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REVIEW 4 major objections 4 minor 13 references

Comparing unsupervised learning methods for local structural identification in colloidal systems

T0 review · 4 major / 4 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read On bulk crystals and confined colloidal clusters, UMAP separates local structural classes more cleanly than PCA, autoencoders, or q4/q6 order parameters, with or without labels.

desk verdict Useful bulk benchmark, but the supraparticle comparison stacks the deck for UMAP and the 'consistently outperforms' claim outruns the evidence. read the letter →

arxiv 2509.07186 v1 pith:5OOB524O submitted 2025-09-08 cond-mat.soft physics.data-an

Alptuğ Ulugöl , Jessi Bückmann , Ruizhi Yang , Roy Hoitink , Alfons van Blaaderen , Frank Smallenburg , Laura Filion This is my paper · ORCID
classification cond-mat.softphysics.data-an
keywords unsupervisedmachinelearninglocalstructureclassificationdimensionalityreductionUMAPbondorientationalorderparameterscolloidalself-assemblyicosahedralsupraparticlesGaussianmixturemodels
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper compares four routes for unsupervised classification of local particle environments in colloidal systems: the classical q4/q6 bond-orientational order parameters, PCA, autoencoders, and UMAP, each followed by Gaussian-mixture clustering with entropy-based merging. On bulk crystals of hard and charged spheres (FCC, HCP, BCC, fluid), UMAP gives nearly perfect separation and the highest normalized mutual information and silhouette scores, with autoencoders close behind. On icosahedrally symmetric supraparticles, where no ground-truth labels exist, UMAP resolves surface, shell, and core environments that the other methods blur or miss, and it does so again on an experimental three-dimensional STED image. The paper argues that UMAP is the best practical trade-off between accuracy, interpretability, and simplicity, since it has essentially one tunable parameter (number of neighbors). If the claim holds, the default pipeline for unsupervised structural discovery in self-assembled systems becomes UMAP embeddings of physically informed descriptors, clustered by GMM and merged by entropy.

What carries the argument

The load-bearing mechanism is the unsupervised pipeline: each particle is described by 13 rotation-invariant scalars, twelve averaged bond-orientational order parameters q_l (l=2..12) and a new local centricity measure delta_r, the normalized distance between a particle and the center of mass of its solid-angle nearest neighbors. These descriptors are compressed to two or three dimensions by PCA, an autoencoder, or UMAP, where UMAP models the data as a fuzzy topological graph and minimizes cross-entropy between high- and low-dimensional neighborhoods. The reduced space is then clustered with a Gaussian mixture model, and components are merged using the entropy-based merging scheme, with the

What would settle it

Run the identical pipeline on a simulated mixture with known labels but complex coexisting motifs (for example, a confined supraparticle annotated by a human or by a supervised classifier) while forcing all methods to the same number of clusters, chosen by the same rule; if UMAP's NMI or silhouette no longer exceeds AE and PCA by the reported margins, the claim of consistent superiority fails. A cheaper check: on the supraparticle data, recalculate silhouette scores with cluster counts equalized at 8, 11, and 16 for every method and see whether UMAP still leads.

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Extended reading notes

Core claim

The paper's central claim is that UMAP, applied to a 13-dimensional descriptor vector (twelve locally averaged bond-orientational invariants q2..q12 plus a new center-of-mass asymmetry parameter delta_r), yields cleaner unsupervised structural classes than PCA, autoencoders, or q4/q6 alone. The evidence is two-fold: in labeled bulk crystals UMAP achieves an NMI of 0.985 and a silhouette score of 0.766 with essentially perfect confusion matrices, while in unlabeled confined supraparticles it separates surface, first-shell, transition, and core domains across radial and planar cuts, with silhouette 0.391 versus 0.151 (AE), 0.091 (PCA), and -0.068 (q4/q6). The experimental STED supraparticle co

Load-bearing premise

The ranking assumes that picking final cluster counts by eye from entropy-curve elbows, at unequal counts across methods (8, 11, and 16), is a fair basis for comparison, and in the unlabeled supraparticle case it assumes the visually identified surface/core features are the true structures.

