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Linear SVM

Linear SVM. From perceptron to kernel methods. Following Scholkopf, see SVM site. Course website: http://horn.tau.ac.il/course06.html. Support Vector Clustering. Given points x in data space, define images in Hilbert space.

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Linear SVM

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  1. Linear SVM From perceptron to kernel methods Following Scholkopf, see SVM site Course website: http://horn.tau.ac.il/course06.html

  2. Support Vector Clustering Given points x in data space, define images in Hilbert space. Require all images to be enclosed by a minimal sphere in Hilbert space. Reflection of this sphere in data space defines cluster boundaries. Two parameters: width of Gaussian kernel and fraction of outliers Ben-Hur, Horn, Siegelmann & Vapnik. JMLR 2 (2001) 125-127

  3. Variation of q allows for clustering solutions on various scales q=1, 20, 24, 48

  4. Example that allows for SVclustering only in presence of outliers. Procedure: limit β <C=1/pN, where p=fraction of assumed outliers in the data. q=3.5 p=0 q=1 p=0.3

  5. Similarity to scale space approach for high values of q and p. Probability distribution obtained from R(x). q=4.8 p=0.7

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