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9.3.1 we learned about linear SVMs for dassifying linearly separable data, what if the data are not linearly separable, as in Figure 9.10?The good news is that the approach described for lincar SVMs can be extended to create nonlinear SVMs for the classification of linearly inseparable data (also called non- linearly separable data, or nonlinear data for short).The linear SVMs we studied would not be able to find a feasible solution here.In such cases, line can be found that would separate the classes.Now what?
9.3.1 we learned about linear SVMs for dassifying linearly separable data, what if the data are not linearly separable, as in Figure 9.10? In such cases, line can be found that would separate the classes. The linear SVMs we studied would not be able to find a feasible solution here. Now what? The good news is that the approach described for lincar SVMs can be extended to create nonlinear SVMs for the classification of linearly inseparable data (also called non- linearly separable data, or nonlinear data for short). Such SVMs are capable of finding "So," you may ask, "how can we extend the linear approach We obtain a nonlinear SVM by extending the approach for lincar SVMs as follows. There are two main steps In the first step, we transform the original input data into a higher dimensional space using a nonlinear mapping. Several common nonlinear mappings can be used in this step, as we will further describe next. Once the data have been transformed into the new higher space, the second step searches for a linear separating hyperplane in the new space. We again end up with a quadratic optimization problem that can be solved using the lincar SVM formulation. The maximal marginal hyperplane found in the new space corresponds to a nonlincar separating hypersurface in the original space
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