TraMineR (version 1.6-2)

dissrep: Extracting sets of representative objects using a dissimilarity matrix

Description

The function extracts a set of representative objects that exhibits the key features of the whole data set, the goal being to get easy sounded interpretation of the latter. The user can set either the desired coverage level (the proportion of objects having a representative in their neighborhood) or the desired number of representatives.

Usage

dissrep(diss, criterion="density",
    score=NULL, decreasing=TRUE,
    trep=0.25, nrep=NULL, tsim=0.1, dmax=NULL)

Arguments

diss

A dissimilarity matrix or a dist object (see dist)

criterion

the representativeness criterion for sorting the candidate list. One of "freq" (frequency), "density" (neighborhood density) or "dist" (centrality). An optional vector containing the scores for sorting the candida

score

an optional vector containing the representativeness scores used for sorting the objects in the candidate list. The length of the vector must be equal to the number of rows/columns in the distance matrix, i.e the number of objects.

decreasing

if a score vector is provided, indicates whether the objects in the candidate list must be sorted in ascending or decreasing order of this score. The first object in the candidate list is supposed to be the most representative.

trep

controls the size of the representative set by setting the desired coverage level, i.e the proportion of objects having a representative in their neighborhood. Neighborhood radius is defined by tsim.

nrep

number of representatives. If NULL (default), trep argument is used to control the size of the representative set.

tsim

threshold for setting the redundancy and neighborhood radius. Defined as a percentage of the maximum (theoretical) distance. Defaults to 0.1 (10%). Object $y$ is considered as redundant to/in the neighborhood of object $x$ if the distance from $y$ to

dmax

maximum theoretical distance. Redundancy and neighborhood diameters are defined as a proportion of this maximum theoretical distance. If NULL, it is derived from the distance matrix.

Value

• An object of class diss.rep. This is a vector containing the indexes of the representative objects with the following additional attributes:
• Scores
  a vector with the representative score of each object given the chosen criterion.
• Distances
  a matrix with the distance of each object to its nearest representative.
• Statistics
  contains several quality measures for each representative in the set: number of objects attributed to the representative, number of object in the representatives neighborhood, mean distance to the representative.
• Quality
  overall quality measure.
• Print and summary methods are available.

encoding

latin1

Details

The representative set is obtained by an heuristic that first builds a sorted list of candidates using a representativeness score and then eliminates redundancy. The available criterions for sorting the candidate list are: sequence frequency, neighborhood density, centrality. Other user defined sorting criterions can be provided using the score argument. The frequency criterion uses the frequencies as representativeness score. The frequency of an object in the data is computed as the number of other objects with whom the dissimilarity is equal to 0. The more frequent an object the more representative it is supposed to be. Hence, objects are sorted in decreasing frequency order. Indeed, this criterion is the neighborhood (see below) criterion with the neighborhood diameter set to 0. The neighborhood density criterion uses the number---density---of objects in the neighborhood of each candidate. This requires indeed to set the neighborhood diameter. We suggest to set it as a given proportion of the maximal (theoretical) distance between two objects. Candidates are sorted in decreasing density order. The centrality criterion uses the sum of distances to all other objects, i.e. the centrality as a representativeness criterion. The smallest the sum, the most representative the candidate. For more details, see Gabadinho et al., 2009.

References

Gabadinho, A., G. Ritschard, M. Studer and N. S. M�ller (2009). Summarizing Sets of Categorical Sequences, In International Conference on Knowledge Discovery and Information Retrieval, Madeira, 6-8 October, INSTICC.

See Also

seqrep, plot.stslist.rep

Examples

## Defining a sequence object with the data in columns 10 to 25
## (family status from age 15 to 30) in the biofam data set
data(biofam)
biofam.lab <- c("Parent", "Left", "Married", "Left+Marr",
"Child", "Left+Child", "Left+Marr+Child", "Divorced")
biofam.seq <- seqdef(biofam, 10:25, labels=biofam.lab)

## Computing the distance matrix
costs <- seqsubm(biofam.seq, method="TRATE")
biofam.om <- seqdist(biofam.seq, method="OM", sm=costs)

## Representative set using the neighborhood density criterion
biofam.rep <- dissrep(biofam.om)
biofam.rep
summary(biofam.rep)