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: SVM Basics

In course

EE-566: Adaptation and learning

In this course, students learn to design and master algorithms and core concepts related to inference and learning from data and the foundations of adaptation and learning theories with applications.

Description

This lecture covers the basics of Support Vector Machines (SVM), focusing on the hard-margin and soft-margin formulations. It explains the concepts of separating hyperplanes, margins, support vectors, and the optimization problems involved in SVM. The lecture also discusses the role of slack variables in handling non-linearly separable data and the importance of regularization in SVM algorithms.

Instructor

Ali H. Sayed

Ali H. Sayed is Dean of Engineering at EPFL, Switzerland, where he also leads the Adaptive Systems Laboratory. He has also served as Distinguished Professor and Chairman of Electrical Engineering at UCLA. He is recognized as a Highly Cited Researcher and is a member of the US National Academy of Engineering. He is also a member of the World Academy of Sciences and served as President of the IEEE Signal Processing Society during 2018 and 2019. Dr. Sayed is an author/co-author of over 570 scholarly publications and six books. His research involves several areas including adaptation and learning theories, data and network sciences, statistical inference, and multiagent systems. His work has been recognized with several major awards including the 2022 IEEE Fourier Award, the 2020 Norbert Wiener Society Award and the 2015 Education Award from the IEEE Signal Processing Society, the 2014 Papoulis Award from the European Association for Signal Processing, the 2013 Meritorious Service Award and the 2012 Technical Achievement Award from the IEEE Signal Processing Society, the 2005 Terman Award from the American Society for Engineering Education, the 2005 Distinguished Lecturer from the IEEE Signal Processing Society, the 2003 Kuwait Prize, and the 1996 IEEE Donald G. Fink Prize. His publications have been awarded several Best Paper Awards from the IEEE (2002, 2005, 2012, 2014) and EURASIP (2015). He is a Fellow of IEEE, EURASIP, and the American Association for the Advancement of Science (AAAS); the publisher of the journal Science.

Official source

Ontological neighbourhood

Theoretical computer science

Algorithms and data structures: Combinatorial optimization

Related concepts (32)

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).

Mathematical optimization

Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.

Linear separability

In Euclidean geometry, linear separability is a property of two sets of points. This is most easily visualized in two dimensions (the Euclidean plane) by thinking of one set of points as being colored blue and the other set of points as being colored red. These two sets are linearly separable if there exists at least one line in the plane with all of the blue points on one side of the line and all the red points on the other side. This idea immediately generalizes to higher-dimensional Euclidean spaces if the line is replaced by a hyperplane.

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.

Hyperplane

In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space. For example, if a space is 3-dimensional then its hyperplanes are the 2-dimensional planes, while if the space is 2-dimensional, its hyperplanes are the 1-dimensional lines. This notion can be used in any general space in which the concept of the dimension of a subspace is defined. In different settings, hyperplanes may have different properties.

Related lectures (33)

Support Vector Machines

Introduces Support Vector Machines, covering Hinge Loss, hyperplane separation, and non-linear classification using kernels.

SVM for Non-separable Datasets

Explains SVM for non-separable datasets, introducing slack variables and optimizing the margin for classification.

Linear Models for Classification

Covers linear models for classification, including SVM, decision boundaries, support vectors, and Lagrange duality.

Support Vector Machines: SVMs

Explores Support Vector Machines, covering hard-margin, soft-margin, hinge loss, risks comparison, and the quadratic hinge loss.

Max-Margin Classifiers