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REVIEW 4 major objections 5 minor 36 references

Unsupervised Parameter-free Outlier Detection using HDBSCAN* Outlier Profiles

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read An elbow in a score curve pins down GLOSH's best settings without any user parameters.

desk verdict Useful and novel heuristic pair for removing two user choices from GLOSH, but the central elbow-to-best-P@n link is empirically asserted on the same datasets used to design it, and the ORD-Profile measure never actually looks at point rankings. read the letter →

arxiv 2411.08867 v1 pith:VMIGNXRD submitted 2024-11-13 cs.LG

Kushankur Ghosh , Murilo Coelho Naldi , Jörg Sander , Euijin Choo This is my paper · ORCID
classification cs.LG
keywords outlierdetectionGLOSHHDBSCAN*minptsselectionautomaticthresholdparameter-freehierarchicaldensity-basedclusteringunsupervisedlearning
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

This paper claims that the two parameters a user must otherwise supply to the GLOSH outlier detector — the HDBSCAN* density parameter minpts and the number of outliers to look for — can be chosen automatically with no loss in detection quality. The authors introduce Auto-GLOSH, which builds a per-point profile of GLOSH scores across a range of minpts values and then reads off the value at which consecutive sorted score lists stop changing chaotically and start changing at a uniform rate. That value, found as the elbow of a dissimilarity curve, is claimed to be the minpts where GLOSH achieves its best or near-best precision at finding the true outliers. A second component, POLAR, finds a knee in the sorted score sequence at that minpts and adjusts it by linear regression to set a cutoff that labels potential outliers without knowing how many there are. The payoff is a fully unsupervised, parameter-free version of GLOSH whose reported precision on global, clumped, and mixed outliers matches or approaches the best achievable with any minpts in the tested range.

What carries the argument

The central objects are the GLOSH–Profile — for each point, the array of its GLOSH scores over minpts values 2 to mmax — and the GLOSH Outlier Rank Dissimilarity–Profile (ORD–Profile), which records 1 minus the Pearson correlation between the sorted GLOSH score sequences at consecutive minpts values. The ORD-Profile's elbow, located by the maximum orthogonal distance from the curve to a chord, is the load-bearing signal: the paper argues that this elbow marks the minpts where rank order and score magnitudes stabilize and where GLOSH's outlier ranking is best. The same maximum-orthogonal-distance geometry, applied to the sorted scores at the chosen minpts and followed by a regression-based adjustment of the knee threshold, carries the threshold-selection half of the argument.

What would settle it

Take a benchmark dataset with ground-truth outliers, compute the ORD-Profile and GLOSH's Precision@n for every minpts from 2 to 100, and check whether the minpts selected by the maximum-orthogonal-distance rule matches the minpts with maximum Precision@n; any dataset where the two differ by a wide margin, or where the ORD-Profile lacks a distinct elbow, would falsify the central claim. A pointed version: construct a mixture where ranking quality peaks at a high minpts but the curve's elbow falls early, showing the chosen setting underperforms the best achievable setting.

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Extended reading notes

Core claim

GLOSH, the outlier detector built into HDBSCAN*, assigns each point a score by comparing its density with the densest point in its cluster in a hierarchical density estimate; the hierarchy, and hence the scores, depend on a user-chosen minpts. The paper's central discovery is an empirical regularity: as minpts increases, the Pearson dissimilarity between the sorted GLOSH score lists of consecutive minpts values is initially large and erratic, then drops to near zero, and the point where it drops — the elbow — coincides with the minpts where GLOSH's Precision@n is best. Auto-GLOSH locates this elbow by maximizing the orthogonal distance from the curve to the straight line joining the curve's maximum and its endpoint, and uses that minpts value. At that value, the sorted GLOSH scores show a knee where outlier scores accelerate away from the inlier trend; POLAR identifies the knee by the same distance rule and then fits a linear regression to the pre-knee inlier scores to set a threshold beyond the knee, so outliers are labelled without a preset count. The paper reports that on 69 datasets spanning global outliers, local outliers, and outlier clumps, this parameter-free pipeline attains the best or near-best GLOSH result on most datasets and is competitive with or better than KNN, LOF, ABOD, and COPOD on the majority of tested cases.

