What is Alpha in dual form of SVM?

Lagrangian multiplier, usually denoted by α is a vector of the weights of all the training points as support vectors. Suppose there are m training examples. Then α is a vector of size m. When you say αi=0, it is just that ith training example has zero weight as a support vector.

What is the dual problem in 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.

What is W and B in SVM?

w is the normal direction of the plane and b is a form of threshold. Given a data point w, if w⋅x is evaluated to to be bigger than b, it belongs to a class. If it is evaluated to be less than b, then it belongs to another class.

What is the dual formulation of SVM?

This is called the dual formulation of SVM, or the dual problem. Any dual problem is always a convex problem. This form can also be solved with quadratic programming, but it changes the problem so that we are minimizing over N variables instead of the original D variables.

How to solve the Lagrangian of SVM optimization?

Here is the overall idea of solving SVM optimization: for the Lagrangian of SVM optimization (with linear constraints), it satisfies all the KKT Conditions. Therefore, we can solve it by solving its dual problem, and the dual problem has some nice properties that allows us to use Kernel trick.

What does SVM stand for?

It introduces Support Vector Machine ( SVM) classifier, the form of its corresponding convex optimization, and how to use Lagrange Duality and KKT Conditions to solve the optimization problem. Additionally, it also introduces how to make use of Kernel tricks to do non-linear classification.

Is a dual problem always a convex problem in SVM?

Any dual problem is always a convex problem. This form can also be solved with quadratic programming, but it changes the problem so that we are minimizing over N variables instead of the original D variables. A student first learning about SVM needn’t concern himself with the exact details of this problem.