Spectral clustering: Difference between revisions

Revision as of 11:58, 3 October 2011

Revision as of 01:35, 4 December 2011

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Given a set of data points A, the [[similarity matrix]] may be defined as a matrix <math>S</math>, where <math>S_{ij}</math> represents a measure of the similarity between points <math>i, j\in A</math>. Spectral clustering techniques make use of the [[Spectrum of a matrix|spectrum]] of the similarity matrix of the data to perform [[dimensionality reduction]] for clustering in fewer dimensions.

One such technique is the '''[[Segmentation_based_object_categorization#Normalized_Cuts|Normalized Cuts algorithm]]''' or ''Shi–Malik algorithm'' introduced by Jianbo Shi and Jitendra Malik,<ref>Jianbo Shi and Jitendra Malik, [http://www.cs.berkeley.edu/~malik/papers/SM-ncut.pdf "Normalized Cuts and Image Segmentation"], IEEE Transactions on PAMI, Vol. 22, No. 8, Aug 2000.</ref> commonly used for [[segmentation (image processing)|image segmentation]]. It partitions points into two sets <math>(S_1,S_2)</math> based on the [[eigenvector]] <math>v</math> corresponding to the second-smallest [[eigenvalue]] of the [[Laplacian matrix]]