Load-bearing premise

The load-bearing premise is empirical rather than proven: the dissimilarity curve between consecutive GLOSH score lists must have a single clean elbow at exactly the density parameter where GLOSH's outlier ranking is best; a real dataset with no such elbow, or with an elbow that does not align with ranking quality, leaves the method without an anchor.

Editorial extensions

If this is right

  • A practitioner can run GLOSH on a new dataset with no parameter choices and obtain Precision@n equal to or close to the best that any minpts in the tested range would give, for global, clumped, and mixed outliers.
  • The automatically chosen minpts frequently outperforms the common hand-picked values (5, 10, 25, 50, 100), so the method removes a source of sensitivity that prior work identified for GLOSH.
  • The POLAR threshold gives F-measure and G-Mean close to the best obtainable threshold on most datasets; when recall matters more than precision, using the unadjusted knee threshold is the paper's stated alternative.
  • Because all hierarchies for the minpts range can be extracted from one core graph (CORE-SG), the entire parameter-free procedure runs in time comparable to a single HDBSCAN* pass rather than mmax separate passes.

Reading between the lines

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

  • Beyond the paper's tests, the elbow rule is a stability-detection heuristic, so an "elbow strength" diagnostic could be added: datasets whose ORD-Profile is flat or has multiple elbows would be flagged as unreliable, instead of silently returning a minpts.
  • The same profile idea may transfer to other parameters of density hierarchies, such as cluster-selection thresholds or mutual-reachability scaling, wherever a stability elbow is expected to mark a regime change in ranking behavior.
  • On datasets with semantically anomalous but locally dense outliers, the paper's Table I suggests these points look like inliers to several methods; an implicit practical conclusion is that Auto-GLOSH is most reliable when suspected outliers are genuinely density-deviant.
  • A testable variant would replace the maximum-distance elbow rule with a model-selection rule, such as a piecewise-linear fit of the ORD-Profile, and check whether the chosen minpts tracks best Precision@n more closely on high-dimensional benchmarks.
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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 / 5 minor

Summary. The paper proposes Auto-GLOSH and POLAR, two unsupervised heuristics for removing the main user choices from GLOSH-based outlier detection. Auto-GLOSH computes a per-point GLOSH-Profile over a range of minpts values, then builds an ORD-Profile of Pearson dissimilarities between consecutive sorted GLOSH score lists; the minpts at the elbow of this profile is selected as m*. POLAR then thresholds the GLOSH scores at m* by locating a knee in the sorted score sequence and adjusting it with a linear-regression extrapolation of the inlier trend. The evaluation covers 69 datasets, mostly Banana/Anisotropic/Circular with synthetic global, clump, and local outliers, plus semi-synthetic datasets built from 15 real one-class-classification inlier sets. The reported results show near-oracle P@n for global outliers and clumps, and weaker results for local outliers.

Significance. If the central regularity were established, the contribution would be practically valuable: users could run GLOSH without choosing minpts or a score threshold or a count n, and the CORE-SG construction gives a credible efficiency argument. The dataset count is broad, the comparison against KNN, LOF, ABOD, and COPOD is useful, and the runtime table (Table V) is informative. However, the load-bearing claim that the ORD-Profile elbow coincides with the minpts of best ranking quality is currently supported mainly by a measure that does not directly test ranking quality, and by visual inspection of the same Banana dataset that later appears in the scored tables. The paper is honest about the local-outlier difficulty, but the abstract and conclusions state a stronger, unrestricted claim. The contribution is promising but not yet established.

