Dissimilarity-based Clustering
Dissimilarity-based clustering groups units of analysis (in our case,
sessions, since that is what we provided as actor) by
directly comparing their observed sequences. In our case, each session
is represented by its sequence of actions, and similarity between
sessions is defined using a distance metric that quantifies how
different two sequences are.
To implement this method using Nestimate, we can use the
cluster_data() function, which takes either raw sequence
data or a network object such as the net object that we
estimated (which also contains the original sequences in
$data):
clust <- cluster_data(net, k = 3)
clust
#> Sequence Clustering
#> Method: pam
#> Dissimilarity: hamming
#> Clusters: 3
#> Silhouette: 0.1311
#> Cluster sizes: 48, 103, 104
#> Medoids: 238, 3, 21The default clustering mechanism uses Hamming distance (number of positions where sequences differ) with PAM (Partitioning Around Medoids).
The result contains the cluster assignments (which
cluster each session belongs to), the cluster sizes, and a
silhouette score that reflects the quality of the
clustering (higher values indicate better separation between clusters),
among other useful information.
# Cluster assignments (first 20 sessions)
head(clust$assignments, 20)
#> [1] 1 2 2 3 3 3 3 2 1 1 2 2 3 1 2 3 3 3 3 1
# Cluster sizes
clust$sizes
#> 1 2 3
#> 48 103 104
# Silhouette score (clustering quality: higher is better)
clust$silhouette
#> [1] 0.1310654Visualizing Clusters
The silhouette plot shows how well each sequence fits its assigned cluster. Values near 1 indicate good fit; values near 0 suggest the sequence is between clusters; negative values indicate possible misclassification.
The MDS (multidimensional scaling) plot projects the distance matrix to
2D, showing cluster separation.
Distance Metrics
A distance metric defines how (dis)similarity between sequences is
measured. In other words, it quantifies how different two sequences are
from each other. Nestimate currently supports 9 distance
metrics for comparing sequences:
| Metric | Description | Best for |
|---|---|---|
hamming |
Positions where sequences differ | Equal-length sequences |
lv |
Levenshtein (edit distance) | Variable-length, insertions/deletions |
osa |
Optimal string alignment | Edit distance + transpositions |
dl |
Damerau-Levenshtein | Full edit + adjacent transpositions |
lcs |
Longest common subsequence | Preserving order, ignoring gaps |
qgram |
Q-gram frequency difference | Pattern-based similarity |
cosine |
Cosine of q-gram vectors | Normalized pattern similarity |
jaccard |
Jaccard index of q-grams | Set-based pattern overlap |
jw |
Jaro-Winkler | Short strings, typo detection |
Different metrics may produce different clustering results. You need to choose this based on your research question:
- Hamming: compares sequences position by position (best for aligned sequences of equal length).
- Edit distances (lv, osa, dl): allow insertions and deletions (best when sequences may be shifted or vary in length).
- LCS: captures shared subsequences (best when overall patterns matter more than exact alignment).
We can specify which distance metric we want to use through the
dissimilarity argument:
# Levenshtein distance (allows insertions/deletions)
clust_lv <- cluster_data(net, k = 3, dissimilarity = "lv")
clust_lv$silhouette
#> [1] 0.1593732
# Longest common subsequence
clust_lcs <- cluster_data(net, k = 3, dissimilarity = "lcs")
clust_lcs$silhouette
#> [1] 0.01282205Some distance metrics may take additional arguments. For example, the Hamming distance accepts temporal weighting to emphasize earlier or later positions:
Clustering Methods
By default, Nestimate uses PAM (Partitioning Around Medoids) to form
clusters, which assigns each sequence to the cluster represented by the
most central sequence (the medoid). Besides PAM, Nestimate
supports hierarchical clustering methods, which build clusters step by
step by progressively merging similar units into a tree-like structure
(a dendrogram):
ward.D2(“Ward’s Method, Squared Distances”): Minimizes the increase in within-cluster variance using squared distances. Typically produces compact, well-separated clusters.ward.D(“Ward’s Method”): An alternative implementation of Ward’s approach using a different distance formulation. Similar behavior, but results may vary slightly.complete(“Complete Linkage”): Defines the distance between clusters as the maximum distance between their members. Produces tight, compact clusters.average(“Average Linkage”): Uses the average distance between all pairs of points across clusters. Provides a balance between compactness and flexibility.single(“Single Linkage”): Uses the minimum distance between points in two clusters. Can capture chain-like structures but may lead to - loosely connected clusters.mcquitty(“McQuitty’s Method” / “WPGMA”): A weighted version of average linkage that gives equal weight to clusters regardless of size.centroid(“Centroid Linkage”): Defines cluster distance based on the distance between cluster centroids (means). Can produce intuitive groupings but may introduce inconsistencies in the hierarchy.
To use any of these methods instead of PAM, we need to provide the
method argument to cluster_data.
Choosing k (Number of Clusters)
To choose the right clustering solution and method, we need to compare the silhouette scores across different k values and clustering methods (and also distance metrics if we want):
methods <- c("pam", "ward.D2", "complete", "average")
silhouettes <- lapply(methods, function(m) {
sapply(2:4, function(k) {
cluster_data(net, k = k, method = m, seed = 42)$silhouette
})
})
names(silhouettes) <- methods
silhouettes
#> $pam
#> [1] 0.1967176 0.1310654 0.1776923
#>
#> $ward.D2
#> [1] 0.8981822 0.7282214 0.6905967
#>
#> $complete
#> [1] 0.8981822 0.8310706 0.7821299
#>
#> $average
#> [1] 0.8981822 0.8310706 0.7821299methods <- names(silhouettes)
colors <- rainbow(length(methods))
plot(2:4, silhouettes[[1]], type = "b", pch = 19, col = colors[1],
xlab = "Number of clusters (k)",
ylab = "Average silhouette width",
ylim = c(0, 1),
main = "Choosing k")
for (i in 2:length(methods)) {
lines(2:4, silhouettes[[i]], type = "b", pch = 19, col = colors[i])
}
legend("topright", legend = methods, col = colors, lty = 1, pch = 19)
Higher silhouette scores indicate better-defined clusters. Look for
an “elbow” or maximum. Here we select ward.D2 with 2
clusters, which yields a reasonable silhouette width.