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: Linear Separability

Description

This lecture covers the concept of linear separability in support vector machines (SVM). It explains how an SVM seeks to find a hyperplane that separates positive and negative points in a dataset. The lecture delves into the margin of a separating hyperplane, the origin of the SVM name, support vectors, and the formulation of SVM with a rigid margin.

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

Official source

Related concepts (15)

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).

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.

Statistical classification

In statistics, classification is the problem of identifying which of a set of categories (sub-populations) an observation (or observations) belongs to. Examples are assigning a given email to the "spam" or "non-spam" class, and assigning a diagnosis to a given patient based on observed characteristics of the patient (sex, blood pressure, presence or absence of certain symptoms, etc.). Often, the individual observations are analyzed into a set of quantifiable properties, known variously as explanatory variables or features.

Machine learning

Machine learning (ML) is an umbrella term for solving problems for which development of algorithms by human programmers would be cost-prohibitive, and instead the problems are solved by helping machines 'discover' their 'own' algorithms, without needing to be explicitly told what to do by any human-developed algorithms. Recently, generative artificial neural networks have been able to surpass results of many previous approaches.

Multiclass classification

In machine learning and statistical classification, multiclass classification or multinomial classification is the problem of classifying instances into one of three or more classes (classifying instances into one of two classes is called binary classification). While many classification algorithms (notably multinomial logistic regression) naturally permit the use of more than two classes, some are by nature binary algorithms; these can, however, be turned into multinomial classifiers by a variety of strategies.

Related lectures (33)

Support Vector Machines: Maximizing Margin

Explores Support Vector Machines, maximizing margin for robust classification and the transition to soft SVM for non-linearly separable data.

SVM - Principle: Linear Classifiers

Covers the history and applications of SVM, as well as the construction of linear classifiers and the concept of classifier margin.

Advanced Machine Learning: Brief review of C-SVM

Covers clustering, classification, and Support Vector Machine principles, applications, and optimization, including non-linear classification and Gaussian kernel effects.

Support Vector Machines

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

Perceptron: Part 2