major comments (4)
  1. [IV-C, Definition 4.2 and Eq. (4)] The ORD-Profile is computed on sorted GLOSH score sequences, which discards the point-to-score mapping. Precision@n depends on whether the true outliers occupy the top n positions, i.e., on exactly that mapping. Two consecutive minpts values can have nearly identical sorted score lists while the top-n membership changes completely; the ORD-Profile would then report near-zero dissimilarity despite a large change in P@n. The text in IV-C states that 'relative order and magnitude' change minimally, but the measure never examines relative order of points. Please provide direct evidence for the claimed correspondence, for example by plotting the Jaccard overlap or rank correlation of the top-n point sets against the ORD-Profile over the same minpts range, across all datasets. This is the central claim of Section IV-C and currently rests on indirect evidence.
  2. [IV-B and IV-C, Figures 2-4 vs Tables II-IV and VI] The central regularity was calibrated on the Banana dataset in Figures 2-4, and the same Banana dataset is included in the main evaluation in Tables II, III, IV, and VI. Since the elbow-to-best-P@n correspondence is asserted from visual inspection of this dataset rather than derived, the near-oracle results on Banana are partly circular. Please report the evaluation on datasets that were not used to motivate the method, or remove Banana from the scored tables, or provide a derivation of the regularity from GLOSH/HDBSCAN* properties.
  3. [IV-B and Table II, local-outlier columns] The paper states in IV-B that for local outliers there is 'no notable gap between the profiles of local outliers and inliers' and that one cannot choose an arbitrary value beyond the elbow. Consistently, the local-outlier P@n values in Table II include 0.35 for STAMPS, 0.22 for BREASTW, and 0.76 for Circular, which are far from the claimed best-or-near-best behavior. The abstract and introduction claim general 'best or near best' outlier detection results without restricting to global outliers and clumps. Please either restrict the central claim to the settings where the regularity holds, or provide additional evidence that Auto-GLOSH and POLAR handle local outliers on datasets beyond the current weak cases.
  4. [IV-B and VI-A] All scored outliers are generated by a single protocol: GMM covariance or mean scaling with alpha=5, uniform global draws, and Tomek-link filtering. The real one-class classification datasets in Table I are explicitly not used for scoring, and the paper argues that their 'labeled outliers' do not behave like statistical outliers. This means the generalization to real outlier structure is unestablished. Please add experiments with different generation settings (varying alpha, noise levels, cluster shapes) or with real OCC datasets under a clearly stated evaluation protocol, and discuss whether the ORD-Profile elbow remains aligned with best P@n when the outlier generation model is changed.
minor comments (5)
  1. [IV-C, Eq. (4)] The sentence in IV-C that high covariance between consecutive sorted score sequences implies high Pearson dissimilarity is backwards: under Eq. (4), high covariance relative to the variances gives a high correlation and hence a dissimilarity close to 0. Please correct the reasoning or the equation.
  2. [V-B] The description of POLAR says to search for the GLOSH score I that is most similar to the extrapolated score R, but 'most similar' is not defined. Specify the distance used and the behavior when R falls outside the observed score range.
  3. [Title and Abstract] The term 'parameter-free' overstates the method: mmax, the i+3 index mapping from the ORD-Profile elbow to minpts, and the linear-regression adjustment are user-specified or heuristic choices. Please qualify the claim, for example by stating that the method removes the need to choose minpts and the outlier count/threshold while retaining a range bound mmax.
  4. [Table II] The header of Table II contains repeated artifacts such as 'Γ5Γ5Γ5' and 'Γ10Γ10Γ10'; please clean the table formatting so that each column is labeled once.
  5. [IV-E] The complexity statement 'assessing the m* value has O(n) time' is imprecise because the ORD-Profile has length O(mmax); please state the complexity consistently in terms of both n and mmax.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the ORD-Profile/P@n alignment is an empirical heuristic, not a construction that makes the prediction equivalent to its inputs.

full rationale

The paper's central claim—that the ORD-Profile elbow marks the minpts where GLOSH achieves its best P@n (Section IV-C)—is presented as an empirical observation illustrated on the Banana dataset, not as a quantity derived from P@n. Auto-GLOSH selects m* solely from the ORD-Profile R_mmax (Equation 5) using a geometric elbow rule; ground-truth labels and P@n enter only in evaluation, not in the selection rule itself. POLAR similarly derives a threshold from sorted GLOSH scores at m* via a knee point and a linear-regression adjustment, again without using labels. No fitted parameter is renamed as a prediction, and no equation reduces to another by construction. Citations to the authors' prior work ([8], [17], [18]) support computational efficiency for extracting multiple hierarchies and the practical choice of mmax < 100; they do not carry the correctness of the outlier-detection claim. The inclusion of Banana in the experimental tables is a data-reuse concern for generalization, but it is not circularity in the sense of the prediction being forced by its own inputs.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The ledger shows the actual price of the method: one user-set search bound (mmax), one hand-chosen offset in the elbow-to-minpts mapping (i+3), an empirically assumed coincidence between a shape feature of score sequences and ranking quality, and an evaluation that presumes one synthetic-outlier recipe represents real outliers. The GLOSH-Profile and ORD-Profile arrays are compositions of existing GLOSH scores, so no new entities are introduced.

