For dataset like p1.1, it's hard to use support vector classifier(soft margin classifier) since no matter where we put the classifier it will have a lot of misclassifications. In order to solve this problem, we can use support vector machine (SVM). The main idea behind SVM is we create a new y-axis and then square the value on x-axis. Now the value is two dimensional. We can then draw a support vector classifier that separates these two groups.

SVM is an extension of support vector classifier, which uses kernels to enlarge features in a certain way like what is depicted in the picture.