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Support Vector Machines (SVM) (Linear machine (construct a hyperplane such…
Support Vector Machines (SVM)
Linear machine
construct a hyperplane such that the
margin of separation
between +ve and -ve examples is maximized
Optimal hyperplane
Optimum weight vector
Optimum bias
approximate implementation of the
method of structural risk minimization
good generalization performance on pattern classification problems
No
problem-domain knowledge
Support vectors
small subset of the training data
points that lie closest to the decision surface (most difficult to classify)
Inner kernel product
between a
support vector
and the vector drawn from the input space
Types of learning machines
Polynomial
Radial basis
2 layer perceptron
Constrained optimization problem
Primal problem
Convex cost function
Linear constraints in W
Dual problem
Lagrange multipliers
Method of
Lagrange multipliers
Saddle point
Minimized wrt W and b
Maximize wrt Lagrange multipliers (alpha)
Kuhn-Tucker conditions
Non-separating patterns
Slack variables
set of non -ve scalar variables
Minimize misclassification error
NP Complete
Regularization parameter C
Experimentally
Analytically