# Classification Trimmed Likelihood Curves

### Description

The function applies `tclust`

several times on a given dataset while parameters `alpha`

and `k`

are altered. The resulting object gives an idea of the optimal trimming level and number of clusters considering a particular dataset.

### Usage

1 2 |

### Arguments

`x` |
A matrix or data frame of dimension |

`k` |
A vector of cluster numbers to be checked. By default cluster numbers from 1 to 5 are examined. |

`alpha` |
A vector containing the alpha levels to be checked. By default alpha levels from 0 to 0.2 (continuously increased by 0.01), are checked. |

`restr.fact` |
The restriction factor passed to |

`...` |
Further arguments (as e.g. |

`trace` |
Defines the tracing level, which is set to |

### Details

These curves show the values of the trimmed classification (log-)likelihoods when altering the trimming proportion `alpha`

and the number of clusters `k`

. The careful examination of these curves provides valuable information for choosing these parameters in a clustering problem. For instance, an appropriate `k`

to be chosen is one that we do not observe a clear increase in the trimmed classification likelihood curve for k with respect to the k+1 curve for almost all the range of alpha values. Moreover, an appropriate choice of parameter alpha may be derived by determining where an initial fast increase of the trimmed classification likelihood curve stops for the final chosen k. A more detailed explanation can be found in García-Escudero et al. (2010).

### Value

The function returns an S3 object of type `ctlcurves`

with components:

`par` |
A list containing all the parameters passed to this function. |

`obj` |
An array containing the objective functions values of each computed cluster-solution. |

`min.weights` |
An array containing the minimum cluster weight of each computed cluster-solution. |

So far there is no output available for `print.ctlcurves`

. Use `plot`

on an `ctlcurves`

object for a graphical interpretation of it.

### Author(s)

Agustin Mayo Iscar, Luis Angel Garcia Escudero, Heinrich Fritz

### References

García-Escudero, L.A.; Gordaliza, A.; Matrán, C. and Mayo-Iscar, A. (2010), "Exploring the number of groups in robust model-based clustering." Statistics and Computing, (Forthcoming).

Preprint available at www.eio.uva.es/infor/personas/langel.html.

### See Also

`plot.ctlcurves`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 | ```
## Not run:
#--- EXAMPLE 1 ------------------------------------------
sig <- diag (2)
cen <- rep (1, 2)
x <- rbind (
rmvnorm (108, cen * 0, sig),
rmvnorm (162, cen * 5, sig * 6 - 2),
rmvnorm (30, cen * 2.5, sig * 50)
)
ctl <- ctlcurves (x, k = 1:4)
## ctl-curves
plot (ctl) ## --> selecting k = 2, alpha = 0.08
## the selected model
plot (tclust (x, k = 2, alpha = 0.08, restr.fact = 7))
#--- EXAMPLE 2 ------------------------------------------
data (geyser2)
ctl <- ctlcurves (geyser2, k = 1:5)
## ctl-curves
plot (ctl) ## --> selecting k = 3, alpha = 0.08
## the selected model
plot (tclust (geyser2, k = 3, alpha = 0.08, restr.fact = 5))
#--- EXAMPLE 3 ------------------------------------------
data (swissbank)
ctl <- ctlcurves (swissbank, k = 1:5, alpha = seq (0, 0.3, by = 0.025))
## ctl-curves
plot (ctl) ## --> selecting k = 2, alpha = 0.1
## the selected model
plot (tclust (swissbank, k = 2, alpha = 0.1, restr.fact = 50))
## End(Not run)
``` |