free parameters (4)
  • mmax (upper bound of minpts search range) = 100 (paper: 'typically chosen to be smaller than 100')
    Auto-GLOSH is called parameter-free, but the GLOSH-Profile is built over [2, mmax]; the user must set mmax. Section IV-A.
  • Elbow-to-minpts index mapping (i + 3) = i + 3
    After finding elbow index i, the minpts is set to i + 3 without justification beyond observation; section IV-D: 'We take i + 3 as the value of m*.' This offset is a hand-chosen design element.
  • Outlier generation scale alpha = 5
    Local and clump outliers are generated with covariance or mean scaled by alpha = 5 per [20]; all evaluation data depends on this choice (sections IV-B and VI.A).
  • POLAR regression fit and similarity rule = null (ordinary least squares, nearest-score rule)
    POLAR fits beta0 and beta1 to the pre-knee scores and picks the score 'most similar' to the projected endpoint R; the similarity rule and fit domain are design choices (section V-B).
assumptions (6)
  • domain assumption Outliers lie in low-density regions of the reference set.
    The paper's premise for all of unsupervised outlier detection, stated in section II: 'Unsupervised outlier detection is based on the premise that potential outliers lie in low-density regions.' Also used to justify GLOSH as reference-set selector.
  • ad hoc to paper The ORD-Profile elbow coincides with the minpts of best GLOSH performance.
    The central regularity behind Auto-GLOSH, asserted from inspection of Figures 2 and 3 on Banana-type data without derivation (sections IV-B and IV-C). This is the paper's own working premise.
  • ad hoc to paper Sorted GLOSH score sequences at m* exhibit a knee followed by an approximately linear inlier trend.
    POLAR's premise that pre-knee scores are approximately linear and that the projected endpoint R provides a good cutoff anchor (section V-A, V-B, Figure 5).
  • domain assumption Synthetic outliers generated per [20] (alpha=5 scaling, uniform draws, Tomek-link filtering) are representative of statistically defined outliers.
    The whole evaluation rests on this; real OCC labeled outliers are excluded in section VI.A with Table I as justification.
  • domain assumption CORE-SG computes all MSTs up to mmax at O(n m_max^2 log n) cost.
    Complexity claim inherited from the authors' prior work [8], used in section IV-E to argue the method is cheaper than naive repeated HDBSCAN* runs.
  • standard math Parallelogram area equals base times height, used to compute orthogonal distances (Eq. 6).
    Standard vector geometry from [24], [25], applied to locate elbows in the ORD-Profile and knees in the sorted score sequence.

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Cite this review

Pith. "Pith review of Unsupervised Parameter-free Outlier Detection using HDBSCAN* Outlier Profiles." pith.science (2026). https://pith.science/paper/VMIGNXRD

@misc{pith2026241108867,
  author       = {Pith},
  title        = {Pith review of: Unsupervised Parameter-free Outlier Detection using HDBSCAN* Outlier Profiles},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VMIGNXRD}},
  note         = {Machine review of arXiv:2411.08867}
}
read the original abstract

In machine learning and data mining, outliers are data points that significantly differ from the dataset and often introduce irrelevant information that can induce bias in its statistics and models. Therefore, unsupervised methods are crucial to detect outliers if there is limited or no information about them. Global-Local Outlier Scores based on Hierarchies (GLOSH) is an unsupervised outlier detection method within HDBSCAN*, a state-of-the-art hierarchical clustering method. GLOSH estimates outlier scores for each data point by comparing its density to the highest density of the region they reside in the HDBSCAN* hierarchy. GLOSH may be sensitive to HDBSCAN*'s minpts parameter that influences density estimation. With limited knowledge about the data, choosing an appropriate minpts value beforehand is challenging as one or some minpts values may better represent the underlying cluster structure than others. Additionally, in the process of searching for ``potential outliers'', one has to define the number of outliers n a dataset has, which may be impractical and is often unknown. In this paper, we propose an unsupervised strategy to find the ``best'' minpts value, leveraging the range of GLOSH scores across minpts values to identify the value for which GLOSH scores can best identify outliers from the rest of the dataset. Moreover, we propose an unsupervised strategy to estimate a threshold for classifying points into inliers and (potential) outliers without the need to pre-define any value. Our experiments show that our strategies can automatically find the minpts value and threshold that yield the best or near best outlier detection results using GLOSH.

