Parameters measuring the size of set families

Maximum Positive Degree

Name: Maximum Positive Degree

Symbol: $\mathrm{d}^+_{\max}$

Definition:

The Maximum Positive Degree of a concept class is the maximum dominance of its $1$-inclusion graph (where dominance is the number of neighbors that are smaller with respect to inclusion).

Category: Graph-based

Symmetric: No

Monotonic: Yes

P-Monotonic: No

Doubly Monotonic: No

Strictly Monotonic: No

Values: None

Relationships (as Parameter 1):

Maximum Positive Degree / Largest Strongly Shattered Set

Relationships (as Parameter 2):

Positive No-Clashing Teaching Dimension / Maximum Positive Degree
Maximum Degree / Maximum Positive Degree