SVD example
This exercise will involve the vsp demo. Make sure you have all the
codes to run it.
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To get started play with the solutions as a function of the number
of singular values, starting with 1, 2, 3, ... What do you observe?
Do you see some trend in the shape of the solution and the data fit
as you increase the number of singular values used?
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Plot some of the eigenvectors, both the U and the V. What trends to
you see in the shapes of these vectors? Does this correspond to you
experience in the fisrt part?
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Plot the weights ("factor" in the scilab code). What does is mean for
a model eigenvector to have a small (large) weight?
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Verify that the V and U vectors are orthonormal.
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Is there a data null space? Is there a model null space?
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Is it possible to fit the data exactly? Verify your conjecture by
using 100 singular values.