Clustering Large Applications
Computes a "clara" object, a list representing a
clustering of the data into k clusters.
clara(x, k, metric = c("euclidean", "manhattan", "jaccard"),
stand = FALSE, cluster.only = FALSE, samples = 5,
sampsize = min(n, 40 + 2 * k), trace = 0, medoids.x = TRUE,
keep.data = medoids.x, rngR = FALSE, pamLike = FALSE, correct.d = TRUE)x |
data matrix or data frame, each row corresponds to an observation, and each column corresponds to a variable. All variables must be numeric. Missing values (NAs) are allowed. |
k |
integer, the number of clusters.
It is required that 0 < k < n where n is the number of
observations (i.e., n = |
metric |
character string specifying the metric to be used for calculating dissimilarities between observations. The currently available options are "euclidean", "manhattan", and "jaccard". Euclidean distances are root sum-of-squares of differences, and manhattan distances are the sum of absolute differences. |
stand |
logical, indicating if the measurements in |
cluster.only |
logical; if true, only the clustering will be computed and returned, see details. |
samples |
integer, say N, the number of samples to be drawn from the
dataset. The default, |
sampsize |
integer, say j, the number of observations in each
sample. |
trace |
integer indicating a trace level for diagnostic output during the algorithm. |
medoids.x |
logical indicating if the medoids should be
returned, identically to some rows of the input data |
keep.data |
logical indicating if the (scaled if
|
rngR |
logical indicating if R's random number generator should
be used instead of the primitive clara()-builtin one. If true, this
also means that each call to |
pamLike |
logical indicating if the “swap” phase (see
|
correct.d |
logical or integer indicating that—only in the case
of Because the new correct formula is not back compatible, for the time
being, a warning is signalled in this case, unless the user explicitly
specifies |
clara is fully described in chapter 3 of Kaufman and Rousseeuw (1990).
Compared to other partitioning methods such as pam, it can deal with
much larger datasets. Internally, this is achieved by considering
sub-datasets of fixed size (sampsize) such that the time and
storage requirements become linear in n rather than quadratic.
Each sub-dataset is partitioned into k clusters using the same
algorithm as in pam.
Once k representative objects have been selected from the
sub-dataset, each observation of the entire dataset is assigned
to the nearest medoid.
The mean (equivalent to the sum) of the dissimilarities of the observations to their closest medoid is used as a measure of the quality of the clustering. The sub-dataset for which the mean (or sum) is minimal, is retained. A further analysis is carried out on the final partition.
Each sub-dataset is forced to contain the medoids obtained from the
best sub-dataset until then. Randomly drawn observations are added to
this set until sampsize has been reached.
When cluster.only is true, the result is simply a (possibly
named) integer vector specifying the clustering, i.e.,clara(x,k, cluster.only=TRUE) is the same as clara(x,k)$clustering but computed more efficiently.
If cluster.only is false (as by default),
an object of class "clara" representing the clustering. See
clara.object for details.
If cluster.only is true, the result is the "clustering", an
integer vector of length n with entries from 1:k.
By default, the random sampling is implemented with a very
simple scheme (with period 2^{16} = 65536) inside the Fortran
code, independently of R's random number generation, and as a matter
of fact, deterministically. Alternatively, we recommend setting
rngR = TRUE which uses R's random number generators. Then,
clara() results are made reproducible typically by using
set.seed() before calling clara.
The storage requirement of clara computation (for small
k) is about
O(n * p) + O(j^2) where
j = \code{sampsize}, and (n,p) = \code{dim(x)}.
The CPU computing time (again assuming small k) is about
O(n * p * j^2 * N), where
N = \code{samples}.
For “small” datasets, the function pam can be used
directly. What can be considered small, is really a function
of available computing power, both memory (RAM) and speed.
Originally (1990), “small” meant less than 100 observations;
in 1997, the authors said “small (say with fewer than 200
observations)”; as of 2006, you can use pam with
several thousand observations.
Kaufman and Rousseeuw (see agnes), originally.
Metric "jaccard": Kamil Kozlowski (@ownedoutcomes.com)
and Kamil Jadeszko.
All arguments from trace on, and most R documentation and all
tests by Martin Maechler.
agnes for background and references;
clara.object, pam,
partition.object, plot.partition.
## generate 500 objects, divided into 2 clusters.
x <- rbind(cbind(rnorm(200,0,8), rnorm(200,0,8)),
cbind(rnorm(300,50,8), rnorm(300,50,8)))
clarax <- clara(x, 2, samples=50)
clarax
clarax$clusinfo
## using pamLike=TRUE gives the same (apart from the 'call'):
all.equal(clarax[-8],
clara(x, 2, samples=50, pamLike = TRUE)[-8])
plot(clarax)
## cluster.only = TRUE -- save some memory/time :
clclus <- clara(x, 2, samples=50, cluster.only = TRUE)
stopifnot(identical(clclus, clarax$clustering))
## 'xclara' is an artificial data set with 3 clusters of 1000 bivariate
## objects each.
data(xclara)
(clx3 <- clara(xclara, 3))
## "better" number of samples
cl.3 <- clara(xclara, 3, samples=100)
## but that did not change the result here:
stopifnot(cl.3$clustering == clx3$clustering)
## Plot similar to Figure 5 in Struyf et al (1996)
## Not run: plot(clx3, ask = TRUE)
## Try 100 times *different* random samples -- for reliability:
nSim <- 100
nCl <- 3 # = no.classes
set.seed(421)# (reproducibility)
cl <- matrix(NA,nrow(xclara), nSim)
for(i in 1:nSim)
cl[,i] <- clara(xclara, nCl, medoids.x = FALSE, rngR = TRUE)$cluster
tcl <- apply(cl,1, tabulate, nbins = nCl)
## those that are not always in same cluster (5 out of 3000 for this seed):
(iDoubt <- which(apply(tcl,2, function(n) all(n < nSim))))
if(length(iDoubt)) { # (not for all seeds)
tabD <- tcl[,iDoubt, drop=FALSE]
dimnames(tabD) <- list(cluster = paste(1:nCl), obs = format(iDoubt))
t(tabD) # how many times in which clusters
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