WeightedCluster

Clustering of states sequences and weighted data.

• Aggregation of identical sequences (in order to save memory and cluster a bigger number of sequences).
• Computation of several clustering quality measure.
• Methods facilitating the choice of the number of groups and cluster algorithm based on cluster quality measures.
• Clustering of weighted data using a distance matrix.
• An optimized PAM algorithm.
• Graphical representation of hierarchical clustering of state sequence (you need to install GraphViz http://www.graphviz.org )

News

• 16.01.2014 New WeightedCluster version 1.2: Speed improvement, bootstrapping cluster quality measure and automatic cluster algorithm comparison using function wcCmpCluster.

WeightedCluster Manuals

Citing WeightedCluster

Help and Contact

Preview

Installation

Some functions of WeightedCluster require the free GraphViz program. It needs to be installed before launching R for these functions to work properly.

The WeightedCluster library can be installed and loaded using the following commands:

install.packages("WeightedCluster")
library(WeightedCluster)

An illustrative example

In this preview, we use the dataset from McVicar and Anyadike 2002 which is distributed with the TraMineR library. This dataset contains sequences of school-to-work transitions in Northern Ireland. The dataset is loaded using :

data(mvad)

wcAggregateCases allows us to identify and aggregate identical state sequences (which are in columns 17:86. We print out the basic information about the aggregation and create the uniqueMvad object which contains only unique sequences.

aggMvad <- wcAggregateCases(mvad[, 17:86])
print(aggMvad)

## Number of disaggregated cases:  712 
## Number of aggregated cases:  490 
## Average aggregated cases:  1.45 
## Average (weighted) aggregation:  1.45

uniqueMvad <- mvad[aggMvad$aggIndex, 17:86]

Using the unique sequence dataset, we build a sequence object and compute dissimilarities between sequences (on this topic, see the TraMineR vignette) . The vector aggMvad$aggWeights store the number of replication of each unique sequence. It is thus used as unique sequence weight.

mvad.seq <- seqdef(uniqueMvad, weights = aggMvad$aggWeights)
diss <- seqdist(mvad.seq, method = "HAM")

Hierarchical clustering

We can regroup similar sequences using hierarchical clustering with "average" method using weights (aggMvad$aggWeights) (any method may be used).

averageClust <- hclust(as.dist(diss), method = "average", members = aggMvad$aggWeights)

The agglomeration schedule can be represented graphically as a tree using:

averageTree <- as.seqtree(averageClust, seqdata = mvad.seq, diss = diss, ncluster = 6)
seqtreedisplay(averageTree, type = "d", border = NA, showdepth = TRUE)

Cluster quality

We can automatically compute several clustering quality measures (presented in table below) for a range of numbers of groups: 2 until ncluster=10.

avgClustQual <- as.clustrange(averageClust, diss, weights = aggMvad$aggWeights,
    ncluster = 10)

Available quality measures

The results can be plotted and used to identify the best number of groups (you can also print them).

plot(avgClustQual)

It is usually easier to choose the number of groups based on standardized scores. Here, five groups seems to be a good solution.

plot(avgClustQual, norm = "zscore")

Alternatively, we can retrieve the two best solutions according to each quality measure:

summary(avgClustQual, max.rank = 2)

##      1. N groups 1.  stat 2. N groups 2.  stat
## PBC           10   0.7616           9    0.761
## HG            10   0.8939           9    0.893
## HGSD          10   0.8910           9    0.890
## ASW            5   0.3966           3    0.393
## ASWw           5   0.4010           6    0.396
## CH             2 181.9886           3  126.780
## R2            10   0.3980           9    0.396
## CHsq           2 338.5174           5  262.451
## R2sq          10   0.6145           9    0.613
## HC            10   0.0598           9    0.060

PAM clustering

The WeightedCluster library also provides an optimized PAM algorithm. We can automatically compute PAM cluster for a range of numbers of groups using:

pamClustRange <- wcKMedRange(diss, kvals = 2:10, weights = aggMvad$aggWeights)

As before, we can plot the quality measures of each solution (not shown here) or retrieve the two best solutions according to each quality measure using:

summary(pamClustRange, max.rank = 2)

##      1. N groups 1.  stat 2. N groups 2.  stat
## PBC            2    0.619           4    0.618
## HG            10    0.845           9    0.845
## HGSD          10    0.842           9    0.842
## ASW            2    0.411           9    0.370
## ASWw           2    0.412           9    0.378
## CH             2  200.286           3  151.245
## R2            10    0.590           9    0.576
## CHsq           2  394.893           4  310.881
## R2sq          10    0.786           9    0.774
## HC             9    0.100          10    0.104

Keeping a solution

The objets returned by as.clustrange or wcKMedRange contain a data.frame with cluster membership (named clustering). For instance, we can plot the sequences according to PAM clustering in 5 groups using:

seqdplot(mvad.seq, group = pamClustRange$clustering$cluster5, border = NA)

Disaggregating data

Once the sequences have been regrouped, it is often useful to “disaggregate” the data. For instance, we may want to add the cluster membership in the original data set (i.e. before unique sequences were identified). This allows us to cross-tabulate cluster membership and father unemployment (variable funemp). This operation is performed using aggMvad$disaggIndex which stores the index of each unique sequence in the original dataset.

uniqueCluster5 <- avgClustQual$clustering$cluster5
mvad$cluster5 <- uniqueCluster5[aggMvad$disaggIndex]
table(mvad$funemp, mvad$cluster5)

##      
##         1   2   3   4   5
##   no  134 348  70  24  19
##   yes  14  69  10  16   8