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Detect main temporal trajectories in group-year DAG

Source: R/trajectories_core.R
detect_main_trajectories.Rd

Identifies the most significant temporal trajectories within a group's evolution over time by building a directed acyclic graph (DAG) from similarity data and extracting highest-scoring disjoint paths using dynamic programming.

Usage

detect_main_trajectories(
  groups_cumulative_trajectories,
  group,
  jaccard_min = 0.05,
  intra_min = 0.1,
  k_out = 2,
  alpha = 1,
  beta = 0.1,
  top_M = 5,
  min_len = 3,
  use_docs_per_group = TRUE
)

Arguments

groups_cumulative_trajectories

List containing three components:

  • groups_similarity: Nested list with similarity data for each group, containing edges with from, to, weight (Jaccard), and documents

  • groups_attributes: Nested list with node attributes for each group, containing quantity_papers, prop_tracked_intra_group, tracked_documents, PY.sd, and network_until

  • docs_per_group: Data frame mapping group IDs to document IDs for accurate unique document counting

group

Character ID of the group to analyze (e.g., "component1_g01")

jaccard_min

Minimum Jaccard similarity for edges (default: 0.05). Higher values create sparser graphs with stronger connections.

intra_min

Minimum proportion of tracked documents within group for nodes (default: 0.10). Higher values filter out weaker nodes.

k_out

Maximum number of outgoing edges to keep per node (default: 2). Controls graph sparsity - lower values create simpler backbone structures.

alpha

Weight for edge strength in path scoring (default: 1). Higher values emphasize transition strength over node quality.

beta

Per-step persistence bonus in path scoring (default: 0.1). Higher values encourage longer trajectories.

top_M

Maximum number of disjoint trajectories to extract (default: 5)

min_len

Minimum number of distinct years for valid trajectory (default: 3)

use_docs_per_group

Whether to use document IDs for accurate unique document counting (default: TRUE). If FALSE, uses approximation.

Value

A list with two components:

  • graph: An igraph object representing the temporal DAG with scoring attributes and optional document IDs

  • trajectories: A tibble of detected trajectories sorted by score, with columns:

    • traj_id: Trajectory identifier ("tr1", "tr2", ...)

    • start, end: First and last year of the trajectory

    • length: Number of distinct years in the trajectory

    • nodes: List of node names along the path (e.g., "y2009g03")

    • score: Total path score from dynamic programming

    • mean_w: Mean edge score along the path

    • sum_docs: Count of unique documents covered by the path

    • mean_size: Mean node size (quantity_papers × proportion tracked)

    • mean_PYsd: Mean publication year standard deviation

Details

This function implements a comprehensive pipeline for detecting significant temporal trajectories in research group evolution:

Algorithm Overview

  1. Build Temporal DAG: Constructs a directed acyclic graph where:

    • Nodes represent group-year combinations filtered by intra_min quality threshold

    • Edges represent transitions between consecutive years filtered by jaccard_min

    • Graph is sparsified to top k_out edges per node

  2. Score Components: Computes node and edge scores:

    • Node score: \(s_v = \log(1 + \text{quantity\_papers}_v \times \text{prop\_tracked\_intra\_group}_v)\)

    • Edge score: \(s_e = \text{weight}_e \times \log(1 + \text{documents}_e)\)

  3. Extract Trajectories: Uses dynamic programming to find heaviest paths:

    • Path score: \(\text{best}(v) = \max\left( s_v, \max_{u \to v} \left( \text{best}(u) + s_v + \alpha \cdot s_{(u,v)} + \beta \right) \right)\)

    • Iteratively extracts top top_M disjoint trajectories

    • Trajectories must span at least min_len distinct years

  4. Count Documents: Calculates unique document coverage:

    • If use_docs_per_group = TRUE: Exact count via set union of document IDs

    • Otherwise: Approximation: \(\sum \text{node documents} - \sum \text{edge documents}\)

Parameter Tuning Guidance

  • For smoother, longer trajectories: Increase beta (persistence bonus)

  • For transition-focused scoring: Increase alpha (edge weight)

  • For denser connectivity: Lower jaccard_min or increase k_out

  • For higher quality nodes: Increase intra_min

  • For exact document counts: Ensure use_docs_per_group = TRUE and provide docs_per_group data

See also

filter_trajectories() for post-processing detected trajectories, plot_group_trajectories_lines_2d() and plot_group_trajectories_lines_3d() for visualization

Examples

if (FALSE) { # \dontrun{
# Basic usage with default parameters
trajectories <- detect_main_trajectories(
  groups_cumulative_trajectories = my_data,
  group = "component1_g01"
)

# Tuned for longer, transition-focused trajectories
trajectories <- detect_main_trajectories(
  groups_cumulative_trajectories = my_data,
  group = "component1_g01",
  jaccard_min = 0.03, # More permissive connectivity
  k_out = 3, # Denser backbone
  alpha = 1.5, # Emphasize edge strength
  beta = 0.2, # Encourage longer paths
  top_M = 8, # Extract more trajectories
  min_len = 4 # Require longer trajectories
)

# Access results
graph <- trajectories$graph
trajectory_data <- trajectories$trajectories

# Plot the top trajectory
top_trajectory <- trajectory_data[1, ]
} # }