| fanny(cluster) | R Documentation |
Returns a list representing a fuzzy clustering of the data into k
clusters.
fanny(x, k, diss = F, metric = "euclidean", stand = F)
x |
data matrix or dataframe, or dissimilarity matrix, depending on the
value of the diss argument.
In case of a matrix or dataframe, each row corresponds to an observation, and each column corresponds to a variable. All variables must be numeric. Missing values (NAs) are allowed.
In case of a dissimilarity matrix,
|
k |
integer, the number of clusters.
It is required that 0 < k < n/2 where n is the number of observations.
|
diss |
logical flag: if TRUE, then x will be considered as a dissimilarity
matrix. If FALSE, then x will be considered as a matrix of observations
by variables.
|
metric |
character string specifying the metric to be used for calculating
dissimilarities between observations.
The currently available options are "euclidean" and "manhattan".
Euclidean distances are root sum-of-squares of differences, and
manhattan distances are the sum of absolute differences.
If x is already a dissimilarity matrix, then this argument will
be ignored.
|
stand |
logical flag: if TRUE, then the measurements in x are standardized before
calculating the dissimilarities. Measurements are standardized for each
variable (column), by subtracting the variable's mean value and dividing by
the variable's mean absolute deviation.
If x is already a dissimilarity matrix, then this argument
will be ignored.
|
In a fuzzy clustering, each observation is "spread out" over the various
clusters. Denote by u(i,v) the membership of observation i to cluster v.
The memberships are nonnegative, and for a fixed observation i they sum to 1.
The particular method fanny stems from chapter 4 of
Kaufman and Rousseeuw (1990).
Compared to other fuzzy clustering methods, fanny has the following
features: (a) it also accepts a dissimilarity matrix; (b) it is
more robust to the spherical cluster assumption; (c) it provides
a novel graphical display, the silhouette plot (see plot.partition).
Fanny aims to minimize the objective function
SUM_v (SUM_(i,j) u(i,v)^2 u(j,v)^2 d(i,j)) / (2 SUM_j u(j,v)^2)
where n is the number of observations, k is the number of clusters and d(i,j) is the dissimilarity between observations i and j.
an object of class "fanny" representing the clustering.
See fanny.object for details.
Cluster analysis divides a dataset into groups (clusters) of observations that
are similar to each other. Partitioning methods like pam, clara, and
fanny require that the number of clusters be given by the user.
Hierarchical methods like agnes, diana, and mona construct a
hierarchy of clusterings, with the number of clusters ranging from one to
the number of observations.
Kaufman, L. and Rousseeuw, P.J. (1990). Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York.
Anja Struyf, Mia Hubert & Peter J. Rousseeuw (1996): Clustering in an Object-Oriented Environment. Journal of Statistical Software, 1. http://www.stat.ucla.edu/journals/jss/
Struyf, A., Hubert, M. and Rousseeuw, P.J. (1997). Integrating Robust Clustering Techniques in S-PLUS, Computational Statistics and Data Analysis, 26, 17-37.
fanny.object, daisy, partition.object, plot.partition, dist.
## generate 25 objects, divided into two clusters, and 3 objects lying
## between those clusters.
x <- rbind(cbind(rnorm(10,0,0.5), rnorm(10,0,0.5)),
cbind(rnorm(15,5,0.5), rnorm(15,5,0.5)),
cbind(rnorm(3,3.5,0.5), rnorm(3,3.5,0.5)))
fannyx <- fanny(x, 2)
fannyx
summary(fannyx)
plot(fannyx)
data(ruspini)
## Plot similar to Figure 6 in Stryuf et al (1996)
plot(fanny(ruspini, 5))