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REVIEW 3 major objections 6 minor 41 references

Adaptive $k$ Nearest Neighbors Classifier via Granular Ball Computing

T0 review · 3 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The paper claims that replacing KNN's fixed $k$ with a granular-ball-induced adaptive neighborhood yields both higher accuracy and lower runtime across benchmark datasets.

desk verdict A useful adaptive KNN variant with a genuine reproducibility hole: Eq. (15) cannot be a purity threshold as written, and the ablation credits that step—so the paper needs a correction before the headline claims can be checked. read the letter →

arxiv 2608.12903 v1 pith:O3FBQO5J submitted 2026-08-13 cs.LG

Xiaoyu Lian , Shuyin Xia , Hongxuan He , Lifeng Shen , Guoyin Wang , Xinbo Gao This is my paper · ORCID
classification cs.LG
keywords adaptivek-nearestneighborsgranular-ballcomputingFishercriterionneighborhoodconstructionnoiserobustnessclassificationlarge-scaledataparameter-freekselection
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 aims to remove the fixed $k$ from $k$-nearest-neighbor classification by representing the training set as a small set of granular balls (spherical clusters labeled by their majority class) and letting each test point's neighborhood size emerge from the ball next to it. In training, the data is first coarsely split into $\sqrt{n}$ balls and then refined under a Fisher-criterion control that balances between-class separation against within-class compactness. In prediction, the method finds the nearest ball by a weighted distance, sets the neighborhood radius to the distance from the test point to the farthest sample inside that ball, and takes $k$ as the number of training samples captured in that neighborhood. On 12 benchmark datasets it reports an average accuracy of 0.8736, above 0.8622 for a purity-controlled variant and 0.8195 for the 2019 granular-ball KNN, with lower runtimes on medium and large datasets. A sympathetic reader would take the central claim to be that coarse ball representation plus a locally adaptive neighbor count can be both more accurate and more efficient than existing KNN variants.

What carries the argument

The load-bearing object is the granular ball, a spherical cluster with center $c$ and radius $r$ that covers the samples within distance $r$ of $c$ and carries the majority class label of those samples. The mechanism that carries the argument is a two-level adaptive pipeline: coarse $\sqrt{n}$-ball initialization by $k$-means, Fisher-criterion-controlled splitting with a category-adaptive purity lower bound and overlap removal during generation, and then a prediction stage in which a weighted boundary distance selects the nearest ball and the distance to its farthest sample sets the neighborhood radius, making $k$ equal to the number of samples caught in that neighborhood. This pipeline is what converts KNN's global $k$ into a local, data-determined value while shrinking the search from all $n$ points to $N$ balls plus a few candidate balls.

What would settle it

Run the implementation accompanying the paper on the 12 benchmark datasets with the documented 8:2 split and 0–30% training-label noise, and inspect the value of $T_{L_j}$ from Eq. (15) at line 13 of Algorithm 1: if the average accuracy does not reach the reported 0.8736, or if the threshold is not between 0 and 1 and therefore cannot be compared with a purity value, the central claim fails.

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Extended reading notes

Core claim

The central discovery claimed is that replacing both the fixed $k$ and the point-level nearest-neighbor search with a two-level granular-ball representation improves KNN's accuracy and efficiency at once. The training stage first runs $k$-means with $k=\sqrt{n}$ to coarsely partition the data, then repeatedly splits each ball with an attention-based fast splitting procedure, accepting a split only when the weighted Fisher value of the child balls exceeds the parent's; a category-adaptive quality lower bound and overlap removal then refine the balls. For a test point, the method selects the nearest ball using a sample-count-weighted boundary distance, constructs a neighborhood of radius $R_{kNN}(x)=\max_{x_i\in GB^*}\Delta(x,x_i)$, and classifies by majority vote over the samples inside that neighborhood. The paper reports that this yields average accuracy 0.8736 on the 12 benchmark datasets, versus 0.8622 for a purity-based variant and 0.8195 for GBKNN 2019, with substantially shorter runtimes on datasets from about five thousand samples upward.

Load-bearing premise

The load-bearing premise is that the category-adaptive purity lower bound in Eq. (15) works as a per-class splitting threshold, even though as written $T_{L_j}$ is a sum of granular-ball sample counts divided by a class-set cardinality, not a purity value, so if the implementation follows the printed formula, Algorithm 1 line 13 cannot gate splitting as claimed.

