lermanIndex {partitionComparison}

Lerman Index

Description

Compute the Lerman index

\frac{N_{11} - E(N_{11})}{\sqrt{\sigma^2(N_{11})}}

Usage

lermanIndex(p, q, c = NULL)

## S4 method for signature 'Partition,Partition,missing'
lermanIndex(p, q, c = NULL)

## S4 method for signature 'Partition,Partition,PairCoefficients'
lermanIndex(p, q, c = NULL)

Arguments

p

The partition P

q

The partition Q

c

PairCoefficients or NULL

Methods (by class)

• lermanIndex(p = Partition, q = Partition, c = missing): Compute given two partitions

• lermanIndex(p = Partition, q = Partition, c = PairCoefficients): Compute given the partitions and pair coefficients

Author(s)

Fabian Ball [e-mail]

References

Lerman IC (1988). “Comparing Partitions (Mathematical and Statistical Aspects).” In Bock H (ed.), Classification and Related Methods of Data Analysis, 121–132.

Hubert L, Arabie P (1985). “Comparing Partitions.” Journal of Classification, 2(1), 193–218.

Denøeud L, Guénoche A (2006). “Comparison of Distance Indices Between Partitions.” In Batagelj V, Bock H, Ferligoj A, Žiberna A (eds.), Data Science and Classification, Studies in Classification, Data Analysis, and Knowledge Organization, 21–28. Springer Berlin Heidelberg. ISBN 978-3-540-34415-5 978-3-540-34416-2.

See Also

normalizedLermanIndex

Examples

isTRUE(all.equal(lermanIndex(new("Partition", c(0, 0, 0, 1, 1)), 
                             new("Partition", c(0, 0, 1, 1, 1))), 2/sqrt(21)))