clara {cluster}R Documentation

Clustering Large Applications


Computes a "clara" object, a list representing a clustering of the data into k clusters.


clara(x, k, metric = "euclidean", stand = FALSE, samples = 5,
      sampsize = min(n, 40 + 2 * k), trace = 0, medoids.x = TRUE, = medoids.x, rngR = FALSE)


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 = nrow(x)).
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.
stand logical, indicating if 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.
samples integer, number of samples to be drawn from the dataset.
sampsize integer, number of observations in each sample. sampsize should be higher than the number of clusters (k) and at most the number of observations (n = nrow(x)).
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 x. If FALSE, must be false as well, and the medoid indices, i.e., row numbers of the medoids will still be returned ( component), and the algorithm saves space by needing one copy less of x. logical indicating if the (scaled if stand is true) data should be kept in the result. Setting this to FALSE saves memory (and hence time), but disables clusplot()ing of the result. Use medoids.x = FALSE to save even more memory.
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 clara() returns a different result – though only slightly different in good situations.


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 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 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.


an object of class "clara" representing the clustering. See clara.object for details.


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 = sampsize, and (n,p) = dim(x). The CPU computing time (again assuming small k) is about O(n * p * j^2 * N), where N = 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; later, the authors said “small (say with fewer than 200 observations)”...


Kaufman and Rousseeuw (see agnes), originally. All arguments from trace on, and most R documentation and all tests by Martin Maechler.

See Also

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)

## `xclara' is an artificial data set with 3 clusters of 1000 bivariate
## objects each.
(clx3 <- clara(xclara, 3))
## 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

[Package cluster version 1.11.5 Index]