How does SVM work if no linear separation exists between classes?

While soft margin classification relaxes the requirement of a hyperplane that must perfectly distinguish between the classes, a separate issue arises when there is no way to define such a hyperplane in the original feature space. In order to address cases where no such linear separation exists, the original data can be mapped into a higher-dimensional space that is linearly separable. Thus, a non-linear decision boundary in the original space can be defined by a linear decision boundary in higher-dimensional space.