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| Gary Tedeschi
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10-27-2004 09:17 PM ET (US)
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If you are willing, could you go over the concept of a convergence factor and how they are obtained from a given algorithm? For example, for the power method, it is said that the algorithm converges at a linear rate with a convergence factor of abs(lambda_1/lambda_2).
Thanks.
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| Louka Dlagnekov
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10-28-2004 01:40 AM ET (US)
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Sanjeev, do you know whether MATLAB uses any of these methods?
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| Rasit Topaloglu
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10-28-2004 03:18 AM ET (US)
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Edited by author 10-28-2004 03:19 AM
The discussion on Krylow subspaces and projection methods makes me wonder the relationship of Krylo subspace and principal component analysis. As the paper says, successive vectors produced by the power method contains valuable information on directions corresponding to the one with the largest magnitude. Similarly, at each step, principal components will be evolving in a structured manner, but how? I think there must have been some work on this relationship.
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| Sanjeev Kumar
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10-28-2004 03:25 AM ET (US)
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Edited by author 10-28-2004 03:41 AM
Louka, Matlab's function eigs (sparse equivalent of eig) uses implicitly restarted arnoldi iteration.
Rasit, since PCA involves eigenvectors corresponding to some largest eigenvalues of the covariance matrix, so there is direct relation with what is happening here.
Gary, here convergence refers to how fast the relative error in eigenvector is decreasing with number of iterations.
More on these things tomorrow.
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| Robin Hewitt
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10-28-2004 10:51 AM ET (US)
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Matlab also offers svds(), which you can use to get the top k eigenvectors. Does that also use implicitly restarted arnoldi iteration?
On a practical note, the author mentions ARPACK, and I see there's an ARPACK++ available for interfacing C++ programs. Well, it's a beta version....
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| Steve Scher
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10-28-2004 12:44 PM ET (US)
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SVDS() calls EIGS() to do its work.
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| Stephen Krotosky
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10-28-2004 02:17 PM ET (US)
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Yeah, I also thought about the relationship between this method and PCA. Has this method been as widely used in computer vision. What sort of applications has it been tried on and does it give better or faster results than PCA or other methods?
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| Hamed Masnadi-Shirazi
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10-28-2004 04:32 PM ET (US)
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an example of a particular vision problem that would greatly benefit from this method would be nice (other than just mentioning SVD )
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07-20-2006 01:56 PM ET (US)
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Deleted by topic administrator 07-21-2006 09:00 AM
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| John Doe
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11-07-2007 07:50 AM ET (US)
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3da0d2058c966a741cc87940b2fb3365
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| Brin
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12-01-2007 11:43 PM ET (US)
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Hello, nice site :)
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02-23-2008 12:11 AM ET (US)
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Deleted by topic administrator 02-25-2008 11:10 AM
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| nokia
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05-05-2008 01:22 AM ET (US)
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Messages 14-16 deleted by topic administrator between 05-16-2008 08:17 AM and 05-17-2008 10:12 AM |
