Spectral clustering: Difference between revisions

Revision as of 12:15, 17 April 2014

Revision as of 20:19, 29 April 2014

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Partitioning may be done in various ways, such as by taking the median <math>m</math> of the components in <math>v</math>, and placing all points whose component in <math>v</math> is greater than <math>m</math> in <math>B_1</math>, and the rest in <math>B_2</math>. The algorithm can be used for hierarchical clustering by repeatedly partitioning the subsets in this fashion.

Alternatively to computiongcomputing just one eigenvector, ''k'' [[eigenvector]]s for some ''k'', are computed, and then another algorithm (e.g. [[k-means clustering]]) is used to cluster points by their respective ''k'' components in these eigenvectors.

An efficiency of spectral clustering may be improved if the solve of the corresponding eigenvalue problem is performed in a [[Matrix-free methods|matrix-free fashion]], i.e., without explicitly manipulating or even computing the similarity matrix, as, e.g., in the [[Lanczos algorithm]].