clara: Clustering Large Applications

In cluster: "Finding Groups in Data": Cluster Analysis Extended Rousseeuw et al.

Clustering Large Applications

Description

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

Usage

clara(x, k, metric = c("euclidean", "manhattan", "jaccard", "gower"),
      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)

Arguments

x	data matrix or data frame, each row corresponds to an observation, and each column corresponds to a variable. All variables must be numeric (or logical). 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", "manhattan", "jaccard", and "gower". For the latter, see daisy(). 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.
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, N = 5, is rather small for historical (and now back compatibility) reasons and we recommend to set samples an order of magnitude larger.
sampsize	integer, say j, the 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)). While computational effort is proportional to j^2, see note below, it may still be advisable to set j = sampsize to a larger value than the (historical) default.
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, keep.data must be false as well, and the medoid indices, i.e., row numbers of the medoids will still be returned (i.med component), and the algorithm saves space by needing one copy less of x.
keep.data	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.
pamLike	logical indicating if the “swap” phase (see pam, in C code) should use the same algorithm as pam(). Note that from Kaufman and Rousseeuw's description this should have been true always, but as the original Fortran code and the subsequent port to C has always contained a small one-letter change (a typo according to Martin Maechler) with respect to PAM, the default, pamLike = FALSE has been chosen to remain back compatible rather than “PAM compatible”.
correct.d	logical or integer indicating that—only in the case of NAs present in x—the correct distance computation should be used instead of the wrong formula which has been present in the original Fortran code and been in use up to early 2016. 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 correct.d.

Details

clara (for "euclidean" and "manhattan") 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.

Value

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.

Note

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 \times 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 \times p \times j^2 \times 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.

Author(s)

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.

Kasper Fischer-Rasmussen provided R and C code for metric = "gower".

See Also

agnes for background and references; clara.object, pam, partition.object, plot.partition.

Examples

## 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
}

cluster documentation built on Nov. 28, 2023, 1:07 a.m.