cs229 support vector Machine for learning notes

function distance and geometric distance

Set the features and class labels to x,y∈{−1,1} x, y \in \{-1,1\}, define the classifier hw,b (x) =g (wtx+b) H_{w,b} (x) =g (W^tx+b), G (z) ={1−1z≥0 z<0 g (z) =\begin{ cases}1&\text{$z \geq 0$}\\-1&\text{$z function Distance

Given training sample (X (i), Y (i)) (x^{(i)},y^{(i)}), the function distance r^ (i) =y (i) (WTx (i) +b) \hat{r}^{(i)}=y^{(i)} (w^tx^{(i)}+b)
If Y (i) =1 y^{(i)}=1, we want wTx (i) +b w^tx^{(i)}+b to be a relatively large positive number. Similarly, if Y (i) =−1 y^{(i)}=-1, we want wTx (i) +b w^tx^{(i)}+b to be a relatively small negative number. This way our predictions are correct and have a high degree of confidence. If Y (i) (WTx (<