Self-Organizing Maps, Principal Components and Non-negative ...
Self-Organizing Maps, Principal Components and Non-negative ...
Self-Organizing Maps, Principal Components and Non-negative ...
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Procedure<br />
<strong>Self</strong> <strong>Organizing</strong> <strong>Maps</strong><br />
<strong>Principal</strong> <strong>Components</strong>, Curves <strong>and</strong> Surfaces<br />
<strong>Non</strong>-<strong>negative</strong> Matrix Factorization<br />
<strong>Principal</strong> <strong>Components</strong><br />
<strong>Principal</strong> Curves<br />
Spectral Clustering<br />
Spectral clustering finds the m smallest eigenvectors to the m<br />
smallest eigenvalues of L.<br />
Consider any vector f<br />
f T Lf =<br />
N<br />
i=1<br />
= 1<br />
2<br />
gif 2<br />
i −<br />
N<br />
N<br />
i=1 i ′ = 1<br />
N<br />
N<br />
i=1 i ′ =1<br />
wii ′(fi − f ′<br />
i ) 2<br />
fifi ′wii ′ (11)<br />
(12)<br />
We have a small value of f T Lf if pairs of points with large wii ′<br />
have coordinates fi <strong>and</strong> fi ′ close together.<br />
Karoline Geissler <strong>Self</strong>-<strong>Organizing</strong> <strong>Maps</strong>, <strong>Principal</strong> <strong>Components</strong> <strong>and</strong> <strong>Non</strong>-<strong>negative</strong> M
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