Clustering and clinical phenotyping

Raha Dastgheyb

2026-10-12

Purpose

Clinical phenotyping uses prespecified features to discover structure in a training cohort, then places later participants in that fixed phenotype space. Clustering is exploratory: fit indices, internal stability, and clean projection do not establish that a phenotype is biologically real. Clinical interpretation and independent-cohort validation remain essential.

Every pipeline in this package uses the same train-once/project-many contract:

• preprocessing and model parameters are learned from training data only;
• DataWithClusters preserves the original row order and columns;
• incomplete cases remain in the output with NA assignments;
• 90% participant subsample stability refits the entire pipeline, including scaling and PCA/MCA when present;
• fit, membership uncertainty or distance, and projection support are reviewed before phenotypes are named.

method = "exploratory" (or the shorter alias "explore") compares candidate settings and gives an advisory AHP-style recommendation. The researcher then creates an explicit method = "finalize" model for projection.

Lifecycle-specific settings are strict. Exploratory ranges (k_range, models, minPts_range, and epsilon grids) cannot be supplied to a finalized fit; finalized settings (final_k, final_model, final_minPts, and final epsilon) cannot be supplied to exploratory review. This catches calls that would otherwise look valid while silently ignoring part of the request.

Breaking output-name changes

The unreleased clustering interface now uses DataWithClusters rather than df_with_clusters, and ClusterVariableName rather than ClusterName. ModelInfo_MClust is the only correctly cased Mclust-specific field; the erroneous ModelInfo_Mclust field has been removed. complete_rows, CandidateAudit and the old .scidr_rowid column are no longer public outputs. Every row-level output instead carries a merge-safe .row_id, labeled "Row ID". Use Specification$n_complete for aggregate training support and the fit_table status/warning/error columns to audit candidates. For example, merge diagnostics back without relying on row order using dplyr::left_join(model$DataWithClusters, model$ProbFit$individual, by = ".row_id").

Every method stores its figures in the same places, so the same review sequence works whichever approach you choose. A figure lives beside the table it summarises rather than in one flat list:

Location	What it shows
fit_plot	candidate solutions across the search grid
ModelInfo$plots	structure of the selected solution
ModelInfo$FitDiagnostics$plots	how individual training cases sit inside that structure
ProbFit$plots	membership confidence
Stability$plots	90% subsample reproducibility
ProjectionFit$plots	projected cases against the frozen training reference

The contents are method-specific: K-means and Gower/PAM give you a silhouette profile, Mclust a BIC curve and an uncertainty map, HDBSCAN a persistence review, LCA item response profiles, and the reduction pipelines a scree plot. The SOM pipeline keeps its own richer set, including the interactive aweSOM maps in ModelInfo_SOM$plots.

Choosing a method

Method	Data and geometry	Primary diagnostics	Projection rule	Ideal situation	Main caveat
SOM + Mclust	Continuous; topology and gradients matter	map fit, posterior, SOM distance, stability	scaling → SOM node → mixture class	phenotype maps and nonlinear gradients	most complex workflow
Mclust	Continuous; Gaussian mixtures	BIC/ICL, entropy, posterior, stability	exact mixture posterior	probabilistic groups with different covariance	sensitive to distributional mismatch
PCA + Mclust	Correlated continuous measures	scree, mixture fit, posterior, stability	frozen PCA → mixture posterior	clustering a lower-dimensional signal space	PCs can obscure individual variables
K-means	Numeric; compact centroid geometry	WSS, silhouette, CH, margin, stability	nearest frozen centroid	simple, interpretable baseline	no probability model
PCA + K-means	Correlated numeric measures	scree, silhouette, distance, stability	frozen PCA → nearest centroid	fast reduced-space baseline	inherits PCA and K-means assumptions
HDBSCAN	Numeric; irregular or unequal-density groups	persistence, membership, noise, support	nearest eligible training core	clusters plus meaningful noise	conservative projection may label many cases noise
Gower + PAM	Mixed numeric/categorical/ordinal	silhouette, medoids, distance, stability	nearest frozen medoid	mixed clinical measures and exemplar participants	coding and variable selection define distance
LCA	Categorical response patterns	BIC, entropy, response probabilities, stability	latent-class posterior	symptom or questionnaire response phenotypes	local-independence assumption
MCA + Mclust	Nominal categorical measures	inertia, mixture fit, posterior, stability	frozen MCA → mixture posterior	reduced categorical response space	MCA dimensions can be abstract

Load the benchmark

Note

The data file is SimulatedPhenotypeData; the codebook is SimulatedPhenotypeVariableTypes. The benchmark contains 320 training and 160 projection participants. TruthCluster, TruthDensityGroup, and Cohort are never supplied to a clustering function. Truth is revealed only as a teaching check after fitting.

The 12 numeric measures are three indicators of each of four independent simulated axes. The default 85% rule therefore retains at least four PCs. Four balanced truth groups use different combinations of these axes. Separate DensityX/DensityY coordinates contain two unequal-density groups and noise; three categorical variables contain deliberately strong class-dependent response patterns. That separation is useful for checking implementation; it is intentionally easier than most real categorical phenotyping problems.

Constructor interface

All clustering constructors use method = "exploratory" to review candidates and method = "finalize" to create a reusable model. Fixed-count methods use k_range and final_k; density methods use minPts_range, epsilon settings, and their matching finalized inputs. Numeric methods use ZScoreType; Scaling is retained as a compatibility alias and must agree if both are supplied.

Workflow	Candidate settings	Finalized settings	Method-specific control
Mclust, PCA + Mclust, MCA + Mclust, SOM + Mclust	k_range, models	final_k, final_model	tidyLPA mclust models: 1 = EEI, 2 = VVI, 3 = EEE, 6 = VVV; models 4 and 5 require OpenMx and are unsupported
K-means, PCA + K-means, Gower + PAM, latent class	k_range	final_k	nstart for K-means; nrep for LCA
HDBSCAN, SOM + HDBSCAN	minPts_range, epsilon range	final_minPts, final epsilon	extracted class count is data-derived

The tidyLPA Mclust model numbers describe which within-cluster variances and covariances may differ between clusters:

Model	mclust code	Meaning
Model 1	EEI	Equal variance across clusters, with covariance fixed at zero
Model 2	VVI	Varying variance across clusters, with covariance fixed at zero
Model 3	EEE	Equal variance and equal covariance across clusters
Model 6	VVV	Varying variance and varying covariance across clusters

Zero covariance assumes the clustering variables are conditionally independent within a cluster. Equal parameters pool the corresponding structure across clusters; varying parameters let each cluster estimate its own structure.

Continuous workflows

Note

The non-SOM workflows below are complete, copyable templates, but their model fits are intentionally not evaluated while this vignette renders. This keeps package checks practical. Run one workflow at a time in an analysis project, then increase stability_resamples when the candidate solution is ready for a real stability assessment.

Mclust

Gaussian mixture models provide posterior membership and allow clusters to differ in covariance (Scrucca et al. 2016).

