In geometry, two sets of points in a two-dimensional space are linearly separable if they can be completely separated by a single line. In general, two point sets are linearly separable in n-dimensional space if they can be separated by a hyperplane.
In more mathematical terms: Let and be two sets of points in an n-dimensional space. Then and are linearly separable if there exists n+1 real numbers , such that every point satisfies and every point satisfies , where is the -th component of .
Three points in two classes ('+' and '-') are always linearly separable in two dimensions. This is illustrated by the three examples in the following figure:
However, not all sets of four points are linearly separable in two dimensions. The following example would need two straight lines and thus is not linearly separable:
Linear separability of hypercubes in n dimensions
|Dimension||Linearly separable Boolean hypercubes|
Linear separability allows simple Classification in machine learning.
- Gruzling, Nicolle (2006). Linear separability of the vertices of an n-dimensional hypercube. M.Sc Thesis. University of Northern British Columbia.
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