Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Support Vector Machines: Dual Formulation for Hard Margin

In course

EE-311: Fundamentals of machine learning

Ce cours présente une vue générale des techniques d'apprentissage automatique, passant en revue les algorithmes, le formalisme théorique et les protocoles expérimentaux. ...

Description

This lecture covers the dual formulation of Support Vector Machines (SVM) for hard margin classification. It explains the optimization problem to find the hyperplane parameters, the decision function, and the concept of support vectors. The instructor discusses the transition from the primal to the dual formulation, the role of Lagrange multipliers, and the conditions for optimal solutions. By exploring the relationship between the dual and primal solutions, the lecture highlights the significance of support vectors in SVM. It also addresses the choice between primal and dual formulations based on data characteristics, emphasizing the interpretation of alpha values and their impact on classification boundaries.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructors (2)

François Fleuret

Michael Stefan Daniel Liebling

Official source

Related concepts (17)

Support vector machine

In machine learning, support vector machines (SVMs, also support vector networks) are supervised learning models with associated learning algorithms that analyze data for classification and regression analysis. Developed at AT&T Bell Laboratories by Vladimir Vapnik with colleagues (Boser et al., 1992, Guyon et al., 1993, Cortes and Vapnik, 1995, Vapnik et al., 1997) SVMs are one of the most robust prediction methods, being based on statistical learning frameworks or VC theory proposed by Vapnik (1982, 1995) and Chervonenkis (1974).

Duality (optimization)

In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. If the primal is a minimization problem then the dual is a maximization problem (and vice versa). Any feasible solution to the primal (minimization) problem is at least as large as any feasible solution to the dual (maximization) problem.

Optimization problem

In mathematics, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete: An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set.

Convex optimization

Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.

Combinatorial optimization

Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the set of feasible solutions is discrete or can be reduced to a discrete set. Typical combinatorial optimization problems are the travelling salesman problem ("TSP"), the minimum spanning tree problem ("MST"), and the knapsack problem. In many such problems, such as the ones previously mentioned, exhaustive search is not tractable, and so specialized algorithms that quickly rule out large parts of the search space or approximation algorithms must be resorted to instead.

Related lectures (33)

Optimization Methods: Theory Discussion

Explores optimization methods, including unconstrained problems, linear programming, and heuristic approaches.

Linear SVM derivation

Covers the derivation of Linear Support Vector Machine (SVM) and the Karush-Kuhn-Tucker (KKT) conditions.

Max-Margin Classifiers

Explores maximizing margins for better classification using support vector machines and the importance of choosing the right parameter.

Support Vector Machines: SVM Basics

Covers the basics of Support Vector Machines, focusing on hard-margin and soft-margin formulations.

Linear Models for Classification