Figures

Figures reproduced from arXiv: 2411.08867 by the authors.

Figure 1
Figure 1. Banana Dataset with different kinds of outliers. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Comparing GLOSH–Profiles (PΓ) with Precision@n (P@n) obtained by GLOSH at different minpts values: The black line in Fig. 2a to 2c shows the P@n at every minpts value. The outliers profiles are in red while the inliers profiles are in gray. The green (dashed) line denotes the specific minpts value where GLOSH first achieves the best P@n within the range [2, 100] of minpts values. The performance of GLOSH is assessed… view at source ↗
Figure 3
Figure 3. compares ORD–Profiles with Precision@n (P@n) for a range of minpts values. First, Fig. 3d to 3f show a high dissimilarity in the ORD–Profile Rmmax for lower minpts values, that evolve to 0 and form an “elbow like” structure. The “elbow” is the point from where GLOSH scores start changing at a similar rate in most profiles. Second, the minpts value where the “elbow” is formed corresponds to the minpts value where GLO… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Illustrating the process of finding the Elbow of the [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: Banana Dataset: Sorted Sequence of GLOSH scores [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: Banana Dataset with clumps: (a) Finding the “knee” [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: GLOSH–Profiles of real one-class classification [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

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Reference graph

Works this paper leans on

36 extracted references · 33 canonical work pages

  1. [1]

    D. M. Hawkins, Identification of outliers . Springer, 1980, vol. 11

    1980

  2. [2]

    Time-window based group-behavior supported method for accurate detection of anomalous users,

    L.-P. Yuan, E. Choo, T. Yu, I. Khalil, and S. Zhu, “Time-window based group-behavior supported method for accurate detection of anomalous users,” 2021 51st Annual IEEE/IFIP International Conference on De- pendable Systems and Networks (DSN) , pp. 250–262, 2021. 9 Dataset POLAR *BestKnee AdjustedRecall F-measure G-Mean Recall F-measure G-Mean F-measure G-M...

    work page 2021

  3. [3]

    One-class versus binary classification: Which and when?

    C. Bellinger, S. Sharma, and N. Japkowicz, “One-class versus binary classification: Which and when?” in 2012 11th International conference on machine learning and applications, vol. 2. IEEE, 2012, pp. 102–106

    work page 2012

  4. [4]

    On the evaluation of outlier detection and one-class classification: a comparative study of algorithms, model selection, and ensembles,

    H. O. Marques, L. Swersky, J. Sander, R. J. Campello, and A. Zimek, “On the evaluation of outlier detection and one-class classification: a comparative study of algorithms, model selection, and ensembles,” Data Mining and Knowledge Discovery , pp. 1–45, 2023

    work page 2023

  5. [5]

    Hierarchical density estimates for data clustering, visualization, and outlier detection,

    R. J. Campello, D. Moulavi, A. Zimek, and J. Sander, “Hierarchical density estimates for data clustering, visualization, and outlier detection,” ACM Transactions on Knowledge Discovery from Data (TKDD), vol. 10, no. 1, pp. 1–51, 2015

    work page 2015

  6. [6]

    Cavalcante Araujo Neto, A Framework for Hierarchical Density- Based Clustering Exploration

    A. Cavalcante Araujo Neto, A Framework for Hierarchical Density- Based Clustering Exploration . Ph.D. thesis, University of Alberta, 2021

    work page 2021

  7. [7]

    A novel subspace outlier detec- tion method by entropy-based clustering algorithm,

    Z. Zuo, Z. Li, P. Cheng, and J. Zhao, “A novel subspace outlier detec- tion method by entropy-based clustering algorithm,” Scientific Reports, vol. 13, p. 15331, 2023

    work page 2023

  8. [8]

