University of Michigan - Ann Arbor

Basic types of kernel functions include:

- **Polynomial Kernel**: $$K(x, y) = (x \cdot y + 1)^p$$
- **Radial Basis Function (RBF) Kernel**: $$K(x, y) = \exp\left(-\frac{||x - y||^2}{2\sigma^2}\right)$$
- **Sigmoid Kernel**: $$K(x, y) = \tanh(C(x \cdot y) + \delta)$$

Basic Kernel Types

Berwick, R. Guide to Support Vector Machines (SVMs). Retrieved from http://web.mit.edu/6.034/wwwbob/svm.pdf

Guide to Support Vector Machines (SVMs)

Non Linear Kernel boundary

1. kernel = "linear": linear SVM  
equation example : $$𝑘(𝑥1,𝑥2)=𝑥𝑇1𝑥2$$

2. kernel = "poly": polynomial kernel  
equation example: $$𝑘(𝑥1,𝑥2)=(y(𝑥T1𝑥2)+coef0)d $$
    - gamma:  𝛾 
    - coef0:  𝜃 
    - degree:  𝑑 

3. kernel = "rbf" or kernel = None: RBF kernel. 
equation example: $$ k(𝑥1,𝑥2)=exp(−y||x1−x2||2) $$
    - gamma:  𝛾 

4. kernel = "sigmoid": sigmoid kernel.  
equation example:$$ 𝑘(𝑥1,𝑥2)=tanh(y(𝑥𝑇1𝑥2)+coef0) $$
    - gamma:  𝛾 
    - coef0:  𝜃

(Note: In the polynomial, RBF, and sigmoid kernels, the parameter gamma specifies the level of influence that a single training example has. The larger gamma is, the more influence a single example has)

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