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Support-Vector Machines

Consider again the challenge of finding a straight line that divides two classes. Figure 9-9 illustrates an example. The averages for each class are shown in the figure, along with the dividing line that they imply.

Linear average classifier misclassifies points

Figure 9-9. Linear average classifier misclassifies points

Notice that the dividing line calculated by using the averages misclassifies two of the points because they are much closer to the line than the majority of the data. The problem is that since most of the data is far away from the line, it’s not relevant for including in the dividing line.

Support-vector machines are a well known set of methods for creating classifiers that solve this problem. They do this by trying to find the line that is as far away as possible from each of the classes. This line is called the maximum-margin hyperplane, and is shown in Figure 9-10.


  

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