Editorial extensions

If this is right

  • The reported 0.8736 versus 0.8622 and 0.8195 averages imply the Fisher-controlled ball splitting plus adaptive neighborhood is worth about 5.4 points and 1.1 points of average accuracy over the two granular-ball baselines.
  • The stated complexity $O(n\sqrt{n}+M(N+\bar{s}))$ means the method trades an $O(n\sqrt{n})$ training cost for a prediction cost far below the $O(Mn)$ scan of plain KNN, which is why the paper reports runtimes on datasets with up to roughly a million samples.
  • Because $k$ is computed per test point as the number of samples in a ball-derived neighborhood, the classifier is free of global $k$ tuning; users no longer need to search a $k$ grid.
  • The group-based ball neighborhood is claimed to absorb label noise better than point-based neighbors, and the reported accuracy on several datasets remains stable even with 30% training-label noise.

Reading between the lines

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

  • The same two-level ball-plus-neighborhood design could be carried over to $k$-NN regression, outlier detection, or imbalanced classification, where a fixed neighbor count is also known to be problematic; the paper does not test these settings.
  • Since the neighborhood is induced by a single nearest ball, a natural variant would blend the two nearest balls' neighborhoods or cap the radius; this is an untested extension rather than a claim in the paper.
  • The printed formula for the category-adaptive purity lower bound, Eq. (15), is not a purity value between 0 and 1, so the ablation gains credited to that mechanism should be checked against the released implementation before being taken at face value.
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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

3 major / 6 minor

Summary. The paper proposes GBKNN, a two-stage adaptive k-nearest-neighbor classifier based on granular-ball computing. In the training stage, the dataset is first split into sqrt(n) initial granular balls by k-means, then each ball is recursively refined with the GBG++ splitting procedure; a split is accepted only when the weighted Fisher criterion of the child balls exceeds that of the parent. A further 'category-adaptive purity lower bound' T_L is introduced to re-split low-quality balls, and a global de-overlap step is applied. In the prediction stage, GBKNN selects the nearest granular ball by a sample-count-weighted boundary distance, constructs an adaptive neighborhood around the test point using the distance to the farthest sample inside that ball, and classifies by majority vote over the neighborhood samples. Experiments on 12 UCI datasets and 5 large-scale datasets report accuracy, noise robustness, runtime, and an ablation study, alongside open-source code.

Significance. If the claims are correct, the paper offers a practically useful adaptive-k KNN variant: the coarse-to-fine granular-ball representation plus neighborhood construction could reduce both sensitivity to k and computational cost on medium and large datasets. The manuscript has genuine strengths: the code is public, the experimental design covers multiple datasets and noise levels, and the ablation study explicitly attributes gains to individual modules. However, the contribution is not yet established as written. The purity threshold in Eq. (15) is not a well-defined quantity, the density theorem in Section IV-E is asserted rather than proved, and the accuracy comparisons lack statistical support. These issues are local and fixable, but they are load-bearing for the central claims, so a major revision is needed.

