Linearly Separable Set

A Linearly Separable Set is a pair of sets of point which satisfies the linear separability condition.

See: Linear Separability; Support Vector Machines, Machine Learning, Euclidean Space.

References

(Wikipedia, 2016) ⇒ http://wikipedia.org/wiki/Linear_separability#Mathematical_definition
- QUOTE: Let [math]\displaystyle{ X_{0} }[/math] and [math]\displaystyle{ X_{1} }[/math] be two sets of points in an n-dimensional Euclidean space. Then [math]\displaystyle{ X_{0} }[/math] and [math]\displaystyle{ X_{1} }[/math] are linearly separable if there exists n + 1 real numbers [math]\displaystyle{ w_{1}, w_{2},..,w_{n}, k }[/math], such that every point [math]\displaystyle{ x \in X_{0} }[/math] satisfies [math]\displaystyle{ \sum^{n}_{i=1} w_{i}x_{i} \gt k }[/math] and every point [math]\displaystyle{ x \in X_{1} }[/math] satisfies [math]\displaystyle{ \sum^{n}_{i=1} w_{i}x_{i} \lt k }[/math], where [math]\displaystyle{ x_{i} }[/math] is the [math]\displaystyle{ i }[/math]-th component of [math]\displaystyle{ x }[/math].