Note

When to use it: continuous measures with approximately mixture-shaped groups. Inspect before naming: BIC/ICL, entropy, posterior confidence, small clusters, subsample ARI/Jaccard, and projected uncertainty.

K-means

K-means is a useful scaled baseline for compact groups (MacQueen 1967).

Note

When to use it: continuous features with roughly compact, similarly shaped groups. Inspect before naming: WSS, silhouette, Calinski–Harabasz index, centroid distance, assignment margin, and subsample stability.

PCA followed by clustering

PCA concentrates correlated variation into orthogonal dimensions (Jolliffe and Cadima 2016). These pipelines refit scaling and PCA inside every stability 90% subsampling, then use the frozen training transformation for projection.

Note

When to use it: correlated continuous variables where a reduced signal space is clearer than the raw feature space. Inspect before naming: scree plot, retained component count/loadings, downstream fit and stability, score space separation, and projection distance or uncertainty.

HDBSCAN

HDBSCAN is designed for irregular clusters, unequal density, and noise (McInnes et al. 2017). A projected 0 is an out-of-support/noise assignment, not a new phenotype.

Note

When to use it: density structure is more plausible than centroid geometry and noise is scientifically meaningful. Inspect before naming: persistence, membership, noise burden, outlier scores, stability, and nearest-core support. All-noise candidates are valid negative results.

SOM followed by Mclust

Self-organizing maps preserve local topology before mixture clustering (Kohonen 1982).

Note

When to use it: a map of phenotype gradients is as useful as the final labels. Inspect before naming: map topology, quantization/SOM distance, node occupancy, posterior confidence, stability, and projected distance flags.

Ordinary SOM fitting defaults to stability_resamples = 0, so model review does not unexpectedly become slow. Use the separate map-design screen below before final cluster selection: it uses the largest requested k to generate coarse, balanced, and fine candidate resolutions (about 10, 20, and 30 nodes per maximum planned phenotype), then holds each candidate grid and topology fixed within three 90% subsample refits and projects every refit back to the full reference cohort. This fast screen compares topology preservation, local neighborhood overlap, projected SOM distance, and map occupancy; it fits no Mclust model and does not choose a grid automatically. After reviewing the result, freeze one grid/topology and compare the clinically meaningful k values on that same map using fit indices, participant-level ARI, and clinical interpretation. The screen reports expected nodes per profile for every requested k; larger cohorts can support a reviewed map, but do not by themselves require more map nodes or more clinical phenotypes. Stability refits run in parallel by default; set stability_cores = 1L for serial execution or a smaller positive value when each SOM or high-dimensional refit needs more memory.

For a finalized SOM + Mclust instrument, ARI is still the primary answer to the narrow question, “do the refits recover the same final participant partition?” StabilityARI_P05 is the fifth percentile across refits: a stress-test lower-tail summary, not a second selection criterion. When an ARI is modest, inspect the stability panel rather than relabeling that result as stable: deletion_curve shows sensitivity at explicitly requested retained fractions, exact memory-safe co_membership_* outputs distinguish within- phenotype cohesion from cross-phenotype mixing, split_merge_* describes fragmentation/merging, and profile_recovery compares matched phenotype means on the frozen training scale. These explain whether membership movement is localized while phenotype profiles are retained; none replace the all-participant ARI. Boundary participants remain assigned and included in that primary metric.

data("SimulatedPhenotypeData")

df_Training <- SimulatedPhenotypeData %>% dplyr::filter(Cohort == "Training")
df_Projection <- SimulatedPhenotypeData %>% dplyr::filter(Cohort == "Projection")
vars_Clust <- paste0("Var", 1:12)

Obj_ClustReview <- CreateClusterModel_SOM_MClust(
  df_Training, vars_Clust, k_range = 2:10, models = c(1, 3),
  method = "exploratory"
)
Obj_ClustFinal <- CreateClusterModel_SOM_MClust(
  df_Training, vars_Clust, final_k = 4, final_model = 3,
  method = "finalize", stability_resamples = 30
)
ObjClustProjected <- ProjectCluster(Obj_ClustFinal, df_Projection)

