How do support vector machines (SVMs) utilize kernel functions to handle non-linear classification problems, and what are some common types of kernel functions?

SVMs use kernel functions to map input data into a higher-dimensional space where linear separation is possible, thus handling non-linear classification problems. Common kernel functions include the linear kernel, polynomial kernel, radial basis function (RBF) kernel, and sigmoid kernel. These functions allow SVMs to create complex decision boundaries, making them versatile and powerful for various classification tasks.