cca {ConsRankClass} | R Documentation |

## K-Median Cluster Component Analysis

### Description

K-Median Cluster Component Analysis, a distribution-free soft-clustering method for preference rankings.

### Usage

```
cca(X, k, control = ccacontrol(...), ...)
```

### Arguments

`X` |
A n by m data matrix containing preference rankings, in which there are n judges and m objects to be judged. Each row is a ranking of the objects which are represented by the columns. |

`k` |
The number of cluster components |

`control` |
a list of options that control details of the |

`...` |
arguments passed bypassing |

### Details

The user can use any algorithm implemented in the `consrank`

function from the ConsRank package. All algorithms allow the user to set the option 'full=TRUE'
if the median ranking(s) must be searched in the restricted space of permutations instead of in the unconstrained universe of rankings of n items including all possible ties.
There are two classification uncertainty measures: Us and Uprods. "Us" is the geometric
mean of the membership probabilities of each individual, normalized in such a way that
in the case of maximum uncertainty Us=1. "Ucca" is the average of all the "Us".
"Uprods" is the product of the membership probabilities of each individual, normalized in such a way that
in the case of maximum uncertainty Uprods=1. "Uprodscca" is the average of all the "Uprods".

### Value

An object of the class "cca". It contains:

pk | the membership probability matrix | |

clc | cluster centers | |

oclc | cluster centers in terms of orderings | |

idc | crisp partition: id of the cluster component associated with the highest membership probability | |

Hcca | Global homogeneity measure (tau_X rank correlation coefficient) | |

hk | Homogeneity within cluster | |

props | estimated proportion of cases within cluster | |

Us | Uncertainty measure per-individual (see details) | |

Ucca | Global uncertainty measure | |

Uprods | Uncertainty measure per-individual (see details) | |

Uprodscca | Global uncertainty measure | |

consrankout | complete output of rank aggregation algorithm, containing eventually multiple median rankings |

### Author(s)

Antonio D'Ambrosio antdambr@unina.it

### References

D'Ambrosio, A. and Heiser, W.J. (2019). A Distribution-free Soft Clustering Method for Preference Rankings. Behaviormetrika , vol. 46(2), pp. 333–351, DOI: 10.1007/s41237-018-0069-5

Heiser W.J., and D'Ambrosio A. (2013). Clustering and Prediction of Rankings within a Kemeny Distance Framework. In Berthold, L., Van den Poel, D, Ultsch, A. (eds). Algorithms from and for Nature and Life.pp-19-31. Springer international. DOI: 10.1007/978-3-319-00035-0_2.

Ben-Israel, A., and Iyigun, C. (2008). Probabilistic d-clustering. Journal of Classification, 25(1), pp.5-26. DOI: 10.1007/s00357-008-9002-z

### See Also

`ccacontrol`

`ranktree`

### Examples

```
data(Irish)
set.seed(135) #for reproducibility
# CCA with four components
ccares <- cca(Irish$rankings, 4, itercca=10)
summary(ccares)
```

*ConsRankClass*version 1.0.1 Index]