Now, let's look at SVM. SVM is a classifier that finds an optimal hyperplane that maximizes the margin between two classes. In SVMs, our optimization objective is to maximize the margin. The margin is defined as the distance between the separating hyperplane (the decision boundary) and the training samples that are closest to this hyperplane, called the support vectors. So, let's start with a very basic example with only two dimensions, X1 and X2. We want a line to separate the circles from the crosses. This is shown in the following diagram:

We have drawn two lines and both perfectly separate the crosses from the circles. However, there has to be an optimal line, or decision boundary, that gives us the best chance to correctly classify most of the additional examples. A reasonable choice may be a line that is evenly spaced between these two classes to give a little bit of a buffer for each class, as shown:

 Now, let's see how we can use SVM to train a classifier for our challenge.