major comments (3)
  1. [Section IV-B, Eq. (15) and Algorithm 1 line 13] Equation (15) cannot be a purity threshold as written. The term T_{L_j} is defined as the sum of |GB_i^*| over all granular balls divided by |L_j|, but GB_i^* is never defined and the expression is not normalized to lie between 0 and 1. If L_j is the class-j subset of the samples contained in the granular-ball set, the denominator is a subset of the samples counted in the numerator, so T_{L_j} >= 1 for any nonempty class; if L_j instead denotes all class-j samples in the dataset, the same inequality holds. Since purity (Definition 3) is at most 1, the predicate 'purity lower than T_{L_j}' in Algorithm 1 line 13 is true for every non-pure ball. The documented quality-optimization stage therefore degenerates into a rule that splits all impure balls, which is not the adaptive threshold described in the text and which Table V explicitly credits with accuracy gains. The paper must define GB_i^*, replace Eq. (15) with a correctly normalized purity threshold, and reconcile the formula with the implementation in the released code.
  2. [Section IV-E, Theorem 1 and Eqs. (17)-(31)] The density comparison theorem is not rigorously established. The proof asserts that direct global k-means produces centers in higher-density regions and smaller radii than recursive 2-means, but that is precisely the claim to be proved; no comparison of the two partition methods under a Lipschitz-continuous density is actually carried out. Equation (29) presents an estimate rho_i = n f(c_i) + n L_i r_i that mixes a leading term with a worst-case upper bound on the bias, and the sign of the error term is not handled consistently when the text argues that smaller radii lead to higher density. Equation (17) is also ill-defined because it puts a summation over all balls inside the definition of rho_i. If the theorem is kept, either provide a complete proof with well-defined density quantities and controlled approximation errors, or explicitly label the argument as a heuristic motivation rather than a theorem.
  3. [Section V-B, Tables II and IV] The central empirical claim that GBKNN outperforms existing KNN variants is not supported by statistical evidence. Table II reports single accuracy averages over one 8:2 split per noise level, with no standard deviations, no repeated random splits, and no significance tests. On several datasets GBKNN is numerically below GBKNN_p (for example, mushroom 0.9896 vs 0.9924 and Skin NonSkin 0.9766 vs 0.9922), so the reported average advantage of 0.0114 over GBKNN_p could plausibly arise from split variance. Table IV reports only GBKNN results with no baselines, making the large-scale section descriptive rather than comparative. The paper should provide statistics over repeated trials, significance tests, and explicit statements about which baselines could not be run on the large-scale datasets.
minor comments (6)
  1. [Section V-F, Table V] The checkmark rows in Table V are not labeled with a legend, and the text refers to rows by number without making it easy to identify which module combination each row corresponds to; please add explicit row labels or a legend.
  2. [Table II] The column header 'phonme' is a typo for 'phoneme', and the dataset name 'Skin Nonskin' appears with inconsistent spacing and capitalization across tables and text.
  3. [Section II-A and Section V-B] The method in reference [23] is called MGKNN in the related-work section and MGNR in the experiments and baseline tables; please use one consistent name throughout.
  4. [Section IV-D] The algorithm description states that the method achieves 'threshold-free and adaptive splitting', but Algorithm 1 line 13 applies the purity threshold T_L; please clarify whether the claim of threshold-freeness excludes this quality-optimization stage, and align the wording with the actual algorithmic flow.
  5. [Section IV-F] The runtime analysis assumes that the de-overlapping cost is negligible and that the GBG++ splitting is O(n), but these assumptions are not justified in the text; a brief remark on when de-overlap could become non-negligible would improve the analysis.
  6. [Section V-E, Table IV] The runtimes in Table IV are not accompanied by a description of whether they cover all noise levels, a single train-test split, or the full experimental protocol; please specify what the reported times include.

Circularity Check

0 steps flagged · score 2.0 of 10

No derivation step reduces to its own input; the main problem is Eq. (15), which is a correctness defect rather than circularity.

full rationale

The claimed derivation chain is: sqrt(n) coarse splitting (k-means with density-based selection, Eq. (32)) -> Fisher-criterion splitting/stopping (Eq. (13)) -> T_L quality refinement (Eq. (15)) -> weighted nearest-ball selection (Eq. (16)) -> neighborhood radius R_kNN(x) = max_{x_i in GB*} Delta(x, x_i) -> adaptive k determined by the number of samples in that neighborhood. At each stage the inputs are training data and class labels only; the effective k is a deterministic function of the test sample and the trained ball structure, and no parameter is fitted to test labels. The accuracy claim in Table II is therefore tested on held-out partitions of 17 datasets and is externally falsifiable. The paper does import GBG++ ([33], same author group) as the splitting engine and cites it for linear-time splitting, but that is a component dependency, not a proof that the new combination is equivalent to its own input. Theorem 1 is a weak, largely asserted density comparison, but even if disregarded it does not make the central results target-absorbing. The one genuine defect is not circularity: Eq. (15) likely yields T_Lj >= 1 for every non-empty class, so the documented 'purity lower than T_Lj' predicate cannot act as the category-adaptive threshold described in Section IV-B and credited in Table V; this is a correctness and reproducibility issue that should be fixed or documented, not a self-referential derivation.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The ledger shows that GBKNN imports most machinery from prior work, including k-means, GBG++ splitting, and Euclidean balls, and adds heuristic control rules such as Fisher acceptance, purity lower bound, and density-based initialization selection. No target variable is used to set constants, so the circularity burden is low despite heavy self-citation.

