# Compute distances to the center of a group

### Description

Computes the dissimilarity between objects and their group center from their pairwise dissimilarity matrix.

### Usage

1 2 |

### Arguments

`diss` |
a dissimilarity matrix such as generated by |

`group` |
if |

`medoids.index` |
if |

`allcenter` |
logical. If |

`weights` |
optional numerical vector containing weights. |

`squared` |
Logical. If |

### Details

This function computes the dissimilarity between given objects and their group center. It is possible that the group center does not belong to the space formed by the objects (in the same way as the average of integer numbers is not necessarily an integer itself).
This distance can also be understood as the contribution to the discrepancy (see `dissvar`

).
Note that when the dissimilarity measure does not respect the triangle inequality, the dissimilarity between a given object and its group center may be negative

It can be shown that this dissimilarity is equal to (see Batagelj 1988):

*d_(xg)=1/n *(sum d_xi - SS)*

where *SS* is the sum of squares (see `dissvar`

).

### Value

A vector with the dissimilarity to the group center for each object, or a list of medoid indexes.

### Author(s)

Matthias Studer (with Gilbert Ritschard for the help page)

### References

Studer, M., G. Ritschard, A. Gabadinho and N. S. Müller (2011). Discrepancy analysis of state sequences, *Sociological Methods and Research*, Vol. 40(3), 471-510.

Studer, M., G. Ritschard, A. Gabadinho and N. S. Müller (2010)
Discrepancy analysis of complex objects using dissimilarities.
In F. Guillet, G. Ritschard, D. A. Zighed and H. Briand (Eds.),
*Advances in Knowledge Discovery and Management*,
Studies in Computational Intelligence, Volume 292, pp. 3-19. Berlin: Springer.

Studer, M., G. Ritschard, A. Gabadinho and N. S. Müller (2009)
Analyse de dissimilarités par arbre d'induction. In EGC 2009,
*Revue des Nouvelles Technologies de l'Information*, Vol. E-15, pp. 7–18.

Batagelj, V. (1988) Generalized ward and related clustering problems. In H. Bock (Ed.),
*Classification and related methods of data analysis*, Amsterdam: North-Holland, pp. 67–74.

### See Also

`dissvar`

to compute the pseudo variance from dissimilarities and for a basic introduction to concepts of pseudo variance analysis

`dissassoc`

to test association between objects represented by their dissimilarities and a covariate.

`disstree`

for an induction tree analyse of objects characterized by a dissimilarity matrix.

`dissmfac`

to perform multi-factor analysis of variance from pairwise dissimilarities.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
## Defining a state sequence object
data(mvad)
mvad.seq <- seqdef(mvad[, 17:86])
## Building dissimilarities (any dissimilarity measure can be used)
mvad.ham <- seqdist(mvad.seq, method="HAM")
## Compute distance to center according to group gcse5eq
dc <- disscenter(mvad.ham, group=mvad$gcse5eq)
## Ploting distribution of dissimilarity to center
boxplot(dc~mvad$gcse5eq, col="cyan")
## Retrieving index of the first medoids, one per group
dc <- disscenter(mvad.ham, group=mvad$Grammar, medoids.index="first")
print(dc)
## Retrieving index of all medoids in each group
dc <- disscenter(mvad.ham, group=mvad$Grammar, medoids.index="all")
print(dc)
``` |