Diagnose the threshold of the matching of clusters across windows

merge_dynamic_clusters() links the clusters of successive windows when they share a majority of their nodes (method = "majority") or have a large enough Jaccard index (method = "jaccard"), and the result depends on the threshold and on the type of similarity. A low threshold links clusters easily and produces a few long-lived dynamic clusters; a high one breaks continuities and produces many short-lived clusters. There is no right value, but there are unstable regions, where a small change of the threshold changes the story. merge_diagnostics() runs the matching for a grid of thresholds and similarity types and summarises, for each setting, how the dynamic clusters change: how many there are, how long they live, how many window clusters find a predecessor, and how the nodes are spread between long-lived and short-lived clusters. plot_merge_diagnostics() draws the result.

Usage

merge_diagnostics(
  graphs,
  cluster_id,
  node_id,
  method = c("majority", "jaccard"),
  thresholds = NULL,
  similarity_types = c("complete", "partial"),
  min_length = 3,
  verbose = TRUE
)

Arguments

graphs: A list of at least two tbl_graphs in chronological order, with the clusters of each window (see add_clusters()).
cluster_id: Character scalar, the node column with the clusters of each window (e.g. "cluster_leiden").
node_id: Character scalar, the node column with an identifier that is stable across windows.
method: "majority" or "jaccard", the rule of merge_dynamic_clusters() to diagnose. Required: run the function once for each rule to compare them.
thresholds: Numeric vector of thresholds to try, in \((0.5, 1]\) for "majority" and \((0, 1]\) for "jaccard". NULL (default) tries 0.51, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8 and 0.9 for "majority", and 0.1 to 0.8 by steps of 0.1 for "jaccard".
similarity_types: Subset of c("complete", "partial"): the types to try (see merge_dynamic_clusters()).
min_length: Whole number, the number of windows from which a dynamic cluster is called persistent (3 by default).
verbose: Logical. If TRUE (default), reports progress.

Value

A data frame with one row per threshold and similarity type, the method and the columns described above, with the table of lifespans in its "lifespans" attribute.

Details

The matching is run for each setting (threshold and similarity type) with merge_dynamic_clusters(). For each setting, with a window cluster meaning a cluster of one window and a dynamic cluster the set of window clusters that share an identifier, the columns of the result are:

n_window_clusters: the number of window clusters (the same for all settings);
n_dynamic_clusters: the number of dynamic clusters;
share_continued: the share of the window clusters of the second window onwards that inherit the identifier of a cluster of the previous window (high: many continuities);
median_lifespan, max_lifespan: the number of windows in which a dynamic cluster exists (median and maximum over dynamic clusters);
share_single_window: the share of dynamic clusters that exist in one window only;
n_persistent: the number of dynamic clusters existing in at least min_length windows;
share_nodes_persistent: the share of the nodes of all windows (a node present in two windows counts twice) that belong to persistent dynamic clusters;
largest_share: the share of those nodes in the largest dynamic cluster.

The table of the lifespans of each dynamic cluster is stored in the attribute "lifespans" and used by plot_merge_diagnostics().

A good threshold is on a plateau: the main dynamic clusters, and the share of nodes in persistent clusters, change little around it. Windows without any shared node cannot be matched whatever the threshold, and are reported in a warning.

Examples

networks <- build_dynamic_networks(
  nodes = subset(Nodes_stagflation, source_type == "Stagflation"),
  directed_edges = Ref_stagflation,
  source_id = "source_id",
  target_id = "target_id",
  time_variable = "source_year",
  time_window = 10,
  window_step = 4,
  method = "angle",
  edges_threshold = 2,
  verbose = FALSE
)
#> Warning: The last window is shorter than the others.
#> ℹ The data end in "2013", but the last window ends in "2016".
networks <- add_clusters(
  networks,
  clustering_method = "leiden",
  objective_function = "modularity",
  seed = 123,
  verbose = FALSE
)

diagnostics <- merge_diagnostics(
  networks,
  cluster_id = "cluster_leiden",
  node_id = "source_id",
  method = "majority",
  thresholds = c(0.51, 0.6, 0.75),
  similarity_types = "partial",
  verbose = FALSE
)
#> Warning: 1 pair of consecutive windows share no node: its clusters cannot be matched,
#> whatever the threshold.
diagnostics[, c("similarity_type", "threshold", "n_dynamic_clusters", "median_lifespan")]
#>   similarity_type threshold n_dynamic_clusters median_lifespan
#> 1         partial      0.51                 15             2.0
#> 2         partial      0.60                 18             1.5
#> 3         partial      0.75                 20             1.0