Linearly separable
Encyclopedia
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 i:th component of 
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, 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
Hyperplane
A hyperplane is a concept in geometry. It is a generalization of the plane into a different number of dimensions.A hyperplane of an n-dimensional space is a flat subset with dimension n − 1...
.
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 i:th component of | Dimension | Linearly separable Boolean hypercubes |
|---|---|
| 2 | 14 |
| 3 | 104 |
| 4 | 1882 |
| 5 | 94572 |
| 6 | 15028134 |
| 7 | 8378070864 |
| 8 | 17561539552946 |
| 9 | 144130531453121108 |