partitionComparison (version 0.2.3)

normalizedMutualInformation: Normalized Mutual Information

Description

Compute the mutual information (\(MI\)) which is normalized either by the minimum/maximum partition entropy (\(H\)) $$\frac{MI(P, Q)}{\varphi(H(P), H(Q))},\ \varphi \in \{\min, \max\}$$ or the sum $$\frac{2 \cdot MI(P, Q)}{H(P) + H(Q)}$$

Usage

normalizedMutualInformation(p, q, type = c("min", "max", "sum"))
# S4 method for Partition,Partition,character
normalizedMutualInformation(p, q,
  type = c("min", "max", "sum"))
# S4 method for Partition,Partition,missing
normalizedMutualInformation(p, q,
  type = NULL)

Arguments

p

The partition \(P\)

q

The partition \(Q\)

type

One of "min" (default), "max" or "sum"

Methods (by class)

• p = Partition,q = Partition,type = character: Compute given two partitions

• p = Partition,q = Partition,type = missing: Compute given two partitions with type="min"

References

Kvalseth1987partitionComparison

See Also

mutualInformation, entropy

Examples

# NOT RUN {
isTRUE(all.equal(normalizedMutualInformation(
                   new("Partition", c(0, 0, 0, 1, 1)),
                   new("Partition", c(0, 0, 1, 1, 1)), "min"),
                 normalizedMutualInformation(
                   new("Partition", c(0, 0, 0, 1, 1)), 
                   new("Partition", c(0, 0, 1, 1, 1)), "max")
                 ))

# }