Singular Value Decomposition of a Large XYZ file

4 views (last 30 days)
Hi everyone, I need to perform Singular Value Decomposition on a XYZ file (surface scan file with 3 columns and millions of row) to simplify the surface. In the papers I have checked in the literature, they present a 2D picture (x-z base) colouring with amplitude (y-height), and state that the fluctuating surface elevation of the surface y(x,z) should be decomposed. Any idea how to turn very narrow randomly lined xyz values into a matrix that we can implement SVD? Cheers.

Accepted Answer

Christine Tobler
Christine Tobler on 14 Aug 2018
First thing that occurs to me would be to interpolate the xyz data to lie on a rectangular grid in the x-z plane, and to then apply SVD to the resulting matrix (millions of rows should translate to a number of rows and columns in the thousands?).
Here is a doc example for how to interpolate xyz-data on a grid.
  1 Comment
Oguzhan M
Oguzhan M on 16 Aug 2018
Thanks for the prompt response. When I interpolate xyz data, I get 3 matrices as expected. Should I apply SVD to x and z matrices separately to reduce number of points, if yes, how can I re-combine new x and z matrices with y matrix (unchanged) to achieve the complete simplified surface? Thanks, Oguzhan.

Sign in to comment.

More Answers (1)

Christine Tobler
Christine Tobler on 16 Aug 2018
The way I thought of it was to use x and z as the 2d grid on which to interpolate, and y as the function value. Something like this:
x = randn(10, 1); y = randn(10, 1); z = randn(10, 1);
[xi,zi] = meshgrid(linspace(-1, 1), linspace(-1, 1));
yi = griddata(x,z,y,xi,zi); % yi is a matrix with the values of y interpolated on the grid (xi, zi)
In this case, you would do SVD of the yi data, I think?
  1 Comment
Oguzhan M
Oguzhan M on 21 Aug 2018
Sorry for the late response. You were right! SVD should be applied on yi then the final matrix can be re-composed using orthogonal matrices and inverse of the diagonal matrix. I'm now facing "out of memory error", which does not make any sense to me as there is a lot more RAM on my PC than matlab requires. .Anyways, I'll raise it on another topic. Thanks, Oguzhan.

Sign in to comment.


Find more on Elementary Polygons in Help Center and File Exchange

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!