Calculate structural similarity among solutions

Calculate pairwise structural similarity among the stored solutions in a solutionset-class object.

Usage

selection_similarity(
  x,
  metric = c("jaccard", "hamming"),
  format = c("long", "matrix")
)

Arguments

x

A solutionset-class object returned by solve.

metric

Character. Similarity metric to use. One of "jaccard" or "hamming".

format

Character. Output format. If "long", return one row per pair of solutions. If "matrix", return a symmetric similarity matrix with solution ids as row and column names.

Value

If format = "long", a data.frame with columns:

• solution_id_1;

• solution_id_2;

• similarity;

• distance.

If format = "matrix", a symmetric numeric matrix of similarities is returned. Its diagonal is equal to one.

The selected metric is stored in the "metric" attribute.

Details

Solutions are compared using their complete planning-unit/action assignment vectors. Consequently, two solutions that select the same planning unit but assign different actions are treated as structurally different.

For simple conservation-planning problems without explicit actions, selected planning units are represented using the canonical action name "conservation".

Two similarity metrics are supported:

• "jaccard" compares the sets of selected planning-unit/action assignments:

  $$ J(A,B) = \frac{|A \cap B|} {|A \cup B|}. $$

  Jaccard similarity focuses on selected assignments and ignores joint absences. It is generally the preferred metric for sparse conservation and management portfolios.

• "hamming" calculates the proportion of decision-vector positions that are equal:

  $$ H(A,B) = \frac{1}{m} \sum_{k=1}^{m} I(A_k = B_k), $$

  where \(m\) is the number of feasible planning-unit/action assignments. Unlike Jaccard similarity, Hamming similarity includes shared non-selections.

For both metrics, similarity ranges from zero to one:

• 1 indicates identical assignment structures;

• 0 indicates no structural agreement under the selected metric.

The corresponding distance is calculated as:

$$ D(A,B) = 1 - S(A,B). $$

The comparison is performed over all stored solutions in the supplied object. To compare only a subset, first use solution_filter or solution_unique.

See also

selection_frequency, solution_filter, solution_unique, get_actions, get_pu

Examples

pu <- data.frame(
  id = 1:4,
  cost = c(1, 2, 3, 4)
)

features <- data.frame(
  id = 1:2,
  name = c("sp1", "sp2")
)

dist_features <- data.frame(
  pu = c(1, 1, 2, 3, 4),
  feature = c(1, 2, 2, 1, 2),
  amount = c(5, 2, 3, 4, 1)
)

actions <- data.frame(
  id = c("conservation", "restoration")
)

effects <- data.frame(
  action = rep(actions$id, each = 2),
  feature = rep(features$id, times = 2),
  multiplier = c(
    1.0, 1.0,
    1.5, 1.5
  )
)

problem <- create_problem(
  pu = pu,
  features = features,
  dist_features = dist_features,
  cost = "cost"
) |>
  add_actions(
    actions = actions,
    cost = c(
      conservation = 1,
      restoration = 2
    )
  ) |>
  add_effects(
    effects = effects,
    effect_type = "after"
  ) |>
  add_constraint_targets_relative(0.05) |>
  add_objective_min_cost(alias = "cost") |>
  add_objective_max_benefit(alias = "benefit") |>
  set_method_weighted_sum(
    aliases = c("cost", "benefit"),
    runs = run_grid(
      n = 5,
      include_extremes = TRUE
    ),
    normalize_weights = TRUE
  )

if (requireNamespace("rcbc", quietly = TRUE)) {
  problem <- set_solver_cbc(
    problem,
    verbose = FALSE
  )

  solutions <- solve(problem)

  # Pairwise Jaccard similarity in long format
  jaccard_long <- selection_similarity(
    solutions
  )

  jaccard_long

  # Symmetric Jaccard similarity matrix
  jaccard_matrix <- selection_similarity(
    solutions,
    format = "matrix"
  )

  jaccard_matrix

  # Hamming similarity includes shared non-selections
  hamming_long <- selection_similarity(
    solutions,
    metric = "hamming"
  )

  hamming_long

  # Compare only structurally unique solutions
  unique_solutions <- solution_unique(
    solutions,
    by = "decisions"
  )

  selection_similarity(
    unique_solutions,
    format = "matrix"
  )
}
#>    s1        s2        s4   s5
#> s1  1 0.0000000 0.0000000 0.00
#> s2  0 1.0000000 0.3333333 0.25
#> s4  0 0.3333333 1.0000000 0.75
#> s5  0 0.2500000 0.7500000 1.00
#> attr(,"metric")
#> [1] "jaccard"