Editing Linear separability (section)

{{Short description|Geometric property of a pair of sets of points in Euclidean geometry}}
[[File:Linearly separable red-blue cropped .svg|thumb|211x211px|The existence of a line separating the two types of points means that the data is linearly separable]]
In [[Euclidean geometry]], '''linear separability''' is a property of two sets of [[point (geometry)|points]]. This is most easily visualized in two dimensions (the [[Euclidean plane]]) by thinking of one set of points as being colored blue and the other set of points as being colored red. These two sets are ''linearly separable'' if there exists at least one [[line (geometry)|line]] in the plane with all of the blue points on one side of the line and all the red points on the other side. This idea immediately generalizes to higher-dimensional Euclidean spaces if the line is replaced by a [[hyperplane]].

The problem of determining if a pair of sets is linearly separable and finding a separating hyperplane if they are, arises in several areas.  In [[statistics]] and [[machine learning]], classifying certain types of data is a problem for which good algorithms exist that are based on this concept.