trimkmeans: Trimmed k-means clustering

In trimcluster: Cluster Analysis with Trimming

Description

The trimmed k-means clustering method by Cuesta-Albertos, Gordaliza and Matran (1997). This optimizes the k-means criterion under trimming a portion of the points.

Usage

  trimkmeans(data,k,trim=0.1, scaling=FALSE, runs=100, points=NULL,
                       countmode=runs+1, printcrit=FALSE,
                       maxit=2*nrow(as.matrix(data)))

  ## S3 method for class 'tkm'
print(x, ...)
  ## S3 method for class 'tkm'
plot(x, data, ...)

Arguments

data	matrix or data.frame with raw data
k	integer. Number of clusters.
trim	numeric between 0 and 1. Proportion of points to be trimmed.
scaling	logical. If TRUE, the variables are centered at their means and scaled to unit variance before execution.
runs	integer. Number of algorithm runs from initial means (randomly chosen from the data points).
points	NULL or a matrix with k vectors used as means to initialize the algorithm. If initial mean vectors are specified, runs should be 1 (otherwise the same initial means are used for all runs).
countmode	optional positive integer. Every countmode algorithm runs trimkmeans shows a message.
printcrit	logical. If TRUE, all criterion values (mean squares) of the algorithm runs are printed.
maxit	integer. Maximum number of iterations within an algorithm run. Each iteration determines all points which are closer to a different cluster center than the one to which they are currently assigned. The algorithm terminates if no more points have to be reassigned, or if maxit is reached.
x	object of class tkm.
...	further arguments to be transferred to plot or plotcluster.

Details

plot.tkm calls plotcluster if the dimensionality of the data p is 1, shows a scatterplot with non-trimmed regions if p=2 and discriminant coordinates computed from the clusters (ignoring the trimmed points) if p>2.

Value

An object of class 'tkm' which is a LIST with components

classification	integer vector coding cluster membership with trimmed observations coded as k+1.
means	numerical matrix giving the mean vectors of the k classes.
disttom	vector of squared Euclidean distances of all points to the closest mean.
ropt	maximum value of disttom so that the corresponding point is not trimmed.
k	see above.
trim	see above.
runs	see above.
scaling	see above.

Author(s)

Christian Hennig [e-mail] http://www.homepages.ucl.ac.uk/~ucakche/

References

Cuesta-Albertos, J. A., Gordaliza, A., and Matran, C. (1997) Trimmed k-Means: An Attempt to Robustify Quantizers, Annals of Statistics, 25, 553-576.

See Also

plotcluster

Examples

  set.seed(10001)
  n1 <-60
  n2 <-60
  n3 <-70
  n0 <-10
  nn <- n1+n2+n3+n0
  pp <- 2
  X <- matrix(rep(0,nn*pp),nrow=nn)
  ii <-0
  for (i in 1:n1){
    ii <-ii+1
    X[ii,] <- c(5,-5)+rnorm(2)
  }
  for (i in 1:n2){
    ii <- ii+1
    X[ii,] <- c(5,5)+rnorm(2)*0.75
  }
  for (i in 1:n3){
    ii <- ii+1
    X[ii,] <- c(-5,-5)+rnorm(2)*0.75
  }
  for (i in 1:n0){
    ii <- ii+1
    X[ii,] <- rnorm(2)*8
  }
  tkm1 <- trimkmeans(X,k=3,trim=0.1,runs=3)
# runs=3 is used to save computing time.
  print(tkm1)
  plot(tkm1,X)

Example output

* trimmed k-means *
trim= 0.1 , k= 3 
Classification (trimmed points are indicated by  4 ):
  [1] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 3 3 3 3 3 3 3 4 3 3 3 3 3 3 3 3 3 3
 [38] 3 3 3 4 3 3 3 3 3 3 3 3 4 3 3 3 3 3 3 3 3 3 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2
 [75] 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 2 2 2 2 2 2 2
[112] 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[149] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[186] 1 1 1 1 1 4 4 4 4 4 4 4 4 4 4
Means:
          [,1]      [,2]
[1,] -4.948673 -4.978344
[2,]  5.125058  5.040808
[3,]  5.139695 -5.083246
Trimmed mean squares:  1.214552 

trimcluster documentation built on Feb. 9, 2020, 5:06 p.m.