Editorial extensions

If this is right

  • For bulk crystalline classification, UMAP separates FCC, HCP, BCC, and fluid into pure clusters, so the pipeline can replace hand-tuned order parameters for distinguishing known polymorphs.
  • On spherically confined hard spheres, UMAP autonomously resolves surface fivefold regions, a transition layer, tetrahedral cores, and interfacial tubes, making those structures discoverable without labels.
  • The same UMAP pipeline transfers to experimental 3D STED images, meaning structural motifs can be identified directly from confocal data without simulation labels.
  • Because UMAP has effectively one tunable hyperparameter, the method is deployable where autoencoder hyperparameter tuning is impractical, especially on large single-particle datasets.
  • The new asymmetry descriptor delta_r adds information beyond angular order and can be reused in other descriptor sets.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If UMAP consistently wins on both labeled and unlabeled colloidal datasets, the local structural variation in these dense systems likely lives on a low-dimensional nonlinear manifold, so linear methods such as PCA will lag regardless of descriptor choice.
  • The same pipeline could be applied to time-resolved trajectories to identify structural transitions between motifs, since the clustering is frame-agnostic and fast enough for large datasets.
  • A testable extension is to replace the visual elbow selection with an automated knee-finder; doing so would remove the main subjective step and could change the relative rankings, possibly shrinking UMAP's margin.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper compares three unsupervised dimensionality-reduction methods (PCA, autoencoder, UMAP) plus a q4/q6 baseline for classifying local particle environments in colloidal systems. Descriptors are averaged bond-orientational order parameters q_l (l=2..12) plus a centrosymmetry measure δr; after embedding, GMM clustering with entropy-based merging assigns structural classes. In a labeled bulk dataset (FCC, HCP, BCC, fluid), UMAP gives the highest NMI and silhouette scores, with autoencoders close behind. In an unlabeled icosahedral supraparticle dataset, UMAP is claimed to give the best separation based on silhouette scores and qualitative radial/planar cuts; a single experimental STED supraparticle is analyzed with UMAP. The paper concludes UMAP consistently outperforms the other methods.

Significance. If the performance claim held, the paper would provide a useful practical recommendation: UMAP + GMM with entropy merging as a default unsupervised structural-discovery pipeline. The bulk benchmark is a genuine strength: it uses a physically meaningful labeled dataset, reports confusion matrices and NMI, and shows nonlinear embeddings outperform q4/q6 and PCA. The main limitation is that the unlabeled supraparticle comparison is not yet a fair test of the central claim, because cluster counts and evaluation metrics are method-dependent. The experimental demonstration is suggestive but not quantitative. With a redesigned comparison, the manuscript would be a solid contribution to the soft-matter ML toolbox.

