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Why do we need dual problems 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 the cost function for SVM?
The Cost Function is used to train the SVM. By minimizing the value of J(theta), we can ensure that the SVM is as accurate as possible. In the equation, the functions cost1 and cost0 refer to the cost for an example where y=1 and the cost for an example where y=0.
How to understand SVM-hinge loss understanding and proof?
The idea is to maximize the margin between different classes of point (within any dimension) as much as possible. So to understand the internal workings of the SVM classification algorithm, I decided to study the cost function, or the Hinge Loss, first and get an understanding of it… Interpreting what the equation means is not so bad.
How to derive primal and dual formulation in SVM?
Intuitively, the constraints ensure that the hyperplane w’x + b =0 be a valid separation of the two categories, while the objective (minimize || w ||) maximizes the margin. To derive the dual form from the primal, just use the KKT conditions.
What does the Alpha mean in the SVM?
First, let’s ignore all terms to do with . is our linear classifier, i.e.,: is our classification function (1 if greater than 0, 0 otherwise). Maximizing its norm is the same as maximizing the margin of classification (hence SVM is a max-margin classifier).
How to derive the dual form from the primal?
To derive the dual form from the primal, just use the KKT conditions. I think for this step nothing would be more intuitive than the mathematical deduction, which is really straightforward. Why is solving in the dual easier than solving in the primal?