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# This or That: Binary Classification

At the very end of Chapter 2, we quickly presented an example of classification. We used heights and weights to predict whether a person was a man or a woman. With our example graph, we were able to draw a line that split the data into two groups: one group where we would predict “male” and another group where we would predict “female.” This line was called a separating hyperplane, but from now on we’ll use the term “decision boundary,” because we’ll be working with data that can’t be classified properly using only straight lines. For example, imagine that your data looked like the data set shown in Example 3-1.

This plot might depict people who are at risk for a certain ailment and those who are not. Above and below the black horizontal lines we might predict that a person is at risk, but inside we would predict good health. These black lines are thus our decision boundary. Suppose that the blue dots represent healthy people and the red dots represent people who suffer from a disease. If that were the case, the two black lines would work quite well as a decision boundary for classifying people as either healthy or sick.

Producing general-purpose tools that let us handle problems where the decision boundary isn’t a single straight line has been one of the great achievements of machine learning. One approach in particular that we’ll focus on later is called the kernel trick, which has the remarkable property ...

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