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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> <strong>Components</strong><br />

<strong>Principal</strong> Curves<br />

Spectral Clustering<br />

provide a sequence of best linear approximations to the given<br />

data in R p , of all ranks q ≤ p<br />

observations x1, ..., xN <strong>and</strong> rank - q linear model<br />

µ ... location vector in R p<br />

f (λ) = µ + Vqλ (3)<br />

Vq ... p × q matrix with q orthogonal unit vectors as columns<br />

λ ... q vector of parameters<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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