Signed distance
Theorem taught in Support vector machines, part of Statistical learning
Signed distance
| Type | Theorem |
| Taught in | Support vector machines |
| Part | Statistical learning |
For w\neq 0, the signed distance from a point x to the hyperplane \{x:w^\top x+b=0\} is (w^\top x+b)/\lVert w\rVert, where \lVert\cdot\rVert is the Euclidean norm. In particular the distance between the parallel hyperplanes w^\top x+b=-1 and w^\top x+b=1 is 2/\lVert w\rVert.
Used in
- Taught in Support vector machines, where the derivation and examples are.
- All 10 questions on Support vector machines
See also
Distance to a hyperplane · Vapnik’s radius–margin bound · Hard-margin primal · Hard-margin dual · Soft-margin primal · Kernel · Linear separators and the margin · Why maximise the margin?