how do i know that data lie in linear subspace or not?
in [Math]
|
Prev: EQUALIZED TO( 555,555,555,554 ^ )+(555,555,555,554)^ =( 576197, 222,222,221)^ Sorry to use new post, some one dumped on the other
Next: 3D Star of David space filler based on truncated tetrahedrons.
From: Yan Tian on 26 Dec 2009 14:36 I have some 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!
From: Virgil on 26 Dec 2009 15:09 In article <4ce788a1-f0e9-48a9-a717-5b5214c8bc29(a)r24g2000yqd.googlegroups.com>, Yan Tian <tianyan1020(a)gmail.com> wrote: > I have some 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! One method: Construct a matrix whose rows are your data points, then use Gauss or Gauss-Jordan row reduction on it. See: http://en.wikipedia.org/wiki/Row_reduction Note, however, that if your data contains even small random errors due to , say, measurement roundoffs, this may make linearly dependent sets of vectors appear independent or vice versa.
From: kevin kitenik on 26 Dec 2009 18:16 thank you a lot for the answer. have a ncie day -- thanks a lot.
From: Robert Israel on 28 Dec 2009 18:09
On Sat, 26 Dec 2009 13:09:54 -0700, Virgil wrote: > In article > <4ce788a1-f0e9-48a9-a717-5b5214c8bc29(a)r24g2000yqd.googlegroups.com>, > Yan Tian <tianyan1020(a)gmail.com> wrote: > >> I have some 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! > > One method: > > Construct a matrix whose rows are your data points, then use Gauss or > Gauss-Jordan row reduction on it. Unless there's something special about the origin, you might want to look for an affine subspace containing the data, not just a linear one. In that case you can start by subtract one data point from the others. Singular value decomposition would probably give you better numerical results. > See: http://en.wikipedia.org/wiki/Row_reduction > > Note, however, that if your data contains even small random errors due > to , say, measurement roundoffs, this may make linearly dependent sets > of vectors appear independent or vice versa. -- Robert Israel israel(a)math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada |