What is the maths intuition behind SVM?

The goal of the algorithm involved behind SVM: Finding a hyperplane with the maximum margin (margin is basically a protected space around hyperplane equation) and algorithm tries to have maximum margin with the closest points (known as support vectors). wT(Φ(x)) + b < 0.

What is primal formulation?

1. The primal formulation of a mathematical programming problem is the original model to be solved.

What is SVM equation?

SVM Lagrange problem α is called the Lagrange multiplier. In terms of the SVM optimization problem, f(w)=12‖w‖2, g(w,b)=yi(w⋅x+b)−1,i=1… m. The Lagrangian function is then L(w,b,α)=12‖w‖2−∑mi=1αi[yi(w⋅x+b)−1].

What is meant by kernel trick brief about the primal form of kernel SVM objective function?

Kernel trick is computing K(x(i),x(j)) without computing ϕ(x(i)) or ϕ(x(j)), and even without the need to know their form explicitly. With that in mind, to answer your questions: Recall that, for SVMs, w is defined as a linear combination of the data points: w=m∑j=1αjϕ(x(j))

What is the relation between primal and dual?

Relationship between the primal problem and the dual problem An infeasible value of the candidate solution is one that exceeds one or more of the constraints. In the dual problem, the dual vector multiplies the constraints that determine the positions of the constraints in the primal.

How to derive the primal formulation of SVM?

In order to derive the primal formulation of SVM, it is necessary to define an analytical formula to tell the distance between the data point and the hyperplane. It is obvious that any data point on the hyperplane satisfy the above equation. is a data point on the hyperplane).

What are the advantages of dual form in SVM?

One of the important advantage of using the dual form in SVM is that it allow us to apply kernels. Kernel search an optimal separating hyperplane in a higher dimensional space without increasing the computational complexity much. Kernel can be applied, if the algorithm takes the data points as input in terms of its inner product .

What is the difference between primal/dual and saddle point?

Primal: Dual: Weak duality: Strong duality: For convex problems with affine constraints Saddle point property If are primal/dual optimal with zero duality gap, they are a saddle pointof , i.e., for all , ,

Why is the separating hyperplane given by a SVM optimal?

The separating hyperplane given by a SVM is optimal because it observes separating hyper plane by maximizing the distance between the two classes on the training data. It solves the below optimization problem to find an optimal separating hyperplane. It is an optimization problem with an inequality constraint.