Why we use Lagrange multipliers in SVM?
The critical thing to note from this definition is that the method of Lagrange multipliers only works with equality constraints. So we can use it to solve some optimization problems: those having one or several equality constraints.
What is dual representation in 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).
How to solve the Lagrangian of the 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. Let’s first get the Lagrangian of the SVM optimization:
How to use Lagrange duality in machine learning?
This article is part of my review of Machine Learning course. 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.
Which is an example of a dual SVM derivation?
Dual SVM derivation (1) – the linearly separable case Original optimization problem: Lagrangian: Rewrite constraints One Lagrange multiplier per example Our goal now is to solve: Dual SVM derivation (2) – the linearly separable case
How does dual form SVM change the training problem?
The dual form SVM approach changes the logic of both the training problem and the classifier rule. Instead of finding an explicit decision boundary, we have found a set of values over our training points that we can use to describe how ‘representative’ each training point is of its class.