kernel SVM

SSU

In its base form, SVM creates a linear bound. Using kernel functions allows us to create complex non-linear bound, which are still linear in parameters. By using kernel functions, we implicitly map inputs into a feature space.

$${\alpha }^{\ast }=\arg \underset{\alpha \in {\mathbb{R}}^m}{\max }\left[\sum _{i=1}^m{\alpha }_i-\frac{1}{2}\sum _{i=1}^m\sum _{j=1}^m{\alpha }_i{\alpha }_j{y}_i{y}_{j}k(x_i,x_j)\right]$$

subject to

$$\sum _{i=1}^m{\alpha }_i{y}_i=0,0\le {\alpha }_i\le C,i\in I_{+}\cup I_{-}.$$

Computing the