Self-Organizing Maps, Principal Components and Non-negative ...

Self-Organizing Maps, Principal Components and Non-negative ... Self-Organizing Maps, Principal Components and Non-negative ...

statistik.tuwien.ac.at
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05.04.2013 Views

Self Organizing Maps Principal Components, Curves and Surfaces Non-negative Matrix Factorization U ... a N × p orthogonal matrix columns uj ... left singular vectors V ... p × p orthogonal matrix columns vj... right singular vectors D... diagonal matrix p × p matrix d1 ≥ d2 ≥ ... ≥ 0... singular values Principal Components Principal Curves Spectral Clustering columns of UD... principal components of X Karoline Geissler Self-Organizing Maps, Principal Components and Non-negative M

Self Organizing Maps Principal Components, Curves and Surfaces Non-negative Matrix Factorization Handwritten Digits sample of 130 handwritten 3’s Principal Components Principal Curves Spectral Clustering We consider these images as points xi in R 256 and compute their principal components via the SVD. Karoline Geissler Self-Organizing Maps, Principal Components and Non-negative M

<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 />

H<strong>and</strong>written Digits<br />

sample of 130 h<strong>and</strong>written 3’s<br />

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

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

Spectral Clustering<br />

We consider these images as points xi in R 256 <strong>and</strong> compute<br />

their principal components via the SVD.<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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