clue (version 0.3-27)

agreement: Agreement Between Partitions or Hierarchies

Description

Compute the agreement between (ensembles) of partitions or hierarchies.

Usage

cl_agreement(x, y = NULL, method = "euclidean", ...)

Arguments

x

an ensemble of partitions or hierarchies and dissimilarities, or something coercible to that (see cl_ensemble).

y

NULL (default), or as for x.

method

a character string specifying one of the built-in methods for computing agreement, or a function to be taken as a user-defined method. If a character string, its lower-cased version is matched against the lower-cased names of the available

...

further arguments to be passed to methods.

Value

• If y is NULL, an object of class "cl_agreement" containing the agreements between the all pairs of components of x. Otherwise, an object of class "cl_cross_agreement" with the agreements between the components of x and the components of y.

Details

If y is given, its components must be of the same kind as those of x (i.e., components must either all be partitions, or all be hierarchies or dissimilarities).

If all components are partitions, the following built-in methods for measuring agreement between two partitions with respective membership matrices $u$ and $v$ (brought to a common number of columns) are available: [object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

If all components are hierarchies, available built-in methods for measuring agreement between two hierarchies with respective ultrametrics $u$ and $v$ are as follows.

[object Object],[object Object],[object Object],[object Object],[object Object]

The measures based on ultrametrics also allow computing agreement with raw dissimilarities on the underlying objects (R objects inheriting from class "dist").

If a user-defined agreement method is to be employed, it must be a function taking two clusterings as its arguments.

Symmetric agreement objects of class "cl_agreement" are implemented as symmetric proximity objects with self-proximities identical to one, and inherit from class "cl_proximity". They can be coerced to dense square matrices using as.matrix. It is possible to use 2-index matrix-style subscripting for such objects; unless this uses identical row and column indices, this results in a (non-symmetric agreement) object of class "cl_cross_agreement".

References

E. Dimitriadou, A. Weingessel and K. Hornik (2002). A combination scheme for fuzzy clustering. International Journal of Pattern Recognition and Artificial Intelligence, 16, 901--912.

E. B. Fowlkes and C. L. Mallows (1983). A method for comparing two hierarchical clusterings. Journal of the American Statistical Association, 78, 553--569. A. D. Gordon (1999). Classification (2nd edition). Boca Raton, FL: Chapman & Hall/CRC. L. Hubert and P. Arabie (1985). Comparing partitions. Journal of Classification, 2, 193--218.

W. M. Rand (1971). Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association, 66, 846--850.

L. Katz and J. H. Powell (1953). A proposed index of the conformity of one sociometric measurement to another. Psychometrika, 18, 249--256.

A. Strehl and J. Ghosh (2002). Cluster ensembles --- A knowledge reuse framework for combining multiple partitions. Journal of Machine Learning Research, 3, 583--617.

See Also

cl_dissimilarity; classAgreement in package e1071.

Examples

## An ensemble of partitions.
data("CKME")
pens <- CKME[1 : 20]		# for saving precious time ...
summary(c(cl_agreement(pens)))
summary(c(cl_agreement(pens, method = "Rand")))
summary(c(cl_agreement(pens, method = "diag")))
cl_agreement(pens[1:5], pens[6:7], method = "NMI")
## Equivalently, using subscripting.
cl_agreement(pens, method = "NMI")[1:5, 6:7]

## An ensemble of hierarchies.
d <- dist(USArrests)
hclust_methods <- c("ward", "single", "complete", "average",
                    "mcquitty", "median", "centroid")
hclust_results <- lapply(hclust_methods, function(m) hclust(d, m))
names(hclust_results) <- hclust_methods 
hens <- cl_ensemble(list = hclust_results)
summary(c(cl_agreement(hens)))
## Note that the Euclidean agreements are *very* small.
## This is because the ultrametrics differ substantially in height:
u <- lapply(hens, cl_ultrametric)
round(sapply(u, max), 3)
## Rescaling the ultrametrics to [0, 1] gives:
u <- lapply(u, function(x) (x - min(x)) / (max(x) - min(x)))
shens <- cl_ensemble(list = lapply(u, as.cl_dendrogram))
summary(c(cl_agreement(shens)))
## Au contraire ...
summary(c(cl_agreement(hens, method = "cophenetic")))
cl_agreement(hens[1:3], hens[4:5], method = "gamma")