    Core-sg: Efficient computation of multiple msts for density-based methods,

    A. C. A. Neto, M. C. Naldi, R. J. Campello, and J. Sander, “Core-sg: Efficient computation of multiple msts for density-based methods,” 2022 IEEE 38th International Conference on Data Engineering (ICDE) , pp. 951–964, 2022

    work page 2022

Show all 36 references
  1. [9]

    A unified notion of outliers: Properties and computation

    E. M. Knorr and R. T. Ng, “A unified notion of outliers: Properties and computation.” KDD, vol. 97, pp. 219–222, 1997

    1997

  2. [10]

    Efficient algorithms for mining outliers from large data sets,

    S. Ramaswamy, R. Rastogi, and K. Shim, “Efficient algorithms for mining outliers from large data sets,” Proceedings of the 2000 ACM SIGMOD international conference on Management of data , pp. 427– 438, 2000

    2000

  3. [11]

    Lof: identifying density-based local outliers,

    M. M. Breunig, H.-P. Kriegel, R. T. Ng, and J. Sander, “Lof: identifying density-based local outliers,” Proceedings of the 2000 ACM SIGMOD international conference on Management of data , pp. 93–104, 2000

    2000

  4. [12]

    Optics: Ordering points to identify the clustering structure,

    M. Ankerst, M. M. Breunig, H.-P. Kriegel, and J. Sander, “Optics: Ordering points to identify the clustering structure,” ACM Sigmod record, vol. 28, no. 2, pp. 49–60, 1999

    1999

  5. [13]

    Swersky, A study of unsupervised outlier detection for one-class classification

    L. Swersky, A study of unsupervised outlier detection for one-class classification. M.Sc. thesis, University of Alberta, 2018

    2018

  6. [14]

    A framework for semi-supervised and unsupervised optimal extraction of clusters from hierarchies,

    R. J. Campello, D. Moulavi, A. Zimek, and J. Sander, “A framework for semi-supervised and unsupervised optimal extraction of clusters from hierarchies,” Data Mining and Knowledge Discovery , vol. 27, pp. 344– 371, 2013

    2013

  7. [15]

    Automatic unsupervised outlier model selection,

    Y . Zhao, R. Rossi, and L. Akoglu, “Automatic unsupervised outlier model selection,” Advances in Neural Information Processing Systems , vol. 34, pp. 4489–4502, 2021

    2021

  8. [16]

    A density-based algorithm for discovering clusters in large spatial databases with noise,

    M. Ester, H.-P. Kriegel, J. Sander, X. Xu et al. , “A density-based algorithm for discovering clusters in large spatial databases with noise,” in kdd, vol. 96, no. 34, 1996, pp. 226–231

    1996

  9. [17]

    Effi- cient computation and visualization of multiple density-based clustering hierarchies,

    A. C. A. Neto, J. Sander, R. J. Campello, and M. A. Nascimento, “Effi- cient computation and visualization of multiple density-based clustering hierarchies,” IEEE Transactions on Knowledge and Data Engineering , vol. 33, no. 8, pp. 3075–3089, 2019

    2019

  10. [18]

    On the internal evaluation of unsupervised outlier detection,

    H. O. Marques, R. J. Campello, A. Zimek, and J. Sander, “On the internal evaluation of unsupervised outlier detection,” in Proceedings of the 27th international conference on scientific and statistical database management, 2015, pp. 1–12

    2015

  11. [19]

    Synthetic dataset for outlier detection,

    P. Koncar, “Synthetic dataset for outlier detection,” Feb. 2018. [Online]. Available: https://doi.org/10.5281/zenodo.1171077

    2018 doi

  12. [20]

    Adbench: Anomaly detection benchmark,

    S. Han, X. Hu, H. Huang, M. Jiang, and Y . Zhao, “Adbench: Anomaly detection benchmark,” Advances in Neural Information Processing Sys- tems, vol. 35, pp. 32 142–32 159, 2022

    2022

  13. [21]

    Internal evaluation of unsupervised outlier detection,

    H. O. Marques, R. J. Campello, J. Sander, and A. Zimek, “Internal evaluation of unsupervised outlier detection,” ACM Transactions on Knowledge Discovery from Data (TKDD) , vol. 14, no. 4, pp. 1–42, 2020

    2020

  14. [22]

