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Brief explanation of Support Vector Machines (SVM) and the related optimization problem

A Support Vector Machine (SVM) is a decision-based prediction algorithm which can classify data into several groups. It is based on the concept of decision planes where thetraining data is mapped to a higher dimensional space and separated by a plane defining the two or more classes of data [1].

A simple example is seen in Figure 1 . Squares are data of class one while circles are data of class two. The SVMsets up the decision plane (in this case a simple line) and separates the two classes.

2-d example

A simple 2-D example for the decision algorithm in an SVM

However, often the data is not distinguishable in two dimensions in which case it is mapped to higher dimensionsand the same process is done. An example is shown in Figure 2.

Mapping in higher dimensional space

When there is no solution in a lower dimension it can be mapped to a higher dimension and a decision plane is easier to construct

Support Vector Machine models can be classified into four major groups.

  • C-SVM classification
  • nu-SVM classification
  • epsilon-SVM regression
  • nu-SVM regression

The first two are classification algorithms which minimize different error functions while the second twoperform similar algorithms by regression [1].

[1] Chih-Chung Chang and Chih-Jen Lin, LIBSVM : a library for support vector machines, 2001. Software available at http://www.csie.ntu.edu.tw/~cjlin/libsvm

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Source:  OpenStax, Intelligent motion detection using compressed sensing. OpenStax CNX. Dec 23, 2005 Download for free at http://cnx.org/content/col10311/1.3
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