   Model Classes     LogLik parameters  n      AIC       AWE      BIC     CAIC
1      1       2 -351.06784         37 25 776.1357 1049.4065 821.2341 858.2341
2      3       2   72.51292        169 25 192.9742 1447.9542 398.9642 567.9642
3      1       3 -277.85952         50 25 655.7190 1025.6102 716.6628 766.6628
4      3       3   93.07687        182 25 177.8463 1529.5171 399.6817 581.6817
5      1       4 -152.90811         63 25 431.8162  898.3946 508.6054 571.6054
6      3       4  121.18864        195 25 147.6227 1595.9843 385.3035 580.3035
7      1       5 -121.23197         76 25 394.4639  957.7331 487.0985 563.0985
8      3       5  132.17612        208 25 151.6478 1696.7001 405.1739 613.1739
9      1       6 -112.97339         89 25 403.9468 1063.9107 512.4267 601.4267
10     3       6  132.01242        221 25 177.9752 1819.7243 447.3467 668.3467
11     1       7 -118.45913        102 25 440.9183 1197.5701 565.2436 667.2436
12     3       7  150.29455        234 25 167.4109 1905.8448 452.6278 686.6278
13     1       8 -110.08009        115 25 450.1602 1303.5040 590.3309 705.3309
14     3       8  157.93308        247 25 178.1338 2013.2585 479.1962 726.1962
15     1       9 -100.13395        128 25 456.2679 1406.3006 612.2840 740.2840
16     3       9  184.01651        260 25 151.9670 2083.7824 468.8747 728.8747
17     1      10  -85.65194        141 25 453.3039 1500.0273 625.1654 766.1654
18     3      10  193.34826        273 25 159.3035 2187.8097 492.0566 765.0566
         CLC      KIC     SABIC       ICL   Entropy  prob_min  prob_max
1   704.0617 816.1357  706.4937 -821.8855 0.9629876 0.9553981 0.9999889
2  -143.0258 364.9742 -125.1205 -398.9642 1.0000000 1.0000000 1.0000000
3   557.7155 708.7190  561.6082 -716.6779 0.9982285 0.9990952 0.9999986
4  -184.1537 362.8463 -164.7172 -399.6817 0.9999973 0.9999996 1.0000000
5   307.8162 497.8162  313.2365 -508.6054 1.0000000 1.0000000 1.0000000
6  -240.3773 345.6227 -219.4096 -385.3035 0.9999977 0.9999992 1.0000000
7   244.4639 473.4639  251.4155 -487.0985 1.0000000 1.0000000 1.0000000
8  -262.3523 362.6478 -239.8534 -405.1740 0.9999933 0.9999963 1.0000000
9   227.9428 495.9468  236.4295 -512.4582 0.9979917 0.9960938 1.0000000
10 -262.0309 401.9752 -237.9948 -447.3914 0.9969976 0.9971487 1.0000000
11  238.9171 545.9183  248.9321 -565.2508 0.9994202 0.9982046 1.0000000
12 -298.5891 404.4109 -273.0279 -452.6278 0.9999994 0.9999994 1.0000000
13  222.1578 568.1602  233.7052 -590.3498 0.9987990 0.9983064 1.0000000
14 -313.8662 428.1338 -286.7738 -479.1962 0.9999962 0.9999942 1.0000000
15  202.2674 587.2679  215.3441 -612.2874 0.9997389 0.9994257 1.0000000
16 -366.0330 414.9670 -337.4094 -468.8747 0.9999966 0.9999924 1.0000000
17  173.3035 597.3039  187.9113 -625.1683 0.9998065 0.9986208 1.0000000
18 -384.6965 435.3035 -354.5417 -492.0566 0.9999992 0.9999966 1.0000000
   BLRTStatistic BLRTPValue MinProfileNodeN MaxProfileNodeN
1             NA         NA               6              19
2             NA         NA               6              19
3             NA         NA               6              13
4             NA         NA               6              13
5             NA         NA               5               8
6             NA         NA               5               8
7             NA         NA               2               6
8             NA         NA               4               6
9             NA         NA               2               6
10            NA         NA               2               6
11            NA         NA               1               6
12            NA         NA               1               6
13            NA         NA               1               6
14            NA         NA               1               5
15            NA         NA               1               6
16            NA         NA               1               5
17            NA         NA               1               5
18            NA         NA               1               5
   MinProfileNodeProportion MaxProfileNodeProportion MinProfileParticipantN
1                      0.24                     0.76                     80
2                      0.24                     0.76                     80
3                      0.24                     0.52                     80
4                      0.24                     0.52                     80
5                      0.20                     0.32                     80
6                      0.20                     0.32                     80
7                      0.08                     0.24                      0
8                      0.16                     0.24                     30
9                      0.08                     0.24                      0
10                     0.08                     0.24                     27
11                     0.04                     0.24                      8
12                     0.04                     0.24                     21
13                     0.04                     0.24                      8
14                     0.04                     0.20                     21
15                     0.04                     0.24                      3
16                     0.04                     0.20                      3
17                     0.04                     0.20                      3
18                     0.04                     0.20                      3
   MinProfileParticipantProportion PosteriorMean PosteriorMedian
1                         0.250000     0.9999309       0.9999990
2                         0.250000     1.0000000       1.0000000
3                         0.250000     1.0000000       1.0000000
4                         0.250000     1.0000000       1.0000000
5                         0.250000     1.0000000       1.0000000
6                         0.250000     1.0000000       1.0000000
7                         0.000000     1.0000000       1.0000000
8                         0.093750     0.9999992       1.0000000
9                         0.000000     0.9990130       1.0000000
10                        0.084375     0.9986431       1.0000000
11                        0.025000     0.9998089       0.9999998
12                        0.065625     0.9999998       1.0000000
13                        0.025000     0.9996616       0.9999992
14                        0.065625     0.9999992       1.0000000
15                        0.009375     0.9999342       0.9999998
16                        0.009375     0.9999992       1.0000000
17                        0.009375     0.9999504       1.0000000
18                        0.009375     0.9999999       1.0000000
   PropLowPosterior StabilitySuccessRate StabilityARI_Mean StabilityARI_P05
1                 0                    1         0.4656616      -0.01524288
2                 0                    1         0.4656616      -0.01524288
3                 0                    1         0.4624432       0.46116314
4                 0                    1         0.4624432       0.46116314
5                 0                    1         0.9958202       0.99205833
6                 0                    1         0.9958202       0.99205833
7                 0                    1         0.9897228       0.98047339
8                 0                    1         0.8956853       0.86045376
9                 0                    1         0.9151670       0.90782561
10                0                    1         0.7626110       0.67909257
11                0                    1         0.8016879       0.77806202
12                0                    1         0.7225818       0.69660212
13                0                    1         0.6866398       0.66857645
14                0                    1         0.7317106       0.69663241
15                0                    1         0.6493978       0.62649461
16                0                    1         0.6964294       0.65997935
17                0                    1         0.7380422       0.70948639
18                0                    1         0.7594990       0.75070975
   StabilityJaccard_Mean StabilityJaccard_Min StabilityCoreProportion
1              0.7083333           0.66666667                       1
2              0.7083333           0.66666667                       1
3              0.6651074           0.49687500                       1
4              0.6651074           0.49687500                       1
5              0.9968943           0.99375000                       1
6              0.9968943           0.99375000                       1
7              0.9921875           0.97500000                       1
8              0.7725000           0.25000000                       1
9              0.7946044           0.31875000                       1
10             0.6132120           0.23750000                       1
11             0.6032487           0.23259494                       1
12             0.5920687           0.28149693                       1
13             0.4869087           0.11164954                       1
14             0.6426372           0.28149693                       1
15             0.4195441           0.03750000                       1
16             0.5609762           0.04592363                       1
17             0.5611938           0.03835784                       1
18             0.6494702           0.04592363                       1
   StabilityARI_Core StabilityJaccard_CoreMean StabilityJaccard_CoreMin
1          0.4656616                 0.7083333               0.66666667
2          0.4656616                 0.7083333               0.66666667
3          0.4624432                 0.6651074               0.49687500
4          0.4624432                 0.6651074               0.49687500
5          0.9958202                 0.9968943               0.99375000
6          0.9958202                 0.9968943               0.99375000
7          0.9897228                 0.9921875               0.97500000
8          0.8956853                 0.7725000               0.25000000
9          0.9151670                 0.7946044               0.31875000
10         0.7626110                 0.6132120               0.23750000
11         0.8016879                 0.6032487               0.23259494
12         0.7225818                 0.5920687               0.28149693
13         0.6866398                 0.4869087               0.11164954
14         0.7317106                 0.6426372               0.28149693
15         0.6493978                 0.4195441               0.03750000
16         0.6964294                 0.5609762               0.04592363
17         0.7380422                 0.5611938               0.03835784
18         0.7594990                 0.6494702               0.04592363
   StabilityNonBoundaryProportion StabilityARI_NonBoundary
1                        1.000000                0.4656616
2                        1.000000                0.4656616
3                        1.000000                0.4624432
4                        1.000000                0.4624432
5                        1.000000                0.9958202
6                        1.000000                0.9958202