major comments (4)
  1. [§III.B, Figs. 10,12,13,15 and Fig. 17] The supraparticle comparison uses different final cluster counts chosen by visual inspection: 8 (q4/q6), 8 (PCA), 11 (AE), 16 (UMAP). Silhouette scores (Eq. 12) are not comparable across these settings: silhouette generally increases with the number of clusters in a given space, and here the distances d(i,j) are computed in different embeddings (original q4/q6 plane, PCA space, AE latent space, UMAP space). UMAP specifically optimizes local neighborhood separation, so a high silhouette in the UMAP space is by construction more likely. To support 'consistently outperforms,' the cluster count must be fixed across methods (or chosen by a single automated criterion), and the comparison should be repeated with a label-free metric less dependent on the embedding's metric or with a held-out physical validation (e.g., ability to predict particle mobility or known shell structure).
  2. [§III.A, Fig. 8(e)] The bulk benchmark is the most trustworthy part, but the claimed consistency is not strongly supported by the numbers: UMAP NMI is 0.985 versus 0.978 for AE, and the confusion matrices are nearly identical (Fig. 8(c,d)). No uncertainty quantification is provided (e.g., bootstrap over particles/configurations or multiple independent simulation seeds). The silhouette advantage (0.766 vs 0.636) is larger but is again computed in the dimension-reduced space of each method, which favors UMAP's embedding objective. The paper should either add error bars / repeated runs and a test of statistical significance, or temper the 'consistently outperforms' claim to 'performs comparably or slightly better on bulk data.'
  3. [§III.C, Fig. 20] The experimental section states that UMAP is 'the only one of the three' that accurately captures the structure, but figure 20 shows only UMAP results. To make this claim, the PCA and AE classifications for the same experimental supraparticle must be shown, and the evaluation needs a quantitative criterion (e.g., agreement with simulated radial-shell assignments or with known symmetry landmarks). As written, this part is anecdotal and cannot independently support the central claim.
  4. [§II.C, entropy merging] The entropy-based merging procedure is presented as an objective way to choose cluster number, but the actual choice is made by visual inspection of elbows/transitions (Figs. 10(b), 12(b), 13(b), 15(b)), and the same visual inspection is used to assert that the resulting clusters are meaningful. For the unlabeled supraparticle data this creates a selection loop: cluster counts that produce visually appealing patterns are chosen, then the method is praised for producing those patterns. Please automate the elbow detection (e.g., L-method with a formal breakpoint) or report the sensitivity of all downstream conclusions to the chosen cluster count.
minor comments (4)
  1. [Abstract, Introduction] The phrase 'noa priori' appears with a missing space in the abstract and in the introduction. This is a typographical issue.
  2. [§II.B.2] No numerical details are given for the autoencoder training (learning rate, epochs, batch size, regularization, activation functions). For reproducibility, these hyperparameters should be specified in the text or in a supplementary table.
  3. [§III.B, Figs. 18-19] The cluster color maps are not described in the captions, and it is unclear whether the same colors represent the same cluster classes across different panels and methods. A shared color legend or consistent cluster labels would make the qualitative comparison much easier to evaluate.
  4. [§III.C] The text first says 'we use the UMAP algorithm to study the structure' and later refers to 'the only one of the three'—please clarify whether PCA and AE were actually run on the experimental data and, if so, why their results are not shown with the same level of detail.

Circularity Check

1 steps flagged · score 4.0 of 10

Supraparticle benchmark has a selection/evaluation loop: UMAP's silhouette advantage partly reduces to its own objective.

  1. other [Section III.B (PCA/AE/UMAP clustering selection) and Section III.B.4, Fig. 17 with Eq. (12)]
    "After visual inspection of the clustering, we select 8 as the final number of clusters to capture the major structural diversity present. ... We therefore select 16 clusters as the final number for classification, balancing resolution of important substructures with avoidance of overfitting. ... As shown in Fig. 17, none of the silhouette scores are extremely high. However, UMAP achieves the highest score (0.391), followed by the autoencoder (0.151), and PCA (0.091)."

    The final cluster number is chosen per method by visually inspecting the same low-dimensional embedding that is later scored (8, 8, 11, 16 clusters for q4/q6, PCA, AE, UMAP). The silhouette score of Eq. (12) is then computed with distances in that same method-specific reduced space. For UMAP, this is a direct reflection of its training objective: the cross-entropy loss in Eq. (6) explicitly pushes non-neighbor points apart in the low-dimensional embedding, which is exactly the separation that silhouette's b(i)-a(i) rewards. Thus UMAP's higher silhouette score in the unlabeled supraparticle test is substantially forced by the evaluation protocol, not an independent measurement of structure discovery. The qualitative radial cuts are also interpreted after knowing which embedding produced the

