clara: Clustering Large Applications
In pimentel/cluster: Cluster Analysis Extended Rousseeuw et al.

Description Usage Arguments Details Value Note Author(s) See Also Examples

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

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clara(x, k, metric = "euclidean", stand = FALSE, samples = 5,
      sampsize = min(n, 40 + 2 * k), trace = 0, medoids.x = TRUE,
      keep.data = medoids.x, rngR = FALSE, pamLike = 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. The default, `5`, is rather small for historical (and now back compatibility) reasons and we recommend to set `samples` an order of magnitude larger.
`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`, `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”.

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.

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 = \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. 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)

## `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
}