Trim outlier cases

trim_outliers() removes a fraction of the least-connected cases from an outrank_similarity() result, before clustering.

Usage

trim_outliers(sim, prop = 0.05, method = c("greedy", "lp"), lp_max = 150L)

Arguments

sim

An outrank_sim object from outrank_similarity().

prop

Fraction of cases to remove (in [0, 1)).

method

"greedy" (default) or "lp".

lp_max

Size above which the "lp" method warns about its cost.

Value

A trimmed outrank_sim, with a trimmed attribute giving the removed case ids.

Details

Let k = floor(prop * n). The "greedy" method removes the k cases with the smallest total similarity to the others (row sums of S with the diagonal excluded). The "lp" method solves the integer linear program of Delias et al. (2023), $$\min_{o, r} \sum_{i,j} s_{ij} r_{ij} \quad \text{s.t.} \quad \sum_i o_i = k,\ o_i \le r_{ij},\ o_i \le r_{ji},\ o, r \in \{0, 1\},$$ which selects the k cases whose incident edges carry the least similarity. A small constant is added to S so that zero entries do not leave r unconstrained. The LP has n + n^2 binary variables and is intended for small n; it warns above lp_max.

References

Delias, P., Doumpos, M., Grigoroudis, E. and Matsatsinis, N. (2023). Improving the non-compensatory trace-clustering decision process. International Transactions in Operational Research, 30(3), 1387-1406. doi:10.1111/itor.13062

Examples

m <- matrix(0.8, 5, 5); m[5, ] <- 0.05; m[, 5] <- 0.05; diag(m) <- 1
dimnames(m) <- list(1:5, 1:5)
crit <- criterion(m, "similarity", indifference = 0.3, similarity = 0.9)
tr <- as_traces(data.frame(case = as.character(1:5), act = "x",
                           ts = as.POSIXct("2020-01-01")),
                "case", "act", "ts")
sim <- outrank_similarity(tr, crit)
trim_outliers(sim, prop = 0.2)
#> <outrank_sim>: 4 cases, 1 criteria
#>   S in [0.833, 1.000], symmetric = TRUE