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how do i know that data lie in linear subspace or not?
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Yan Tian
Dec 26, 2009, 2:38:16 PM12/26/09
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I have some high dimension data, and I want to reduce the dimension at
first, if the data lie in linear subspace, I can use PCA, otherwise I
can use manifold or something esle, but how do i know that data lie in
linear subspace or not? does anyone know it? Thank you!
first, if the data lie in linear subspace, I can use PCA, otherwise I
can use manifold or something esle, but how do i know that data lie in
linear subspace or not? does anyone know it? Thank you!
Eb Oesch
Dec 27, 2009, 1:55:20 PM12/27/09
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PCA will tell you the size of the smallest linear subspace that
contains your data. For instance, if the fourth largest PCA component
is so small that it could be written off as measurement or roundoff
error, then that is consistent with the notion that your data belong
to a 3-dimensional linear subspace. On the other hand, if there are 7
significant PCA components, but you know (somehow) that your data lie
on the surface of a 3-dimensional manifold, then clearly that manifold
is not entirely linear.
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