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B.1 Power method with deflation
The power method is a common method to extract the eigenvector with the largest eigenvalue (Diamantaras and Kung, 1996). Starting with a random vector
, the principal eigenvector of a matrix
is computed by iterating:
max(![$ \bf K$](img185.gif)
) is the component of the vector
![$ \bf K$](img185.gif)
with the largest absolute value (some variants of the power method use
|
| instead).
This iteration converges to the largest eigenvector with the eigenvalue
= |max(![$ \bf K$](img185.gif)
)|. Further eigenvectors are obtained using deflation. After the eigenvector
(number i, ordered by the size of the corresponding eigenvalue) is computed, a new matrix
is obtained from the previous one
by iterating
where
is the eigenvalue corresponding to
.
Next: B.2 Kernel PCA speed-up
Up: B. Algorithms
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Heiko Hoffmann
2005-03-22