Decision Boundary and Hyperplanes

Use case

A Decision boundary is a line or plane that separates classes. It determined by using a suitable discriminant function.

Hyper planes

They are decision boundaries that are linear.

Mathematically

For a Linearly separable classes with $k$ =2, the hyperplane with the parameter vector $\mathbf{w}$ :

$$\boxed{{\mathbf{w}}^T\mathbf{x}+w_0=0}$$

Classification (here for 2 classes): Class 0

$${\mathbf{w}}^T\mathbf{x}+w_0<0$$

Class 1

$${\mathbf{w}}^T\mathbf{x}+w_0>0$$

Decision boundary

$${\mathbf{w}}^T\mathbf{x}+w_0=0$$