full rationale

The bulk crystalline benchmark (Section III.A) is an independent, externally labeled test: confusion matrices, NMI, and silhouette are computed against known FCC/HCP/BCC/fluid labels. That part is self-contained and gives UMAP the highest NMI (0.985 vs 0.978 for AE), though the margin is tiny. No fitted parameter is passed off as a prediction there, and no load-bearing self-citation is used; Ref. 37 is cited only for the AE architecture. The circularity concern is confined to the unlabeled supraparticle comparison (Section III.B). There, the cluster count is selected by visual inspection of the embedding that is later evaluated, and silhouette is computed in each method's own reduced space. Because UMAP's loss function directly optimizes low-dimensional separation, its superior silhouette score is partly a consequence of the method's objective rather than of superior structural discovery. This is a partial selection/evaluation loop, not a full derivation collapse, so the score is 4 rather than 6+.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central claim relies on a handful of modeling and evaluation choices: the sufficiency of the 13-dimensional descriptor vector, the assumption that UMAP's manifold model applies, the validity of entropy-based cluster merging, and the fairness of comparing silhouette scores at different cluster counts. No new physical entities are introduced.

free parameters (5)
  • UMAP n_neighbors = 25
    Chosen by hand for both bulk and supraparticle datasets; affects the neighborhood graph and the resulting embedding.
  • UMAP min_dist = 1e-4
    Chosen by hand; the authors state it mostly affects visual compactness but this is not systematically tested.
  • Final cluster count (supraparticle) = 8 (q4/q6), 8 (PCA), 11 (AE), 16 (UMAP)
    Selected via visual inspection of entropy elbow curves; differs by method and biases silhouette comparison.
  • Initial GMM component count = 7-8 (bulk), 15 (PCA), 20 (AE/UMAP)
    Set conservatively before entropy merging; the authors state they err on the side of large numbers.
  • AE architecture hyperparameters = not given (from Ref. 37)
    Widths, activations, learning rate and training length are not stated; they are taken from Ref. 37, limiting reproducibility.
assumptions (5)
  • standard math UMAP correctly models the data as lying on a low-dimensional Riemannian manifold
    The paper relies on UMAP's theoretical framework (Ref. 36) without testing its assumptions on the descriptor distributions.
  • domain assumption 13-dimensional descriptor vector (q_l for l=2..12 plus delta-r) is sufficient to distinguish the relevant local environments
    Sec. II A; the paper does not validate that this descriptor set separates the structures of interest; it only tests the pipeline on known systems.
  • domain assumption Entropy-based merging and the L-method identify the physically meaningful number of clusters
    Sec. II C; the final cluster count is chosen by visual elbow detection, and this selection drives the method comparison.
  • domain assumption Labels for bulk phases (FCC, HCP, BCC, fluid) are correct
    Sec. III A; MC simulations generate known phases, but BCC is produced in a point Yukawa system whose parameters are not fully specified.
  • domain assumption GMM components are a valid representation of structural classes in the reduced space
    Sec. II C; the paper notes true local environments may be non-Gaussian and anisotropic, yet uses GMM throughout.

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Cite this review

Pith. "Pith review of Comparing unsupervised learning methods for local structural identification in colloidal systems." pith.science (2026). https://pith.science/paper/5OOB524O

@misc{pith2026250907186,
  author       = {Pith},
  title        = {Pith review of: Comparing unsupervised learning methods for local structural identification in colloidal systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5OOB524O}},
  note         = {Machine review of arXiv:2509.07186}
}
read the original abstract

Quantifying local structures in self-assembled systems is a central challenge in soft matter and materials science. When no a priori knowledge of the relevant structures is available, traditional order parameters often fall short. Unsupervised machine learning provides a convenient route to autonomously uncover structural motifs directly from particle configurations. In this work, we systematically compare three popular dimensionality reduction techniques; Principal Component Analysis (PCA), Autoencoders (AE), and Uniform Manifold Approximation and Projection (UMAP), for classifying local environments in self-assembled systems. We first apply these methods to fluid and crystal configurations of hard and charged spheres. Thereafter, we apply it to an icosahedral arrangement of spheres that self-assembled in spherical confinement, both from simulations as well as from experiments. We demonstrate that UMAP consistently outperforms the other methods in capturing complex structural features, offering a robust tool for structural classification without supervision.

