# SVM (Support Vector Machine) A Training Algorithm for Optimal Margin Classifiers(1992) [[paper link]](http://www.svms.org/training/BOGV92.pdf) Phoebe Huang Pytorch Tainan 2019/7/20 --- ## Task Discription  Find decision function $D(\mathbb{x})$,  ---- SVM Main Idea: Maximum Margin ${M}$  ---- The decision functions $D(\mathbb{x})$ must be linear in their parameters but are not restricted to linear dependences of $\mathbb{x}$.  ---- In the dual space the decision functions are of the form  The function $K$ is a predefined kernel  ---- Provided that the expansion stated in equation 5 exists, equations 3 and 4 are **dual representations** of the same decision function and  First, the margin between the class boundary and the training patterns is formulated in the **direct space**. This problem description is then transformed into the **dual space** by means of the **Lagrangian**. --- ## In the Direct Space In the direct space,   ---- The distance between this hyperplane and pattern $\mathbb{x}$ is $\frac{ D(\mathbb{x})}{||\mathbb{w}||}$. All data satisfying  ---- The objective of the training algorithm is to find $\mathbb{w}$ that maximum $M$  <!-- ?? --> The bound $M^{*}$ is attained for those patterns satisfying  ----   ----  --- ## In the Dual Space  ----   ----   ----   --- # 3 Properties of this Algorithm ## 3.1 Properties of the solution