7                        1.000000                0.9897228
8                        0.962500                0.9103017
9                        0.993750                0.9170130
10                       0.956250                0.7682828
11                       0.978125                0.8135826
12                       0.937500                0.7363608
13                       0.968750                0.6955504
14                       0.928125                0.7469045
15                       0.968750                0.6564588
16                       0.928125                0.7070187
17                       0.962500                0.7468363
18                       0.921875                0.7678478
   StabilityARI_NonBoundary_P05 StabilityJaccard_NonBoundaryMean
1                   -0.01524288                        0.7083333
2                   -0.01524288                        0.7083333
3                    0.46116314                        0.6651074
4                    0.46116314                        0.6651074
5                    0.99205833                        0.9968943
6                    0.99205833                        0.9968943
7                    0.98047339                        0.9921875
8                    0.87298331                        0.7725000
9                    0.90954936                        0.7945837
10                   0.67788872                        0.6131948
11                   0.78985527                        0.6041955
12                   0.70457768                        0.5922588
13                   0.67774734                        0.4876779
14                   0.71257501                        0.6452262
15                   0.63276808                        0.4201939
16                   0.66837196                        0.5607031
17                   0.71759872                        0.5634501
18                   0.75732105                        0.6521223
   StabilityJaccard_NonBoundaryMin ReproducibilityScore_All
1                       0.66666667                0.4656616
2                       0.66666667                0.4656616
3                       0.49687500                0.4624432
4                       0.49687500                0.4624432
5                       0.99375000                0.9958202
6                       0.99375000                0.9958202
7                       0.97500000                0.9897228
8                       0.23529412                0.8956853
9                       0.32692308                0.9151670
10                      0.22058824                0.7626110
11                      0.20000000                0.8016879
12                      0.27525253                0.7225818
13                      0.11164954                0.6866398
14                      0.27525253                0.7317106
15                      0.03896104                0.6493978
16                      0.04861111                0.6964294
17                      0.04031385                0.7380422
18                      0.04861111                0.7594990
   ReproducibilityScore BoundaryParticipantProportion
1             0.4656616                      0.000000
2             0.4656616                      0.000000
3             0.4624432                      0.000000
4             0.4624432                      0.000000
5             0.9958202                      0.000000
6             0.9958202                      0.000000
7             0.9897228                      0.000000
8             0.8956853                      0.037500
9             0.9151670                      0.006250
10            0.7626110                      0.043750
11            0.8016879                      0.021875
12            0.7225818                      0.062500
13            0.6866398                      0.031250
14            0.7317106                      0.071875
15            0.6493978                      0.031250
16            0.6964294                      0.071875
17            0.7380422                      0.037500
18            0.7594990                      0.078125
   MaxClusterBoundaryProportion MixtureParameters MixtureNodes
1                    0.00000000                37           25
2                    0.00000000               103           25
3                    0.00000000                50           25
4                    0.00000000               116           25
5                    0.00000000                63           25
6                    0.00000000               129           25
7                    0.00000000                76           25
8                    0.20000000               142           25
9                    0.03703704                89           25
10                   0.21052632               155           25
11                   0.20000000               102           25
12                   0.21052632               168           25
13                   0.20000000               115           25
14                   0.21052632               181           25
15                   0.20000000               128           25
16                   0.21052632               194           25
17                   0.20000000               141           25
18                   0.21052632               207           25
   ParticipantsPerNode OccupancyCompliant NodesPerParameter Overparameterized
1                 12.8               TRUE         0.6756757              TRUE
2                 12.8               TRUE         0.2427184              TRUE
3                 12.8               TRUE         0.5000000              TRUE
4                 12.8               TRUE         0.2155172              TRUE
5                 12.8               TRUE         0.3968254              TRUE
6                 12.8               TRUE         0.1937984              TRUE
7                 12.8               TRUE         0.3289474              TRUE
8                 12.8               TRUE         0.1760563              TRUE
9                 12.8               TRUE         0.2808989              TRUE
10                12.8               TRUE         0.1612903              TRUE
11                12.8               TRUE         0.2450980              TRUE
12                12.8               TRUE         0.1488095              TRUE
13                12.8               TRUE         0.2173913              TRUE
14                12.8               TRUE         0.1381215              TRUE
15                12.8               TRUE         0.1953125              TRUE
16                12.8               TRUE         0.1288660              TRUE
17                12.8               TRUE         0.1773050              TRUE
18                12.8               TRUE         0.1207729              TRUE
        SupportStatus AIC_scaled  BIC_scaled Entropy_scaled
1  over-parameterized -2.3217180 -2.57142713    -3.98596017
2  over-parameterized  0.7235624  1.03870975     0.29597332
3  over-parameterized -1.6928999 -1.67740986     0.09103470
4  over-parameterized  0.8025605  1.03257570     0.29566559
5  over-parameterized -0.5236752  0.10134775     0.29597317
6  over-parameterized  0.9603884  1.15549972     0.29570174
7  over-parameterized -0.3286210  0.28521775     0.29597333
8  over-parameterized  0.9393696  0.98562035     0.29519501
9  over-parameterized -0.3781406  0.06867773     0.06363850
10 over-parameterized  0.8018875  0.62507018    -0.05137539
11 over-parameterized -0.5712063 -0.38287255     0.22890167
12 over-parameterized  0.8570542  0.57991985     0.29590390
13 over-parameterized -0.6194677 -0.59735287     0.15702885
14 over-parameterized  0.8010588  0.35277774     0.29553557
15 over-parameterized -0.6513624 -0.78503789     0.26576360
16 over-parameterized  0.9377027  0.44101974     0.29557465
17 over-parameterized -0.6358843 -0.89516541     0.27359220
18 over-parameterized  0.8993913  0.24282944     0.29587976
   Reproducibility_scaled Posterior_scaled  ahp_index Eligible Recommended
1            -1.460958081       0.26536601 -2.5850158    FALSE       FALSE
2            -1.460958081       0.44719763  0.1493218    FALSE       FALSE
3            -1.478535111       0.44719716 -1.1894526    FALSE       FALSE
4            -1.478535111       0.44719763  0.1630667    FALSE       FALSE
5             1.434447183       0.44719763  0.3270232    FALSE       FALSE
6             1.434447183       0.44719763  0.9615093    FALSE       FALSE
7             1.401147205       0.44719762  0.4134293    FALSE       FALSE
8             0.887571052       0.44515837  0.7769390    FALSE       FALSE
9             0.993968265      -2.14876252  0.1870360    FALSE       FALSE
10            0.160799529      -3.12154031  0.3840955    FALSE       FALSE
11            0.374213962      -0.05534519 -0.0877408    FALSE       FALSE
12           -0.057815682       0.44678403  0.4187656    FALSE       FALSE
13           -0.254108935      -0.44289951 -0.3284752    FALSE       FALSE
14           -0.007959829       0.44513967  0.3603531    FALSE       FALSE
15           -0.457502390       0.27411167 -0.4070348    FALSE       FALSE
16           -0.200644329       0.44504462  0.3684132    FALSE       FALSE
17            0.026619558       0.31686578 -0.3077095    FALSE       FALSE
18            0.143803611       0.44689206  0.3954760    FALSE       FALSE
      GridDesignPolicy GridDesignK TargetNodesPerProfile SOMNodeCount
1  explicit_dimensions          10                    20           25
2  explicit_dimensions          10                    20           25
3  explicit_dimensions          10                    20           25
4  explicit_dimensions          10                    20           25
5  explicit_dimensions          10                    20           25
6  explicit_dimensions          10                    20           25
7  explicit_dimensions          10                    20           25
8  explicit_dimensions          10                    20           25
9  explicit_dimensions          10                    20           25
10 explicit_dimensions          10                    20           25
11 explicit_dimensions          10                    20           25
12 explicit_dimensions          10                    20           25
13 explicit_dimensions          10                    20           25
14 explicit_dimensions          10                    20           25
15 explicit_dimensions          10                    20           25
16 explicit_dimensions          10                    20           25
17 explicit_dimensions          10                    20           25
18 explicit_dimensions          10                    20           25
   ExpectedNodesPerProfile
1                12.500000
2                12.500000
3                 8.333333
4                 8.333333
5                 6.250000
6                 6.250000
7                 5.000000
8                 5.000000
9                 4.166667
10                4.166667
11                3.571429
12                3.571429
13                3.125000
14                3.125000
15                2.777778
16                2.777778
17                2.500000
18                2.500000

