Sequence Distances, Clustering, and Stability
In gp3sequences: Transparent Analysis of Ordered Categorical Sequences

knitr::opts_chunk$set(collapse = TRUE, comment = "#>")
library(gp3sequences)

Synthetic paths

paths <- list(
  s1 = c("A", "B", "C", "D"),
  s2 = c("A", "B", "C", "C"),
  s3 = c("A", "C", "C", "D"),
  s4 = c("D", "C", "B", "A"),
  s5 = c("D", "C", "A", "A"),
  s6 = c("D", "B", "B", "A")
)
sequence_data <- do.call(rbind, lapply(seq_along(paths), function(i) {
  data.frame(sequence_id = names(paths)[i],
             sequence_order = seq_along(paths[[i]]),
             state = paths[[i]], stringsAsFactors = FALSE)
}))

Transparent distance families

levenshtein <- compute_sequence_distance(sequence_data, method = "levenshtein")
lcs <- compute_sequence_distance(sequence_data, method = "lcs")
om <- compute_sequence_distance(
  sequence_data,
  method = "optimal_matching",
  indel_cost = 1,
  substitution_cost = 2,
  normalise = "max_length"
)
transition <- compute_sequence_distance(sequence_data, method = "transition")
summarise_sequence_distance(lcs)$overall

The distance method and all costs are retained as object attributes. The transition method compares first-order transition-probability profiles; it is not a general stochastic-process model.

Clustering and validation

fit <- cluster_sequences(lcs, k = 2L, method = "hierarchical", linkage = "average")
fit$assignments
validate_sequence_clusters(fit)$overall
extract_representative_sequences(fit)

Subsampling stability

stability <- bootstrap_sequence_clusters(
  lcs,
  k = 2L,
  n_boot = 20L,
  sample_fraction = 0.8,
  seed = 100L
)
summarise_sequence_cluster_stability(stability)$overall

Cluster stability describes reproducibility under the selected resampling and clustering settings. It does not establish that the clusters are natural, causal, or substantively meaningful.

Co-association ensemble

transition_fit <- cluster_sequences(
  transition,
  k = 2L,
  method = "hierarchical",
  linkage = "average"
)
ensemble <- create_sequence_cluster_ensemble(
  fit,
  transition_fit,
  k = 2L
)
ensemble$assignments
ensemble$coassociation

The ensemble records how often pairs are assigned together across supplied solutions. It does not automatically validate the number or meaning of clusters.

Optional PAM and CLARA interfaces

if (requireNamespace("cluster", quietly = TRUE)) {
  pam_fit <- cluster_sequences(lcs, k = 2L, method = "pam", seed = 11L)
  clara_fit <- cluster_sequences(
    lcs,
    k = 2L,
    method = "clara",
    seed = 11L,
    samples = 5L,
    sampsize = 5L
  )
  list(pam = pam_fit$assignments, clara = clara_fit$assignments)
}

PAM uses the supplied dissimilarities directly. CLARA uses a documented classical multidimensional-scaling embedding because cluster::clara() expects observations rather than a dissimilarity object.