Support Vector Machine (Svm)

• SVM stands for Support Vector Machine
• Definitions:
  • Support Vector
  • Margin in SVM
  • Maximal Margin Classifier
  • Soft Margin in SVM
  • Kernel in SVM
  • Kernel Trick
• SVM can handle non-linear data using Kernel in SVM
  • Use Kernel Trick not to project the data all time to save computation
• Two types of SVM
  1. Hard SVM - No misclassification - Similar to Maximal Margin Classifier with Kernel
  2. Soft SVM - Allow misclassification - Similar to SVC with Kernel

[!def] Equation of SVM
$$
\begin{align*}
wx_i - b \geq +1 \text{ if } y_i &= +1 \\ > wx_i - b \leq -1 \text{ if } y_i &= -1
\end{align*}
$$
In combination,
$$
y_i(wx_i - b) \geq 1
$$
Minimize Euclidian Norm $||w||$ subject to $y_i(wx_i - b) \geq 1$