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 or dissimilarities).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],[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.
For hard partitions, the pair-bonds (Boorman-Arabie $D$) distance is identical to the Rand distance, and can also be written as the Manhattan distance between the co-membership matrices corresponding to the partitions, or equivalently, their symdiff distance, normalized by $n (n - 1)$.
If all components are hierarchies, available built-in methods for measuring dissimilarity between two hierarchies with respective ultrametrics $u$ and $v$ are as follows.
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The measures based on ultrametrics also allow computing dissimilarity
with "dist").
If a user-defined dissimilarity 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
S. A. Boorman and D. C. Olivier (1973).
Metrics on spaces of finite trees.
Journal of Mathematical Psychology, 10, 26--59.
I. Charon, L. Denoeud, A. Guénoche and O. Hudry (2005).
Maximum Transfer Distance Between Partitions.
Technical Report 2005D003, Ecole Nationale Supérieure des
Télécommunications --- Paris.
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.
N. Jardine and E. Sibson (1971). Mathematical Taxonomy. London: Wiley.
M. Meila (2003). Comparing clusterings by the variation of information. In B. Sch��lkopf and M. K. Warmuth (eds.), Learning Theory and Kernel Machines, pages 173--187. Springer-Verlag: Lecture Notes in Computer Science 2777.
C. Rajski (1961). A metric space of discrete probability distributions, Information and Control, 4, 371--377.
J. Rubin (1967). Optimal classification into groups: An approach for solving the taxonomy problem. Journal of Theoretical Biology, 15, 103--144.
D. Zhou, J. Li and H. Zha (2005).
A new Mallows distance based metric for comparing clusterings.
In Proceedings of the 22nd international Conference on Machine
Learning (Bonn, Germany, August 07--11, 2005), pages 1028--1035.
ICML '05, volume 119.
ACM Press, New York, NY.
DOI:
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")
## Hierarchical clustering.
d <- dist(USArrests)
x <- hclust(d)
cl_dissimilarity(x, d, "cophenetic")
cl_dissimilarity(x, d, "gamma")Run the code above in your browser using DataLab