Linear separability

Two linearly separable from each other in relations.

Linear separability (also separability, or classifiability ) called in mathematics the property of two relations ( sets of tuples ) for which a hyperplane (or a linear discriminant function ) exists, which separates them in the -dimensional vector space of each other.

In a 2- dimensional space, this means that a straight line can be set between two points linearly separable sets.

Formal definition

Two subsets are called linearly separable if n 1 real numbers exist, such that for all the inequalities

. apply Points out, applies to the form the separating hyperplane.

Linear separable functions

Binary features (ie with ) are called linearly separable if the preimages of 0 and 1 are separable. The linearly separable functions play a role, especially in machine learning. For example, the simple perceptron learning only linearly separable functions.

An example of a non-linear function is separable, the XOR operation. As the graph shows, it is not possible a linear separation of the two resulting values ​​.