[1] "No eligible SOM mixture candidate is available for composite recommendation."

# A tibble: 18 × 18
   Model Classes StabilitySuccessRate StabilityARI_Mean StabilityARI_P05
   <int>   <int>                <dbl>             <dbl>            <dbl>
 1     1       2                    1             0.466          -0.0152
 2     3       2                    1             0.466          -0.0152
 3     1       3                    1             0.462           0.461
 4     3       3                    1             0.462           0.461
 5     1       4                    1             0.996           0.992
 6     3       4                    1             0.996           0.992
 7     1       5                    1             0.990           0.980
 8     3       5                    1             0.896           0.860
 9     1       6                    1             0.915           0.908
10     3       6                    1             0.763           0.679
11     1       7                    1             0.802           0.778
12     3       7                    1             0.723           0.697
13     1       8                    1             0.687           0.669
14     3       8                    1             0.732           0.697
15     1       9                    1             0.649           0.626
16     3       9                    1             0.696           0.660
17     1      10                    1             0.738           0.709
18     3      10                    1             0.759           0.751
# ℹ 13 more variables: StabilityJaccard_Mean <dbl>, StabilityJaccard_Min <dbl>,
#   StabilityCoreProportion <dbl>, StabilityARI_Core <dbl>,
#   StabilityJaccard_CoreMean <dbl>, StabilityJaccard_CoreMin <dbl>,
#   StabilityNonBoundaryProportion <dbl>, StabilityARI_NonBoundary <dbl>,
#   StabilityARI_NonBoundary_P05 <dbl>, StabilityJaccard_NonBoundaryMean <dbl>,
#   StabilityJaccard_NonBoundaryMin <dbl>, ReproducibilityScore_All <dbl>,
#   ReproducibilityScore <dbl>

# A tibble: 3 × 9
  Model Classes RetainedFraction StabilitySuccessRate StabilityARI_Mean
  <int>   <int>            <dbl>                <dbl>             <dbl>
1     3       4             0.8                     1             1
2     3       4             0.9                     1             0.996
3     3       4             0.95                    1             1
# ℹ 4 more variables: StabilityARI_P05 <dbl>, StabilityVI_Mean <dbl>,
#   StabilityNMI_Mean <dbl>, StabilityFowlkesMallows_Mean <dbl>

# A tibble: 24 × 8
   ReferenceCluster ReferenceParticipants Cohesion CrossMixing Model Classes
              <int>                 <dbl>    <dbl>       <dbl> <int>   <int>
 1                1                    80    1         0           3       4
 2                2                    80    1         0           3       4
 3                3                    80    1         0           3       4
 4                4                    80    1         0           3       4
 5                1                    80    1         0           3       4
 6                2                    80    1         0.00417     3       4
 7                3                    80    1         0           3       4
 8                4                    80    0.975     0.00417     3       4
 9                1                    80    1         0           3       4
10                2                    80    1         0           3       4
# ℹ 14 more rows
# ℹ 2 more variables: Replicate <int>, RetainedFraction <dbl>

# A tibble: 24 × 9
   ReferenceCluster DominantRefitCluster DominantRefitShare
              <int>                <int>              <dbl>
 1                1                    3              1
 2                2                    4              1
 3                3                    1              1
 4                4                    2              1
 5                1                    1              1
 6                2                    4              1
 7                3                    3              1
 8                4                    2              0.988
 9                1                    4              1
10                2                    1              1
# ℹ 14 more rows
# ℹ 6 more variables: EffectiveRefitClusters <dbl>, BestJaccard <dbl>,
#   Model <int>, Classes <int>, Replicate <int>, RetainedFraction <dbl>

# A tibble: 24 × 8
   ReferenceCluster MatchedRefitCluster ProfileCorrelation ProfileRMSE Model
              <int>               <int>              <dbl>       <dbl> <int>
 1                1                   3              1          0          3
 2                2                   4              1          0          3
 3                3                   1              1          0          3
 4                4                   2              1          0          3
 5                1                   1              1          0          3
 6                2                   4              1.000      0.0158     3
 7                3                   3              1          0          3
 8                4                   2              1.000      0.0111     3
 9                1                   4              1          0          3
10                2                   1              1          0          3
# ℹ 14 more rows
# ℹ 3 more variables: Classes <int>, Replicate <int>, RetainedFraction <dbl>

Interpreting a SOM projection

The SOM map is a frozen phenotype instrument. Each new model uses one seeded, full-cohort batch SOM fit from a deterministic initial codebook. This keeps training fast and reproducible while retaining the fitted scaling, prototypes, grid, topology, neighbourhood, and node-level mixture for projection. When dimensions are omitted, the automatic square grid is k-informed: exploratory fits use max(k_range), finalized fits use final_k, and the engineering default targets about 20 SOM nodes per planned phenotype. That density gives each plausible phenotype multiple local prototypes without allowing a larger cohort alone to create a more sparse map or more clinical phenotypes. Sample size is instead reviewed through occupancy and map-health diagnostics. Set som_xdim and som_ydim to preserve a reviewed map design explicitly; that frozen map is then used for every compared k and all future projections.

Hard projection uses the Mclust class of the best-matching node. Soft projection combines Mclust node posterior probabilities from the nearest soft_n_nodes codebook nodes using normalized inverse-squared standardized feature distances. Both Cluster_Hard and Cluster_Soft are retained, while assignment controls which is exposed as canonical Cluster (soft-3 by default). SoftEntropy is the normalized entropy of the soft membership probabilities and SoftMargin is the gap between the two largest probabilities. Boundary status (SoftMargin < boundary_margin_threshold or SoftEntropy > boundary_entropy_threshold) is a confidence diagnostic only; it never removes or suppresses a participant.

ProbFit answers the assignment question. Its node-level prob_* columns are Mclust posteriors for codebook nodes; participant-level SoftProb_*, SoftEntropy, and SoftMargin are proximity-weighted membership diagnostics. Use ProbFit$individual for these values and for Cluster, Cluster_Hard, and Cluster_Soft.