    Instance reduction for one-class classification,

    B. Krawczyk, I. Triguero, S. Garc ´ıa, M. Wo ´zniak, and F. Herrera, “Instance reduction for one-class classification,” Knowledge and Infor- mation Systems, vol. 59, pp. 601–628, 2019

    2019

  15. [23]

    On evaluation of outlier rankings and outlier scores,

    E. Schubert, R. Wojdanowski, A. Zimek, and H.-P. Kriegel, “On evaluation of outlier rankings and outlier scores,” in Proceedings of the 2012 SIAM international conference on data mining . SIAM, 2012, pp. 1047–1058

    2012

  16. [24]

    Anton and C

    H. Anton and C. Rorres, Elementary linear algebra: applications version. John Wiley & Sons, 2013

    2013

  17. [25]

    D. C. Lay, Linear algebra and its applications . Pearson Education India, 2003

    2003

  18. [26]

    Parallel cover trees and their applications,

    Y . Gu, Z. Napier, Y . Sun, and L. Wang, “Parallel cover trees and their applications,” in Proceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures , 2022, pp. 259–272

    2022

  19. [27]

    Hierarchical density-based clustering using mapreduce,

    J. A. d. Santos, T. I. Syed, M. C. Naldi, R. J. G. B. Campello, and J. Sander, “Hierarchical density-based clustering using mapreduce,” IEEE Transactions on Big Data , vol. 7, no. 1, pp. 102–114, 2021

    2021

  20. [28]

    Linear regression,

    G. James, D. Witten, T. Hastie, R. Tibshirani, and J. Taylor, “Linear regression,” in An Introduction to Statistical Learning: With Applications in Python. Springer, 2023, pp. 69–134

    2023

  21. [29]

    Benchmarking unsupervised outlier de- tection with realistic synthetic data,

    G. Steinbuss and K. B ¨ohm, “Benchmarking unsupervised outlier de- tection with realistic synthetic data,” ACM Transactions on Knowledge Discovery from Data (TKDD) , vol. 15, no. 4, pp. 1–20, 2021

    2021

  22. [30]

    Angle-based outlier de- tection in high-dimensional data,

    H.-P. Kriegel, M. Schubert, and A. Zimek, “Angle-based outlier de- tection in high-dimensional data,” in Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining, 2008, pp. 444–452

    2008

  23. [31]

    Copod: copula-based outlier detection,

    Z. Li, Y . Zhao, N. Botta, C. Ionescu, and X. Hu, “Copod: copula-based outlier detection,” in 2020 IEEE international conference on data mining (ICDM). IEEE, 2020, pp. 1118–1123

    2020

  24. [32]

    The milky way project second data release: bubbles and bow shocks,

    T. Jayasinghe, D. Dixon, M. S. Povich, B. Binder, J. Velasco, D. M. Lepore, D. Xu, S. Offner, H. A. Kobulnicky, L. D. Anderson et al. , “The milky way project second data release: bubbles and bow shocks,” Monthly Notices of the Royal Astronomical Society , vol. 488, no. 1, pp....

    2019

  25. [33]

    Aircraft atypical approach detection using functional principal component analysis,

    G. Jarry, D. Delahaye, F. Nicol, and E. Feron, “Aircraft atypical approach detection using functional principal component analysis,” Journal of Air Transport Management, vol. 84, p. 101787, 2020

    2020

  26. [34]

    Similarity- based unsupervised evaluation of outlier detection,

    H. O. Marques, A. Zimek, R. J. Campello, and J. Sander, “Similarity- based unsupervised evaluation of outlier detection,” in International Conference on Similarity Search and Applications . Springer, 2022, pp. 234–248

    2022

  27. [35]

    Station layout optimization and route selection of urban rail transit planning: A case study of shanghai pudong interna- tional airport,

    P. Yin and M. Peng, “Station layout optimization and route selection of urban rail transit planning: A case study of shanghai pudong interna- tional airport,” Mathematics, vol. 11, no. 6, p. 1539, 2023

    2023

  28. [36]

    Learning from imbalanced data sets with weighted cross-entropy func- tion,

    Y . S. Aurelio, G. M. De Almeida, C. L. de Castro, and A. P. Braga, “Learning from imbalanced data sets with weighted cross-entropy func- tion,” Neural processing letters , vol. 50, pp. 1937–1949, 2019. 10

    1937

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.