- Radial Basis Function (RBF) Kernel
- Polynomial Kernel

Popular SVM Kernel Functions

The kernel function does not transform the original data points to the new high dimensional feature space. Instead, the kernelized SVM can compute these more complex decision boundaries just in terms of similarity calculations between pairs of points in the high dimensional space where the transformed feature representation is implicit.

SVM Kernel Trick

What does SVM do to solve the linear inseparable problem:

What does SVM do to solve the linear inseparable problem?

The kernel function in an SVM model calculates the similarity in the new feature space of two points in the original feature space.

The SVM Gaussian kernel function is more complicated than the linear kernel function model, and it is easy to overfit.

University of Michigan - Ann Arbor

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.

Support Vector Classifier vs Support Vector Machine

SVM Kernel Function

Pros:
1. SVM can perform well on a range of datasets,

2. SVM is versatile: different kernel functions can be specified, or custom kernels can be defined for specific datatypes.

3. SVM works well for both low and high dimensional data.

Cons:
1. Efficiency decreases as training set size increases.

2. SVM needs careful normalization of input data and parameter tuning.

3. SVM provides no direct probability estimates (but can be estimated using e.g., Platt scaling).

4. It is difficult to interpret why a prediction was made.

5. It is with high time complexity, which is $O(n^2)$ and n represents the number of data points.

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