Figures

Figures reproduced from arXiv: 2509.07186 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic representation of UMAP’s working principle. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The dataset used in the bulk structure analysis. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Clustering of bulk structures in the [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (16 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Dimensionality analysis of bulk structures. (a) Variance ex [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Clustering of bulk structures in the PCA projected plane. (a) [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Clustering of bulk structures in the autoencoder projected [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 9
Figure 9. Figure 9: FIG. 9. One of the configurations used in the self-assembled icosa [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 8
Figure 8. Figure 8: FIG. 8. (a–d) Confusion matrices showing the correlation between [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Dimensionality analysis of spherically confined hard [PITH_FULL_IMAGE:figures/full_fig_p010_11.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Clustering of icosahedral supraparticles in the [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]
Figure 16
Figure 16. Figure 16: At 4 clusters, the clustering distinguishes broadly be [PITH_FULL_IMAGE:figures/full_fig_p010_16.png]
Figure 13
Figure 13. Figure 13: FIG. 13. Clustering of icosahedral supraparticles in the autoencoder [PITH_FULL_IMAGE:figures/full_fig_p011_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14. Entropy-based cluster merging of an icosahedral supraparti [PITH_FULL_IMAGE:figures/full_fig_p011_14.png]
Figure 17
Figure 17. Figure 17: FIG. 17. Silhouette scores for clustering in the supraparticle dataset [PITH_FULL_IMAGE:figures/full_fig_p012_17.png]
Figure 15
Figure 15. Figure 15: FIG. 15. Clustering of icosahedral supraparticles in the UMAP. (a) [PITH_FULL_IMAGE:figures/full_fig_p012_15.png]
Figure 16
Figure 16. Figure 16: FIG. 16. Entropy-based cluster merging of an icosahedral supraparti [PITH_FULL_IMAGE:figures/full_fig_p012_16.png]
Figure 18
Figure 18. Figure 18: FIG. 18. Final cluster assignments for each method (columns) across radial cuts of the same supraparticle configuration (rows). [PITH_FULL_IMAGE:figures/full_fig_p013_18.png]
Figure 19
Figure 19. Figure 19: FIG. 19. Final cluster assignments for each method shown by a [PITH_FULL_IMAGE:figures/full_fig_p014_19.png]
Figure 20
Figure 20. Figure 20: FIG. 20. The cluster assignments of an experimental icosahedral [PITH_FULL_IMAGE:figures/full_fig_p015_20.png]

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Reference graph

Works this paper leans on

13 extracted references · 13 canonical work pages

  1. [1]

    It achieves this by computing the eigenvectors of the covariance matrix of the input data and projecting each data point onto the leading eigenvectors (prin- cipal components)

    Principal component analysis (PCA) PCA is a linear dimensionality reduction technique that identifies directions in feature space along which the variance of the data is maximized34. It achieves this by computing the eigenvectors of the covariance matrix of the input data and projecting each data point onto the leading eigenvectors (prin- cipal components...

    work page

  2. [2]

    Autoencoder (AE) Autoencoders are a class of artificial neural networks de- signed to learn efficient representations of input data41,42. An autoencoder consists of two parts: an encoder that maps high- dimensional inputs to a low-dimensional latent space (the bot- tleneck), and a decoder that attempts to reconstruct the orig- inal inputs from this latent...

    work page

  3. [3]

    At its core, UMAP assumes that the data lies on a low- dimensional Riemannian manifold embedded in a higher- dimensional space

