A decision boundary that separates data points of different classes in the feature space.
In a 2D space, the hyperplane is a line; in 3D, it’s a plane; and in higher dimensions, it’s a flat affine subspace of one dimension less than the feature space.
Key Properties:
- The optimal hyperplane is the one that maximizes the margin between the two classe
- The margin is the distance between the hyperplane and the nearest data points from each class (called support vectors
- The equation of a hyperplane in n-dimensional space is:
\mathbf{w} \cdot \mathbf{x} + b = 0
where:
\mathbf{w} is the weight vector (normal to the hyperplane),
\mathbf{x} is a point in the space,
b is the bias term.
In geometry, a hyperplane is a generalization of a two-dimensional plane in three-dimensional space to mathematical spaces of arbitrary dimension. Like a plane in space, a hyperplane is a flat hypersurface, a subspace whose dimension is one less than that of the ambient space. Two lower-dimensional examples of hyperplanes are one-dimensional lines in a plane and zero-dimensional points on a line.
