Okay, terrific Matt - thanks for that example. I think that will get me started on the right path.

Thanks again, mitch