normalizedMutualInformation {partitionComparison}

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 signature 'Partition,Partition,character'
normalizedMutualInformation(p, q, type = c("min", "max", "sum"))

## S4 method for signature '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)

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

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

Author(s)

Fabian Ball [e-mail]

References

Kvalseth TO (1987). “Entropy and Correlation: Some Comments.” IEEE Transactions on Systems, Man and Cybernetics, 17(3), 517–519. ISSN 0018-9472, doi:10.1109/TSMC.1987.4309069.

See Also

mutualInformation, entropy

Examples

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")
                 ))