VC Dimension

Name: VC Dimension

Symbol: $\mathrm{VC}$

Definition:

The VC dimension of a family $\mathcal{H}$, denoted by $\VC(\mathcal{H})$, is the largest integer $d$ such that there exists a set $S\subset \mathcal{X}$, of size $d$ such that $S$ is shattered by $\mathcal{H}$, i.e. $$ |\mathcal{H|_{|S}} = 2^{|S|}\,. $$

Description:

Vapnik-Chervonenkis Dimension [vc71].

Category: Shattering

Symmetric: Yes

Monotonic: Yes

P-Monotonic: Yes

Doubly Monotonic: Yes

Strictly Monotonic: No

Values:

Relationships (as Parameter 1):

Relationships (as Parameter 2):

Legend