Introduction To SVM

This document discusses support vector machines and maximum margin hyperplanes. It introduces key concepts such as margins, support vectors, and using a maximum margin hyperplane to perform optimal separating of data points. The maximum margin hyperplane is the hyperplane that creates the largest possible margin or distance between the separating hyperplane and the nearest data points of each class.

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Introduction To SVM

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Pooja Patwari

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Introduction to SVM

Margins and Support vectors

Support Vector machines
Separating HP
Maximum Margin
Support Vectors
Maximum margin
Some concepts of HP geometry
HP –weights and bias
• the weight vector w is orthogonal to the
hyperplane, since it is orthogonal to any
arbitrary vector (a1 −a2) on the hyperplane.
• the bias b fixes the offset of hyperplane, in the
d-dimensional space.
• NOTE: The bias weight in SVM DOES NOT
have corresponding feature vector = 1 ( as we
saw in perceptron, ANN and LR)
Further let xp be the projection of x on the hyperplane. Let r
be the offset of x along the weight vector w
What is the distance of the origin from the HP?
Given any two points on the hyperplane
, say p = (p1, p2) = (4, 0), and q = (q1, q2) = (2, 5),
Given a training dataset, Margin of a classifier is defined as
the minimum distance of a point from the separating HP
• All the points (or vectors) that achieve this
minimum distance are also called support
vectors for the linear classifier.
• a support vector, is a point that lies
precisely on the margin of the classifier.
The scaler s
Geometrical and Functional Margin
Maximum Margin Hyperplane
The summary

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Introduction To SVM

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Introduction To SVM

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Introduction to SVM

Margins and Support vectors

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