ProjectionFit answers the transportability question: how well do these new participants fit the frozen training SOM? ProjectionFit$individual contains each participant’s best-matching SOM_Node, SOM_Distance, percentile in the training distance distribution, and support flags. A high distance means the participant is less well represented by the training map; it does not by itself invalidate the assigned cluster.

ProjectionFit$out_of_support lists variables with values below the observed training minimum or above the observed training maximum. Projection continues for complete cases, but those values are extrapolations and should be reviewed. ProjectionFit$by_cluster shows whether that concern concentrates in a specific cluster.

ProjectionFit$summary includes node_occupancy_js_divergence, a Jensen–Shannon comparison of the training and projected proportions mapped to each frozen SOM node. A value of zero means identical node occupancy; larger values indicate cohort-level use of a different part of the map. It is not an individual fit score and does not by itself mean the model failed.

Mixed and categorical workflows

Gower distance followed by PAM

Gower distance combines mixed feature types, while PAM represents clusters by observed medoids (Gower 1971; Kaufman and Rousseeuw 1990). Projection uses training ranges, levels, and medoids rather than recalculating them in the new cohort.

Note

When to use it: numeric, binary, ordinal, and nominal measures must be clustered together. Inspect before naming: candidate silhouette, size balance, medoids, numeric and categorical profiles, distance/margin, and subsample stability.

Latent class analysis

LCA models class-specific categorical response probabilities (Linzer and Lewis 2011).

Note

When to use it: symptom, diagnosis, questionnaire, or assay-call items are the phenotype definition. Inspect before naming: BIC, entropy, class size, response-probability heatmap, posterior confidence, and subsample stability. Low posterior confidence is evidence of weak class separation.

MCA followed by Mclust

MCA is a dimension-reduction method for nominal categorical measures (Greenacre 2017). Each 90% subsample refits MCA before refitting the mixture.

Note

When to use it: several nominal variables form a useful lower-dimensional category space. Inspect before naming: inertia/scree plot, MCA dimensions, mixture fit, score-space separation, posterior confidence, and stability.

Reveal truth for teaching only

The benchmark truth was not used during fitting. ARI is label-invariant, so cluster numbers do not need to match the truth labels. Strong simulation recovery confirms that the examples behave as designed; it is not external or biological validation.

Compare and interpret profiles

The final label is not the phenotype interpretation. Compare occupancy and feature distributions across plausible models, then use codebook labels when describing the profiles.

Reproducibility

Candidate metrics and SOM + Mclust workflow

All clustering functions have two modes. method = "exploratory" compares the requested 2:10 candidate settings and returns the fit table, candidate audit, and AHP advisory only. method = "finalize" requires the selected setting and returns assignments, profiles, fit diagnostics, and a reusable projection model. AHP is advisory; its selected row is retained in the table but is never highlighted on a figure.

SizeBalance is the smallest extracted cluster/class size divided by the largest (1 is perfectly balanced). MinClusterN/MinClassN is the smallest group size. Subsample ARI measures agreement for the entire partition, whereas per-cluster Jaccard recovery measures whether each reference phenotype reappears after refitting. ReproducibilityScore is the mean of subsample mean ARI and mean Jaccard recovery; subsample success rate is reported separately.

Complementary stability diagnostics

Every successful SOM + Mclust 90% subsample refit projects the complete reference cohort through that refit’s preprocessing, map, and node mixture before calculating ARI. StabilityARI_Mean and StabilityARI_P05 are the primary whole-partition measures. StabilityARI_NonBoundary is secondary: it uses the same reference-defined soft margin/entropy mask in every refit, while the primary ARI always retains boundary participants. Sampling and model seeds are recorded for each replicate. participant_inclusion reports the probability that a participant returns to its reference cluster’s label-matched subsample cluster; cluster_inclusion summarizes that probability by reference cluster.

For complete-case cohorts of 2,000 or fewer participants, coassignment contains the subsample probability that each pair is assigned together and Stability$plots$coassignment displays it. Above that size, the matrix is skipped with a recorded reason to avoid unbounded memory use. For density-based methods, noise remains in global partition metrics but is excluded from inclusion and co-assignment summaries. These diagnostics explain instability; they cannot make a weak phenotype stable.

SOM + Mclust candidate-table fields

CreateClusterModel_SOM_MClust() uses tidyLPA with its mclust backend to fit latent profiles to frozen SOM node codebooks. ShowFitTable() in its help example is only a local display helper: it rounds a table and displays it with a frozen header; it is not a SciDataReportR function.

Field	Definition and interpretation
AIC, AWE, BIC, CAIC, CLC, KIC, SABIC, ICL	Likelihood/information criteria from the LPA fit. Lower values are preferred only when comparing candidates fitted to the same SOM nodes and data. AWE, CLC, and ICL incorporate classification uncertainty (Celeux and Soromenho 1996); KIC is based on symmetric Kullback divergence (Cavanaugh 1999), and SABIC is sample-size adjusted (Sclove 1987). CAIC and CLC are separate criteria, not one combined CAICCLC field.
Entropy	Classification separation summary; higher values indicate cleaner profile separation.
MinProfileNodeN, MaxProfileNodeN	Integer SOM-node counts in the smallest and largest profile.
MinProfileNodeProportion, MaxProfileNodeProportion	The corresponding node counts divided by the total SOM-node count. These replace tidyLPA’s ambiguous decimal n_min and n_max fields.
BLRTStatistic, BLRTPValue	Bootstrap likelihood-ratio statistic and raw p-value for comparing the k-profile fit with k - 1 profiles (Nylund et al. 2007). A small p-value supports the additional profile’s statistical fit, but does not by itself establish stability, clinical meaning, or a final choice; it is unavailable for one profile. The last candidate-review panel displays −log10(BLRTPValue) and marks −log10(0.05), approximately 1.301.
StabilityARI_Mean	Mean adjusted Rand index across successful full-pipeline 90% participant subsample refits without replacement. It may be negative: this means agreement is worse than expected by chance, not an error.
StabilityARI_P05	Fifth percentile of whole-partition ARI across successful refits. It describes the lower tail of reproducibility rather than average agreement.
StabilityARI_NonBoundary, StabilityARI_NonBoundary_P05	Secondary ARI summaries restricted to participants classified as non-boundary in the reference model using the recorded soft margin and entropy thresholds. Boundary participants remain in the primary metrics.
StabilityJaccard_Mean	Mean label-matched, per-profile Jaccard recovery across successful 90% participant subsample refits without replacement.
ReproducibilityScore	Equals StabilityARI_Mean for SOM + Mclust, so final participant-partition agreement remains the primary reproducibility measure. StabilitySuccessRate remains separate.
Reproducibility_scaled	Min-max rescaling of ReproducibilityScore across the current candidate table. It is used only as an AHP input (Akogul and Erisoglu 2017), not as an independently interpretable reproducibility metric.