    Uniform manifold approximation and projection (UMAP) UMAP is a nonlinear dimensionality reduction algorithm introduced in 2018 36 that constructs a low-dimensional rep- resentation of high-dimensional data by modeling its intrinsic geometry. At its core, UMAP assumes that the data lies on a low- dimensional Riemannian manifold embedded in a higher- dimens...

    work page 2018

  4. [4]

    In the second step, a fluorescent shell was grown around the particles, through which the particles could be detected with confocal/STED microscopy

    Supraparticle formation The particles were made in three steps, where small sil- ica seeds are created in the first step, to provide a reason- ably monodisperse starting point. In the second step, a fluorescent shell was grown around the particles, through which the particles could be detected with confocal/STED microscopy. Finally, a larger non-fluoresce...

    work page

  5. [5]

    The supra- particles were index-matched within 0.002 using a mixture of 82.5 wt% glycerol/water

    Supraparticle Analysis After several washing steps to remove surfactants, all supra- particles were dried on a #1.5H high precision cover slip (Menzel Gläser), glued to a standard microscopy slide (Men- zel Gläser) in which a 8 mm hole was drilled. The supra- particles were index-matched within 0.002 using a mixture of 82.5 wt% glycerol/water. All confoca...

    work page

  6. [6]

    We first analyze the variance explained by each principal component

    Principal component analysis Next, we assess the performance of PCA as a dimension- ality reduction technique for the classification of bulk crys- talline structures. We first analyze the variance explained by each principal component. As shown in Fig.4(a), the first two principal com- ponents account for a substantial fraction of the total variance. The ...

    work page

  7. [7]

    Mo- tivated by the results of the PCA analysis, we design the autoencoder to project the structural descriptors into a two- dimensional latent space

    Autoencoders We now turn to autoencoders (AE) as a nonlinear dimen- sionality reduction technique for structural classification. Mo- tivated by the results of the PCA analysis, we design the autoencoder to project the structural descriptors into a two- dimensional latent space. After training the network to min- imize reconstruction loss, we project the d...

    work page

  8. [8]

    Based on the PCA analysis, we project the data onto a two-dimensional space

    Uniform Manifold Approximation and Projection Finally, we evaluate the performance of UMAP as a non- linear dimensionality reduction method for the bulk structural classification. Based on the PCA analysis, we project the data onto a two-dimensional space. After training UMAP using 25 nearest-neighbors and expected minimum distance 10 −4 as hyperparameter...

    work page

Show all 13 references
  1. [9]

    Summary of Bulk Structure Classification Since we tested each method on labeled data here (data aris- ing from simulations of the individual phases), we have access to model accuracies. As a first way to estimate the accuracy, we calculate the confusion matrices, which list fo...

  2. [10]

    The variance explained by each principal component, shown in Fig.11(a), indicates that the first three principal components capture a substantial fraction of the total variance

    Principal component analysis We next apply PCA to the supraparticle dataset. The variance explained by each principal component, shown in Fig.11(a), indicates that the first three principal components capture a substantial fraction of the total variance. The cumu- lative expla...

  3. [11]

    Autoencoders We next apply a neural network-based autoencoder to per- form nonlinear dimensionality reduction on the supraparti- 10 FIG. 10. Clustering of icosahedral supraparticles in the q4 vs. q6 plane. (a) AIC and BIC scores for GMM clustering. (b) Entropy as a function of...

  4. [12]

    The GMM clustering procedure is shown in Fig

    Uniform Manifold Approximation and Projection We now apply UMAP to the supraparticle dataset using the same hyperparameters that we use for the bulk structures, and again project onto three dimensions. The GMM clustering procedure is shown in Fig. 15(a), where both the AIC and...

  5. [13]

    soft-matter/trackpy: v0.6.4,

    Summary of Supraparticle Structure Classification To quantitatively evaluate the performance of the differ- ent dimensionality reduction methods on the supraparticle dataset, we compute the silhouette score for each method. Re- call that the silhouette score quantifies the deg...

    2019 arXiv

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