# clara

##### Clustering Large Applications

Computes a `"clara"`

object, a list representing a clustering of
the data into `k`

clusters.

- Keywords
- cluster

##### Usage

```
clara(x, k, metric = c("euclidean", "manhattan", "jaccard"),
stand = 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. 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", 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

`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, 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

`NA`

s 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`

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.

##### Value

an object of class `"clara"`

representing the clustering. See
`clara.object`

for details.

##### 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.

##### See Also

`agnes`

for background and references;
`clara.object`

, `pam`

,
`partition.object`

, `plot.partition`

.

##### Examples

```
# NOT RUN {
## 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$clusinfo
## using pamLike=TRUE gives the same (apart from the 'call'):
all.equal(clarax[-8],
clara(x, 2, samples=50, pamLike = TRUE)[-8])
plot(clarax)
## `xclara' is an artificial data set with 3 clusters of 1000 bivariate
## objects each.
data(xclara)
(clx3 <- clara(xclara, 3))
## "better" number of samples
cl.3 <- clara(xclara, 3, samples=100)
## but that did not change the result here:
stopifnot(cl.3$clustering == clx3$clustering)
## Plot similar to Figure 5 in Struyf et al (1996)
# }
# NOT RUN {
plot(clx3, ask = TRUE)
# }
# NOT RUN {
## Try 100 times *different* random samples -- for reliability:
nSim <- 100
nCl <- 3 # = no.classes
set.seed(421)# (reproducibility)
cl <- matrix(NA,nrow(xclara), nSim)
for(i in 1:nSim)
cl[,i] <- clara(xclara, nCl, medoids.x = FALSE, rngR = TRUE)$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
}
# }
```

*Documentation reproduced from package cluster, version 2.0.7-1, License: GPL (>= 2)*