Method	Candidate metrics
Mclust, PCA + Mclust, MCA + Mclust	BIC/ICL/AIC (information criteria), entropy, maximum posterior uncertainty, minimum cluster size, size balance
K-means, PCA + K-means	WSS, between-cluster sum of squares, silhouette width, Calinski–Harabasz index, minimum size, size balance
Gower + PAM	silhouette width, mean distance to assigned medoid, minimum size, size balance
Latent class	BIC, AIC, log likelihood, entropy, minimum class size, size balance
HDBSCAN and SOM + HDBSCAN	persistence, noise proportion, membership probability, minimum size, size balance; extracted class count is data-derived
SOM + Mclust	LPA AIC/BIC/entropy plus SOM node occupancy and subsample stability

Candidate-metric definitions for every clustering model

All exploratory fit_tables retain the raw metrics produced by their fitted method. AHP is advisory only: any *_scaled field is a within-search rescaling used to construct its index, not a standalone scientific result.

Metric	Definition
Classes	Requested class/cluster count for fixed-count methods. HDBSCAN variants instead report the data-derived number extracted from each density setting.
MinClusterN / MinClassN	Smallest extracted participant cluster/class size. SizeBalance is smallest divided by largest extracted participant group size. SOM + Mclust reports its separate integer node-count and node-proportion fields above.
StabilitySuccessRate	Proportion of requested 90% subsample refits that successfully complete. It is reported separately and is never multiplied into reproducibility.
StabilityARI_Mean, StabilityARI_P05	Mean and fifth percentile of the adjusted Rand index comparing sampled participants’ full-data and subset-refit assignments (Hubert and Arabie 1985). ARI is invariant to cluster numbering and can be negative when agreement is worse than chance.
StabilityJaccard_Mean, StabilityJaccard_Min	Mean cluster-level Jaccard recovery and the minimum cluster-specific mean recovery across successful 90% participant subsample refits (Jaccard 1901).
ReproducibilityScore	Mean of finite StabilityARI_Mean and StabilityJaccard_Mean; it is unavailable when neither component is estimable.
AHPIndex / ahp_index and *_scaled	Advisory within-candidate ranking, calculated from the documented method-specific raw metrics. The recommendation does not finalize a model or alter any fit plot.

Pipeline	Method-specific candidate metrics
Mclust, PCA + Mclust, MCA + Mclust	BIC, ICL, AIC, entropy, and maximum posterior uncertainty. BIC and ICL are reported on the scale mclust returns them on, where higher is better (Scrucca et al. 2016); AIC is reported on the conventional scale, where lower is better. Entropy is higher-is-better and uncertainty is lower-is-better.
K-means, PCA + K-means	Within-cluster sum of squares (WSS; lower), between-cluster sum of squares (BSS; higher), mean silhouette width (higher), and Calinski–Harabasz index (higher) (Calinski and Harabasz 1974; Rousseeuw 1987).
Gower + PAM	Mean silhouette width (higher) and mean assigned-medoid Gower distance (lower). The latter is a dissimilarity, not a probability (Gower 1971; Kaufman and Rousseeuw 1990).
Latent class analysis	Log likelihood (higher), AIC/BIC (lower), and entropy (higher) from the fitted item-response model (Linzer and Lewis 2011).
HDBSCAN	Persistence (mean cluster persistence; higher), NoiseProportion (lower), and the data-derived extracted class count. Membership probability and outlier score are assignment diagnostics, not candidate-selection probabilities (McInnes et al. 2017).
SOM + Mclust	The LPA criteria, node allocation, BLRT, and subsample metrics defined in the dedicated SOM + Mclust table below. SOM distances describe map representation, not phenotype probability (Kohonen 1982).
SOM + HDBSCAN	Node-codebook HDBSCAN persistence, noise proportion, extracted node-cluster count, and 90% participant subsample stability. minPts and epsilon are requested settings; class count is data-derived.

CreateClusterModel_SOM_MClust() is the explicit SOM + Mclust API. CreateSOMClusterModel() remains available for compatibility but is deprecated. The SOM first freezes Z-score preprocessing and learns map nodes; Mclust then clusters those node prototypes. A SOM distance is the distance, in this frozen scaled feature space, between a participant and their best-matching map node. Lower values mean the participant is better represented by the map; they do not mean stronger membership in a phenotype. Interpret it against the frozen training distribution only: distances above the training p95 flag a case that is poorly represented by the training phenotype space.

Specification$rng_kind is R’s RNGkind() configuration: the uniform random number generator, normal random-number generator, and sampling algorithm in effect when the model was fitted. It is provenance for reproducing seeded fits, not a clustering tuning parameter.

How projection works

Every fitted clustering object freezes its preprocessing and records it in Specification; every projected object reports participant-level diagnostics in ProjectionFit$individual, cohort summaries in ProjectionFit$summary, cluster summaries in ProjectionFit$by_cluster, support violations in ProjectionFit$out_of_support, and the applied thresholds in ProjectionFit$policy.

Workflow	Frozen projection rule	Assignment evidence
Mclust	Gaussian-mixture predict() after training scaling	Posterior probabilities and assigned-component Mahalanobis distance
K-means	Nearest frozen centroid	Euclidean centroid distance and second-centroid margin; not a probability
PCA/MCA + clustering	Training scaling and frozen reduction, then the fitted downstream model	The downstream model’s metric/probability
Gower + PAM	Nearest frozen observed medoid using training ranges and levels	Gower medoid distance and runner-up margin
Latent class	Frozen class prevalence and item-response probabilities	Posterior class probabilities
HDBSCAN	Conservative nearest in-training-cluster support rule	Nearest-core distance and support flag; not native HDBSCAN prediction
SOM + Mclust	Frozen scaling, SOM BMU, and node mixture probabilities	BMU distance and node-derived posterior probability
SOM + HDBSCAN	Frozen scaling, SOM BMU, and node HDBSCAN label	BMU distance and inherited node cluster/noise label; not native HDBSCAN prediction

ReproducibilityScore is the mean of subsample mean ARI and mean per-cluster Jaccard recovery. ARI summarizes agreement for the whole partition, whereas Jaccard asks whether each individual phenotype was recovered. Subsample success rate is reported separately and is not folded into the score.

