What is primal and dual problem in SVM?

This comes from the duality principle which states that optimization problems may be viewed as primal (in this case minimising over w and b) or dual (in this case, maximising over a). For a convex optimisation problem, the primal and dual have the same optimum solution.

What is primal problem in SVM?

PRIMAL FORM Let’s talk about the above optimization problem, it’s an optimization problem where we are trying to minimize (W and biases) such that alphas are maximized. Basically, it’s a MIN(MAX) problem where we are trying to minimize the product of W'(transpose) and W such that y_k*[W’*X_k + b] >= 1.

What is dual problem SVM?

In mathematical optimization theory, duality means that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem (the duality principle). The solution to the dual problem provides a lower bound to the solution of the primal (minimization) problem. Wikipedia.

What is the reason to use dual form in SVM?

Dual form of SVM: basically, we can separate each data point by projecting it into the higher dimension by adding relevant features to it as we do in logistic regression. But with SVM there is a powerful way to achieve this task of projecting the data into a higher dimension.

What is dual representation SVM?

The dual representation is the expression of a solution as a linear combination of training point locations (their actual location in input space if the kernel is linear; or their location in a high-dimensional feature space induced by the kernel, if non-linear).

What is meant by dual problem?

The dual problem is an LP defined directly and systematically from the primal (or original) LP model. The two problems are so closely related that the optimal solution of one problem automatically provides the optimal solution to the other. A dual variable is defined for each primal (constraint) equation.

What is primal dual?

The primal-dual algorithm is a method for solving linear programs inspired by the Ford–Fulkerson method. Instead of applying the simplex method directly, we start at a feasible solution and then compute the direction which is most likely to improve that solution.

What is dual problem in support vector machine?

In mathematical optimization theory, duality means that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem (the duality principle). The solution to the dual problem provides a lower bound to the solution of the primal (minimization) problem.

What is a dual representation in a support vector machine?

Support vector machines are ways of getting the advantages of many nonlin- ear features without the pains. The dual representation is a way of writing a linear classifier not in terms weights wj, j ∈ 1 : p over features, but rather in terms of weights αi, i ∈ 1 : n over train- ing vectors.

Should you use the primal or the dual form of the SVM problem to train a model on a training set with millions of instances and hundreds of features?

So if there are millions of instances, you should definitely use the primal form, because the dual form will be much too slow. Say you trained an SVM classifier with an RBF kernel.