cl_dissimilarity(x, y = NULL, method = "euclidean")cl_ensemble).NULL (default), or as for x.y is NULL, an object of class
"cl_dissimilarity" containing the dissimilarities between all
pairs of components of x. Otherwise, an object of class
"cl_cross_dissimilarity" with the dissimilarities between the
components of x and the components of y.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).If all components are partitions, the following built-in methods for measuring dissimilarity 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]
For hard partitions, both Manhattan and squared Euclidean dissimilarity give twice the transfer distance (Charon et al., 2005), which is the minimum number of objects that must be removed so that the implied partitions (restrictions to the remaining objects) are identical. This is also known as the $R$-metric in Day (1981), i.e., the number of augmentations and removals of single objects needed to transform one partition into the other, and the partition-distance in Gusfield (2002), and equals twice the number of single element moves distance of Boorman and Arabie.
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]
If a user-defined agreement method is to be employed, it must be a function taking two clusterings as its arguments.
Symmetric dissimilarity objects of class "cl_dissimilarity" are
implemented as symmetric proximity objects with self-proximities
identical to zero, 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 dissimilarity) object of class
"cl_cross_dissimilarity".
Symmetric dissimilarity objects also inherit from class
"dist" (although they currently do not
A. D. Gordon and M. Vichi (2001). Fuzzy partition models for fitting a set of partitions. Psychometrika, 66, 229--248.
D. Gusfield (2002). Partition-distance: A problem and class of perfect graphs arising in clustering. Information Processing Letters, 82, 159--164.
C. Rajski (1961). A metric space of discrete probability distributions, Information and Control, 4, 371--377.
J. Rubin, J (1967). Optimal classification into groups: An approach for solving the taxonomy problem. Journal of Theoretical Biology, 15, 103--144.
cl_agreement## An ensemble of partitions.
data("CKME")
pens <- CKME[1 : 30]
diss <- cl_dissimilarity(pens)
summary(c(diss))
cl_dissimilarity(pens[1:5], pens[6:7])
## Equivalently, using subscripting.
diss[1:5, 6:7]
## Can use the dissimilarities for "secondary" clustering
## (e.g. obtaining hierarchies of partitions):
hc <- hclust(diss)
plot(hc)
## Example from Boorman and Arabie (1972).
P1 <- as.cl_partition(c(1, 2, 2, 2, 3, 3, 2, 2))
P2 <- as.cl_partition(c(1, 1, 2, 2, 3, 3, 4, 4))
cl_dissimilarity(P1, P2, "BA/A")
cl_dissimilarity(P1, P2, "BA/C")Run the code above in your browser using DataLab