Session information

R version 4.6.1 (2026-06-24)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 24.04.5 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0

locale:
 [1] LC_CTYPE=C.UTF-8       LC_NUMERIC=C           LC_TIME=C.UTF-8
 [4] LC_COLLATE=C.UTF-8     LC_MONETARY=C.UTF-8    LC_MESSAGES=C.UTF-8
 [7] LC_PAPER=C.UTF-8       LC_NAME=C              LC_ADDRESS=C
[10] LC_TELEPHONE=C         LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C

time zone: UTC
tzcode source: system (glibc)

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base

other attached packages:
[1] ggplot2_4.0.3          dplyr_1.2.1            SciDataReportR_21.15.0

loaded via a namespace (and not attached):
  [1] RColorBrewer_1.1-3     rstudioapi_0.19.0      jsonlite_2.0.0
  [4] datawizard_1.4.0       correlation_0.8.8      magrittr_2.0.5
  [7] estimability_2.0.0     farver_2.1.2           rmarkdown_2.32
 [10] vctrs_0.7.3            paletteer_1.7.0        CompQuadForm_1.4.4
 [13] base64enc_0.1-6        rstatix_1.1.0          htmltools_0.5.9
 [16] forcats_1.0.1          progress_1.2.3         haven_2.5.5
 [19] broom_1.0.13           Formula_1.2-6          parallelly_1.48.0
 [22] htmlwidgets_1.6.4      gsubfn_0.7             plyr_1.8.9
 [25] sandwich_3.1-3         emmeans_2.0.4          zoo_1.9-1
 [28] mime_0.13              lifecycle_1.0.5        pkgconfig_2.0.3
 [31] sjlabelled_1.2.0       R6_2.6.1               fastmap_1.2.0
 [34] future_1.76.0          shiny_1.14.0           digest_0.6.39
 [37] colorspace_2.1-4       rematch2_2.1.2         ps_1.9.3
 [40] patchwork_1.3.2        Hmisc_5.3-0            labeling_0.4.3
 [43] gtsummary_2.6.1        progressr_1.0.0        httr_1.4.9
 [46] abind_1.4-8            compiler_4.6.1         withr_3.0.3
 [49] pander_0.6.6           htmlTable_2.5.0        S7_0.2.2
 [52] backports_1.5.1        viridis_0.6.5          carData_3.0-6
 [55] psych_2.6.9            fastDummies_1.7.6      R.utils_2.13.0
 [58] MASS_7.3-65            scatterplot3d_0.3-45   tools_4.6.1
 [61] pbivnorm_0.6.0         MplusAutomation_1.3    foreign_0.8-91
 [64] otel_0.2.0             httpuv_1.6.17          future.apply_1.20.2
 [67] statsExpressions_2.1.2 nnet_7.3-20            R.oo_1.27.1
 [70] glue_1.8.1             quadprog_1.5-8         dbscan_1.2.7
 [73] nlme_3.1-169           promises_1.5.0         grid_4.6.1
 [76] checkmate_2.3.4        cluster_2.1.8.2        generics_0.1.4
 [79] gtable_0.3.6           labelled_2.16.1        R.methodsS3_1.8.2
 [82] tidyr_1.3.2            aweSOM_1.3             data.table_1.18.6.1
 [85] hms_1.1.4              car_3.1-5              RANN_2.6.3
 [88] pillar_1.11.1          stringr_1.6.0          later_1.4.8
 [91] lattice_0.22-9         ggstatsplot_1.1.2      tidyselect_1.2.1
 [94] knitr_1.52             gridExtra_2.3.1        stats4_4.6.1
 [97] xfun_0.61              texreg_1.40            stringi_1.8.9
[100] proto_1.0.0            yaml_2.3.12            boot_1.3-32
[103] evaluate_1.0.5         codetools_0.2-20       nonnest2_0.5-9
[106] tibble_3.3.1           cli_3.6.6              RcppParallel_6.2.1
[109] rpart_4.1.27           xtable_1.8-8           parameters_0.29.3
[112] lavaan_0.7-3           dichromat_2.0-1        Rcpp_1.1.2
[115] tidySEM_0.2.12         globals_0.20.0         coda_0.19-4.1
[118] parallel_4.6.1         kohonen_3.0.13         rstantools_2.7.1
[121] prettyunits_1.2.0      mclust_6.1.3           bayestestR_0.19.0
[124] listenv_1.1.0          viridisLite_0.4.3      mvtnorm_1.4-2
[127] scales_1.4.0           insight_1.5.4          purrr_1.2.2
[130] crayon_1.5.3           rlang_1.3.0            mnormt_2.1.2
[133] poLCA_1.6.0.2          tidyLPA_2.0.2         

References

Akogul, Serkan, and Mahir Erisoglu. 2017. “An Approach for Determining the Number of Clusters in a Model-Based Cluster Analysis.” Entropy 19 (9): 452.

Calinski, Tadeusz, and Jerzy Harabasz. 1974. “A Dendrite Method for Cluster Analysis.” Communications in Statistics 3: 1–27.

Cavanaugh, Joseph E. 1999. “A Large-Sample Model Selection Criterion Based on Kullback’s Symmetric Divergence.” Statistical Methodology 61: 165–80.

Celeux, Gilles, and Gilda Soromenho. 1996. “An Entropy Criterion for Assessing the Number of Clusters in a Mixture Model.” Journal of Classification 13: 195–212.

Gower, John C. 1971. “A General Coefficient of Similarity and Some of Its Properties.” Biometrics 27: 857–71.

Greenacre, Michael. 2017. Correspondence Analysis in Practice. 3rd ed. Chapman; Hall/CRC.

Hubert, Lawrence, and Phipps Arabie. 1985. “Comparing Partitions.” Journal of Classification 2: 193–218.

Jaccard, Paul. 1901. “Etude Comparative de La Distribution Florale Dans Une Portion Des Alpes Et Des Jura.” Bulletin de La Société Vaudoise Des Sciences Naturelles 37: 547–79.

Jolliffe, Ian T, and Jorge Cadima. 2016. “Principal Component Analysis: A Review and Recent Developments.” Philosophical Transactions of the Royal Society A 374 (2065): 20150202.

Kaufman, Leonard, and Peter J Rousseeuw. 1990. Finding Groups in Data: An Introduction to Cluster Analysis. Wiley.

Kohonen, Teuvo. 1982. “Self-Organized Formation of Topologically Correct Feature Maps.” Biological Cybernetics 43: 59–69.

Linzer, Drew A, and Jeffrey B Lewis. 2011. “poLCA: An r Package for Polytomous Variable Latent Class Analysis.” Journal of Statistical Software 42 (10): 1–29.

MacQueen, James B. 1967. “Some Methods for Classification and Analysis of Multivariate Observations.” Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability 1: 281–97.

McInnes, Leland, John Healy, and Steve Astels. 2017. “Hdbscan: Hierarchical Density Based Clustering.” Journal of Open Source Software 2 (11): 205.

Nylund, Karen L, Tihomir Asparouhov, and Bengt O Muthén. 2007. “Deciding on the Number of Classes in Latent Class Analysis and Growth Mixture Modeling: A Monte Carlo Simulation Study.” Structural Equation Modeling 14 (4): 535–69.

Rousseeuw, Peter J. 1987. “Silhouettes: A Graphical Aid to the Interpretation and Validation of Cluster Analysis.” Journal of Computational and Applied Mathematics 20: 53–65.

Sclove, Stanley L. 1987. “Application of Model-Selection Criteria to Some Problems in Multivariate Analysis.” Psychometrika 52: 333–43.

Scrucca, Luca, Michael Fop, Thomas B Murphy, and Adrian E Raftery. 2016. “Mclust 5: Clustering, Classification and Density Estimation Using Gaussian Finite Mixture Models.” Journal of Statistical Software 71 (11): 1–29.