Must-link and cannot-link constraints

Inject domain knowledge into the credibility matrix by rewarding pairs that should share a cluster (must_link()) or severing pairs that should not (cannot_link()), following Delias et al. (2023).

Usage

must_link(sim, pairs_or_attribute, reward = 2)

cannot_link(sim, pairs_or_attribute)

Arguments

sim

An outrank_sim object from outrank_similarity().

pairs_or_attribute

A two-column matrix of case-id pairs, or a length-one attribute name (requires that sim carries case attributes).

reward

Positive amount added to S for each must-linked pair.

Value

The outrank_sim with an updated S.

Details

With a symmetric 0/1 constraint mask M (zero diagonal), $$\text{must\_link:}\quad S \leftarrow \min(S + \text{reward}\cdot M,\ 1),$$ $$\text{cannot\_link:}\quad S \leftarrow S \odot (1 - M).$$ The constraint set is given either as a two-column matrix of case-id pairs, or as the name of a case attribute: must_link() then links cases with an equal attribute value, and cannot_link() severs cases whose values differ.

Examples

m <- matrix(0.2, 4, 4); diag(m) <- 1; dimnames(m) <- list(1:4, 1:4)
crit <- criterion(m, "similarity", indifference = 0.1, similarity = 0.9)
tr <- as_traces(data.frame(case = as.character(1:4), act = "x",
                           ts = as.POSIXct("2020-01-01")),
                "case", "act", "ts")
sim <- outrank_similarity(tr, crit)
sim <- must_link(sim, cbind("1", "2"))
cannot_link(sim, cbind("3", "4"))$S
#>       1     2     3     4
#> 1 1.000 1.000 0.125 0.125
#> 2 1.000 1.000 0.125 0.125
#> 3 0.125 0.125 1.000 0.000
#> 4 0.125 0.125 0.000 1.000