Linear separability
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Equivalently, two sets are linearly separable precisely when their respective convex hulls are disjoint (colloquially, do not overlap).
Example
Three points in two classes ('+' and '-') are always linearly separable in two dimensions. This is illustrated by the three examples in the following figure:
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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:
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Linear separability of hypercubes in n dimensions
| Dimension | Linearly separable Boolean hypercubes |
|---|---|
| 2 | 14 |
| 3 | 104 |
| 4 | 1882 |
| 5 | 94572 |
| 6 | 15028134 |
| 7 | 8378070864 |
| 8 | 17561539552946 |
| 9 | 144130531453121108 |
Usage
Linear separability allows simple Classification in machine learning.
See also
References
- ^
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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