kernel trick

support vector classifiers can be written as $b+{\sum }_i{\alpha }_i{x}^T{x}^{(i)},$ where

• $b$ is the bias
• ${\alpha }_i$ is the parameter
• $x^{(i)}$ is the observation

The kernel trick is to replace the dot product with a functional $k:{\mathbb{R}}^n\times {\mathbb{R}}^n\to \mathbb{R}$:

$b+{\sum }_i{\alpha }_{i}k(x,x^{(i)}).$

It allows for non-linear decision boundaries.