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Conference rusure::math

Title:	Mathematics at DEC

Moderator:	RUSURE::EDP

Created:	Mon Feb 03 1986
Last Modified:	Fri Jun 06 1997
Last Successful Update:	Fri Jun 06 1997
Number of topics:	2083
Total number of notes:	14613

1693.0. "Code for Karhunen-Loeve Transform?" by SDOGUS::DRAKE (Dave (Diskcrash) Drake DTN 534-2660) Mon Nov 09 1992 22:34

    Does anyone have Fortran or C code to perform a 2 dimensional
    Karhunen-Loeve (AKA Hotelling , AKA eigenvector) transform ?
    
    The concept is to obtain the eigenvectors of an image covariance
    matrix. This competes with the Fourier Transform well, but is highly
    compute intensive. As I understand it, it doesn't do well on vector
    machines and requires a FAST scalar processor to run it well.
    (It might make a darned excellent showcase benchmark for Alpha AXP.)
    
    I might be able to code one up but I figured it would probably stink.
    So any helpful advice...?  TNX D^2

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1693.1 3D::ROTH Geometry is the real life! Tue Nov 10 1992 12:32 11

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1693.1		3D::ROTH	Geometry is the real life!	`Tue Nov 10 1992 12:32`	11
	You could probably use an SVD routine either from LINPACK or even from Numerical Recipes since this is one of the ways for obtaining principal components (or eigenvectors of covariance matrices, which is what the KL transform basically does.) The SVD has been used for image processing in its own right as well. I've seen suggestions where the singular values are used to give a weighted sum of the outer products of the columns of the left and right basis matrices in the SVD. - Jim

   You could probably use an SVD routine either from LINPACK or
   even from Numerical Recipes since this is one of the ways for
   obtaining principal components (or eigenvectors of covariance matrices,
   which is what the KL transform basically does.)

   The SVD has been used for image processing in its own right as well.
   I've seen suggestions where the singular values are used to give a
   weighted sum of the outer products of the columns of the left and
   right basis matrices in the SVD.

   - Jim