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DATA MINING from data to information Ronald Westra Dep. Mathematics Maastricht University 7 December, 2006 SUPPORT VECTOR MACHINES Theory Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines The VC dimension (Vapnik Chervonenkis dimension) is a measure of the capacity of a statistical classification algorithm. Consider a classification model f with some parameter vector θ. The model f can shatter a set of data points if, for all assignments of labels to those data points, there exists a θ such that the model f makes no errors when evaluating that set of data points. The VC dimension of a model f is the maximum h such that some data point set of cardinality h can be shattered by f. Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines Support Vector Machines The End