Eigen vector calculation
- From: "Shailesh Patel" <shaileshrpatel@xxxxxxxxx>
- Date: 3 Jul 2006 02:10:28 -0700
Hi
I have one problem regarding Eigen vector calculation. I want to
split up the covariance matrix by SVD (Singular Value Decomposition)
Let say X- Data Matrix having dimension m * n
m - observations and n - no of variables
if m < n (Observations are less than variables (unknowns)
we carry following step to calculate eigen vector calculation (to
get the uncorrelate direction that describe the data)
1) covariance= (X * X' ) / (m-1) (X-data matrix)
2) [U E V}=svd(covariance)
3) V=X' * V; (These 3 stpes are used to
calculate loading vectors)
Now, I want to apply Generalized Singular Value Decomposition(GSVD)
instead of simple SVD, can you tell me the calculation steps for eigen
vactor calculation if I use GSVD.
Generalized Singular Value Decomposition :
X = A * D * B
such that A' * inv(Gr) * A = I (Identity matrix)
B' * inv(Gr) * B = I (Identity matrix)
D : is eigen value matrix
Thanking you
Shailesh Patel
.
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