Re: SVD when calculated for a corpus of similar category?
- From: spellucci@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (Peter Spellucci)
- Date: Wed, 15 Nov 2006 11:05:52 +0000 (UTC)
In article <1163579376.066684.82740@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"paluri" <santoshpaluri@xxxxxxxxx> writes:
Hello everybody,
I have a doubt regarding SVD. Suppose i compute SVD for a huge corpus
of similar category, and i have the decomposition as [USV^T] . Are the
singular values in the diagonal matrix S arranged in descending order
along the diagonal will be very near to each other? i mean , is the
numerical difference between one singular value and the next in the
diagonal will be negligible?. I would be thankful for the response...
???????? what please is a "huge corpus of similar category"?
you mean a set of nearby matrices ???
then the answer is yes:
let sigma(A,i) denote the singualr values of A in descending order
and sigma(B,i) those of B. Then
|sigma(A,i)-sigma(B,i)|<= ||A-B|| for all i
||A-B||=sigma(A-B,1)
hence if A is near B, then all the singular values of A and B can be paired
corresponding to this order with this universal error bound
(follows from the courant-fischer-minimax characterization of eigenvalues)
hth
peter
.
- Follow-Ups:
- References:
- Prev by Date: Re: how to avoid cases like "0/inf" or "inf/0"
- Next by Date: Re: significane of eigenvalues and singular values
- Previous by thread: SVD when calculated for a corpus of similar category?
- Next by thread: Re: SVD when calculated for a corpus of similar category?
- Index(es):
Relevant Pages
|
Loading
