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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<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 />
Construction of a principal curve of a distribution<br />
f (λ) = [f1(λ), f2(λ), ..., fp(λ)] ... coordinate function<br />
X T = (X1, ..., Xp)<br />
Consider the following alternating steps<br />
1 ˆ fj(λ) ←− E(Xj | λ(X ) = λ)<br />
2 ˆλf (x) ←− arg minλ x − ˆf (λ)<br />
The first equation fixes λ<br />
The second fixes the curve <strong>and</strong> finds the closest point to each<br />
data point.<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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