This function searches for k (or less) spherical clusters
in a data matrix x, whereas the ceiling(alpha n) most outlying
observations are trimmed.
tkmeans(
x,
k,
alpha = 0.05,
nstart = 500,
niter1 = 3,
niter2 = 20,
nkeep = 5,
iter.max,
points = NULL,
center = FALSE,
scale = FALSE,
store_x = TRUE,
parallel = FALSE,
n.cores = -1,
zero_tol = 1e-16,
drop.empty.clust = TRUE,
trace = 0
)The function returns the following values:
cluster - A numerical vector of size n containing the cluster assignment
for each observation. Cluster names are integer numbers from 1 to k, 0 indicates
trimmed observations. Note that it could be empty clusters with no observations
when equal.weights=FALSE.
obj - The value of the objective function of the best (returned) solution.
size - An integer vector of size k, returning the number of observations contained by each cluster.
centers - A matrix of size p x k containing the centers (column-wise) of each cluster.
code - A numerical value indicating if the concentration steps have converged for the returned solution (2).
cluster.ini - A matrix with nstart rows and number of columns equal to
the number of observations and where each row shows the final clustering
assignments (0 for trimmed observations) obtained after the niter1
iteration of the nstart random initializations.
obj.ini - A numerical vector of length nstart containing the values
of the target function obtained after the niter1 iteration of the
nstart random initializations.
x - The input data set.
k - The input number of clusters.
alpha - The input trimming level.
A matrix or data.frame of dimension n x p, containing the observations (row-wise).
The number of clusters initially searched for.
The proportion of observations to be trimmed.
The number of random initializations to be performed.
The number of concentration steps to be performed for the nstart initializations.
The maximum number of concentration steps to be performed for the
nkeep solutions kept for further iteration. The concentration steps are
stopped, whenever two consecutive steps lead to the same data partition.
The number of iterated initializations (after niter1 concentration steps) with the best values in the target function that are kept for further iterations
(deprecated, use the combination nkeep, niter1 and niter2)
The maximum number of concentration steps to be performed.
The concentration steps are stopped, whenever two consecutive steps lead
to the same data partition.
Optional initial mean vectors, NULL or a matrix with k
vectors used as means to initialize the algorithm. If initial mean vectors are
specified, nstart should be 1 (otherwise the same initial means are
used for all runs).
Optional centering of the data: a function or a vector of length p which can optionally be specified for centering x before calculation
Optional scaling of the data: a function or a vector of length p which can optionally be specified for scaling x before calculation
A logical value, specifying whether the data matrix x shall be
included in the result object. By default this value is set to TRUE, because
some of the plotting functions depend on this information. However, when big data
matrices are handled, the result object's size can be decreased noticeably
when setting this parameter to FALSE.
A logical value, specifying whether the nstart initializations should be done in parallel.
The number of cores to use when paralellizing, only taken into account if parallel=TRUE.
The zero tolerance used. By default set to 1e-16.
Logical value specifying, whether empty clusters shall be omitted in the resulting object. (The result structure does not contain center estimates of empty clusters anymore. Cluster names are reassigned such that the first l clusters (l <= k) always have at least one observation.
Defines the tracing level, which is set to 0 by default. Tracing level 1 gives additional information on the stage of the iterative process.
Valentin Todorov, Luis Angel Garcia Escudero, Agustin Mayo Iscar.
Cuesta-Albertos, J. A.; Gordaliza, A. and Matrán, C. (1997), "Trimmed k-means: an attempt to robustify quantizers". Annals of Statistics, Vol. 25 (2), 553-576.
# \dontshow{
set.seed(0)
# }
##--- EXAMPLE 1 ------------------------------------------
sig <- diag(2)
cen <- rep(1,2)
x <- rbind(MASS::mvrnorm(360, cen * 0, sig),
MASS::mvrnorm(540, cen * 5, sig),
MASS::mvrnorm(100, cen * 2.5, sig))
## Two groups and 10\% trimming level
(clus <- tkmeans(x, k = 2, alpha = 0.1))
plot(clus)
plot(clus, labels = "observation")
plot(clus, labels = "cluster")
#--- EXAMPLE 2 ------------------------------------------
data(geyser2)
(clus <- tkmeans(geyser2, k = 3, alpha = 0.03))
plot(clus)
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