free parameters (3)
  • Initial granular-ball count sqrt(n) = sqrt(n), structural choice
    The algorithm fixes the number of initial k-means clusters at sqrt(n) for every dataset. This is not fitted to data, but it controls the granularity of the entire pipeline and is justified only by heuristic arguments.
  • Number of random initial point selections = 10
    The implementation repeats random initialization 10 times and selects the split maximizing Eq. (32). This fixed implementation hyperparameter is not analyzed in the ablation.
  • Purity lower bound T_Lj = undefined as written
    Introduced in Section IV.B and used in Algorithm 1 line 13 as a stopping and refinement threshold. The formula in Eq. (15) is not a valid per-class purity threshold as written, yet the ablation credits it with accuracy gains.
assumptions (4)
  • ad hoc to paper k-means with sqrt(n) clusters gives a better initial partition than recursive 2-means splitting.
    Theorem 1 attempts to prove this, but the proof relies on qualitative assertions about k-means behavior. This assumption is used in Step 1 of Algorithm 1 and in the motivation of Section IV.B.
  • ad hoc to paper Accepted Fisher-criterion splits improve classification accuracy.
    The paper gives no theory linking the Fisher value comparison W < F_GBj to downstream classification accuracy. The only support is the ablation in Table V.
  • domain assumption Euclidean distance and spherical granular balls adequately represent class structure.
    Definitions 1 through 3 in Section III assume Euclidean balls with mean centers and radii, which may be poor in high dimensions or elongated clusters.
  • domain assumption The nearest-ball radius neighborhood contains the most relevant local samples for classification.
    Section IV.C sets the neighborhood radius to the maximum distance from the test point to samples in the nearest ball. This assumes that the nearest granular ball provides the correct local group for every test point.

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Cite this review

Pith. "Pith review of Adaptive $k$ Nearest Neighbors Classifier via Granular Ball Computing." pith.science (2026). https://pith.science/paper/O3FBQO5J

@misc{pith2026260812903,
  author       = {Pith},
  title        = {Pith review of: Adaptive $k$ Nearest Neighbors Classifier via Granular Ball Computing},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/O3FBQO5J}},
  note         = {Machine review of arXiv:2608.12903}
}
abstract

The $k$-Nearest Neighbor~(KNN) algorithm is widely used across various tasks. The selection of the $k$ value is a key issue because it significantly impacts performance. In this paper, an adaptive and efficient KNN approach via granular-ball computing is proposed. The method consists of two stages. \textcolor{black}{In the training stage, the dataset is first coarsely partitioned to reduce the complexity of data distributions within a granular ball, and then the Fisher criterion is introduced to control ball splitting and stopping, yielding a multi-granularity granular ball representation. In the prediction stage, the nearest granular ball is first located through a weighted distance mechanism, and an adaptive neighborhood is then constructed around the test sample. The effective $k$ value is dynamically determined by the actual number of samples contained in this neighborhood. The neighborhood induced by the nearest granular ball provides more stable local group information, thereby improving robustness against noise and local perturbations.} Experimental results demonstrate that the proposed method outperforms existing KNN variants across multiple datasets in terms of both accuracy and efficiency. The code has been open-sourced for reproducibility: https://github.com/lianxiaoyu724/Adaptive-GBKNN.

Figures

Figures reproduced from arXiv: 2608.12903 by the authors.

Figure 1
Figure 1. The effectiveness of k selection on KNN classification, [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Comparison between GBG++ and GBG++ with initial [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. The GBKNN, as illustrated in the overall flowchart, consists of two main modules: i) granular ball generation; ii) classification decision. further enhance decision boundary representation, a new pu￾rity lower bound based on label information is introduced, followed by a global overlap removal strategy to improve the structural clarity of granular balls. In the classification decision stage ( [PITH_FULL_IMAGE:figur… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Accuracy of different methods on six datasets under different noise conditions. but degrade rapidly as noise increases, reflecting their lack of mechanisms to handle data perturbations. NaNEKNN and SMKNN exhibit performance close to GBKNN on specific datasets such as ‘…

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Works this paper leans on

41 extracted references · 34 canonical work pages

  1. [1]

    A simple knn algorithm for text catego- rization,

    P. Soucy and G. W. Mineau, “A simple knn algorithm for text catego- rization,” inProceedings 2001 IEEE International Conference on Data Mining. IEEE, 2001, pp. 647–648

    work page 2001

  2. [2]

