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Partitioning around medoids (PAM)

Source: vignettes/articles/criterion-pam.Rmd
criterion-pam.Rmd

The k-medoids cost: the training individuals act as medoids of the target.

Type Clustering
Direction Smaller is better
Uses a test set yes
Score a given set pam_score()
Search with it optTrain(method = "PAM")

Definition

∑imin⁡j∈T‖x0i−xj‖\sum_i \min_{j \in T}\lVert x_{0i} - x_j\rVert over target rows ii. The classical algorithm of Kaufman and Rousseeuw (1990) searches medoids freely; here the search is the exchange search of optTrain().

Use in TSDFGS 

library(TSDFGS)
data(geno)
pam_score(geno[1:50, ], geno[51:100, ])
## [1] 6588.776
fit <- optTrain(geno, cand = 1:404, n.train = 50, method = "PAM",
                 min.iter = 300, console = FALSE, seed = 1)
fit$OPTtrain
##  [1] 156 309  74 184 108 131 381 245 277 133 119 263 122  33 325 281 100 217 393
## [20]  31  41 288  70  96 289 256 368 399  42 305  20 372 262  43 153  60 172 390
## [39] 379 221  67 298 162  76 161 375 220 199 301 139
# targeted: the test set is known
fit2 <- optTrain(geno, cand = 1:300, n.train = 50, test = 301:404,
                  method = "PAM", min.iter = 300, console = FALSE, seed = 1)
fit2$OPTtrain
##  [1] 221 129 142  34  85  67  93 264 298  43 127 217  71  89 169  72 122  44   3
## [20] 199  40 245  58 109  69  39  31 220 130  90 216 283  24 193 161 137 204 103
## [39] 263 289 183  29 157  76 178 163  64   4 156  99

The search is a random-start exchange (hill-climbing) search; see How the scores are computed. Use min.iter larger than 300 on real data and check fit$converged.

Original work

Kaufman, L., & Rousseeuw, P. J. (1990). Finding groups in data: an introduction to cluster analysis. Wiley. https://doi.org/10.1002/9780470316801

Fernández-González, J., Akdemir, D., & Isidro y Sánchez, J. (2023). A comparison of methods for training population optimization in genomic selection. Theoretical and Applied Genetics, 136, 30. https://doi.org/10.1007/s00122-023-04265-6

Repository or website of the original authors: Algorithm in textbooks and the R package cluster (GPL >= 2).

License review

Formulas and algorithms are ideas and methods, which copyright does not protect. Where an original package is under a GPL license, we read it to check our results and credit it; TSDFGS is GPL-3, which is compatible with GPL-3 and GPL (>= 3) code. This is our reading of the public record, not legal advice; see the license review.

  • Original software: none required; the cost is a textbook definition.
  • Verdict: included.

Reviewed 2026-11-04. All criteria and the ones left out.