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Machine Learning For Dummies
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SVMs are quite mathematically demanding. Up to now, you’ve seen some formulations that help you understand that SVMs are an optimization problem that strives to classify all the examples of two classes. When solving the optimization in SVMs, you use a partitioning hyperplane having the largest distance from the class boundaries. If classes aren’t linearly separable, the search for the optimal separating hyperplane allows for errors (quantified by the value of C) in order to deal with noise.
In spite of allowing a small cost for errors, the SVM’s linear hyperplane can’t recover nonlinear relationships between classes unless you transform the features appropriately. For instance, you can correctly classify only a part of the examples like the ones depicted in Figure 17-2 if you don’t transform the existing two dimensions into other dimensions using multiplication or powers.
FIGURE 17-2: A case of nonlinearly separable points requiring...
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