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# Understanding Kernel Methods

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Consider what would happen if you tried to use the linear classifier on a dataset similar to the one in Figure 9-7.

Where would the average points be for each class? They would both be in exactly the same place! Even though it’s clear to you and me that anything inside the circle is an X and everything outside the circle is an O, the linear classifier is unable to distinguish these two classes.

But consider what happens if you square every x and y value first. A point that was at (−1,2) would now be at (1,4), a point that was at (0.5,1) would now be at (0.25,1), and so on. The new plot would look like Figure 9-8.