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Why Is SVM Effective on High Dimensional Data?

• The complexity of trained classifier is characterized by the # of support vectors rather than the dimensionality of the data
• The support vectors are the essential or critical training examples —they lie closest to the decision boundary (MMH)
• If all other training examples are removed and the training is repeated, the same separating hyperplane would be found
• The number of support vectors found can be used to compute an (upper) bound on the expected error rate of the SVM classifier, which is independent of the data dimensionality
• Thus, an SVM with a small number of support vectors can have good generalization, even when the dimensionality of the data is high