Self-Organizing Maps, Principal Components and Non-negative ...
Self-Organizing Maps, Principal Components and Non-negative ... Self-Organizing Maps, Principal Components and Non-negative ...
Self Organizing Maps Principal Components, Curves and Surfaces Non-negative Matrix Factorization Principal Points Set of k prototypes. Principal Components Principal Curves Spectral Clustering For each point x in the support of a distribution the closest prototype. (responsible prototype) The set of k points that minimize the exspected distance from X to its prototype are called the principal points. k = 1...the mean vector (circular normal distribution) k = ∞... principal curves Karoline Geissler Self-Organizing Maps, Principal Components and Non-negative M
Self Organizing Maps Principal Components, Curves and Surfaces Non-negative Matrix Factorization Principal Components Principal Curves Spectral Clustering Construction of a principal curve of a distribution f (λ) = [f1(λ), f2(λ), ..., fp(λ)] ... coordinate function X T = (X1, ..., Xp) Consider the following alternating steps 1 ˆ fj(λ) ←− E(Xj | λ(X ) = λ) 2 ˆλf (x) ←− arg minλ x − ˆf (λ) The first equation fixes λ The second fixes the curve and finds the closest point to each data point. Karoline Geissler Self-Organizing Maps, Principal Components and Non-negative M
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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> Points<br />
Set of k prototypes.<br />
<strong>Principal</strong> <strong>Components</strong><br />
<strong>Principal</strong> Curves<br />
Spectral Clustering<br />
For each point x in the support of a distribution the closest<br />
prototype. (responsible prototype)<br />
The set of k points that minimize the exspected distance from<br />
X to its prototype are called the principal points.<br />
k = 1...the mean vector (circular normal distribution)<br />
k = ∞... principal curves<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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