    Application of k-nearest-neighbor decision rule in vowel recognition,

    K. K. Paliwal and P. Rao, “Application of k-nearest-neighbor decision rule in vowel recognition,”IEEE Transactions on Pattern Analysis and Machine Intelligence, no. 2, pp. 229–231, 1983

    work page 1983

  3. [3]

    High-resolution mobile fingerprint matching via deep joint knn-triplet embedding,

    F. Zhang and J. Feng, “High-resolution mobile fingerprint matching via deep joint knn-triplet embedding,” inProceedings of the AAAI Conference on Artificial Intelligence, vol. 31, no. 1, 2017

    work page 2017

  4. [4]

    Handwritten character recog- nition using cnn, knn and svm,

    U. P. Wani, Y . Gatagat, and M. Thalor, “Handwritten character recog- nition using cnn, knn and svm,”International Journal of Technology Engineering Arts Mathematics Science, vol. 1, no. 2, pp. 2583–1224, 2022

    work page 2022

  5. [5]

    Intelligent handwritten recognition using hybrid cnn architectures based-svm classifier with dropout,

    A. A. A. Ali and S. Mallaiah, “Intelligent handwritten recognition using hybrid cnn architectures based-svm classifier with dropout,”Journal of King Saud University-Computer and Information Sciences, vol. 34, no. 6, pp. 3294–3300, 2022

    work page 2022

  6. [6]

    Hierarchical text classification with multi-label contrastive learning and knn,

    J. Zhang, Y . Li, F. Shen, Y . He, H. Tan, and Y . He, “Hierarchical text classification with multi-label contrastive learning and knn,”Neurocom- puting, vol. 577, p. 127323, 2024

    2024

  7. [7]

    Efficientnet-lite and hybrid cnn-knn implementation for facial expression recognition on raspberry pi,

    M. N. Ab Wahab, A. Nazir, A. T. Z. Ren, M. H. M. Noor, M. F. Akbar, and A. S. A. Mohamed, “Efficientnet-lite and hybrid cnn-knn implementation for facial expression recognition on raspberry pi,”IEEE Access, vol. 9, pp. 134 065–134 080, 2021

    work page 2021

  8. [8]

    Distance encoded product quanti- zation for approximate k-nearest neighbor search in high-dimensional space,

    J.-P. Heo, Z. Lin, and S.-E. Yoon, “Distance encoded product quanti- zation for approximate k-nearest neighbor search in high-dimensional space,”IEEE Transactions on Pattern Analysis and Machine Intelli- gence, vol. 41, no. 9, pp. 2084–2097, 2018. 15

    work page 2018

Show all 41 references
  1. [9]

    K-nearest neighbor finding using maxnearestdist,

    H. Samet, “K-nearest neighbor finding using maxnearestdist,”IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 30, no. 2, pp. 243–252, 2007

    2007

  2. [10]

    Fast k-nearest neighbor classification using cluster-based trees,

    B. Zhang and S. N. Srihari, “Fast k-nearest neighbor classification using cluster-based trees,”IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 4, pp. 525–528, 2004

    2004

  3. [11]

    A fast k nearest neighbor finding algorithm based on the ordered partition,

    B. S. Kim and S. B. Park, “A fast k nearest neighbor finding algorithm based on the ordered partition,”IEEE Transactions on Pattern Analysis and Machine Intelligence, no. 6, pp. 761–766, 1986

    1986

  4. [12]

    Classification bias of the k-nearest neighbor algorithm,

    J. E. Goin, “Classification bias of the k-nearest neighbor algorithm,” IEEE Transactions on Pattern Analysis and Machine Intelligence, no. 3, pp. 379–381, 1984

    1984

  5. [13]

    Survey on exact knn queries over high-dimensional data space,

    N. Ukey, Z. Yang, B. Li, G. Zhang, Y . Hu, and W. Zhang, “Survey on exact knn queries over high-dimensional data space,”Sensors, vol. 23, no. 2, p. 629, 2023

    2023

  6. [14]

    On optimum choice of k in nearest neighbor classifi- cation,

    A. K. Ghosh, “On optimum choice of k in nearest neighbor classifi- cation,”Computational Statistics & Data Analysis, vol. 50, no. 11, pp. 3113–3123, 2006

    2006

  7. [15]

    Locally adaptive metric nearest-neighbor classification,

    C. Domeniconi, J. Peng, and D. Gunopulos, “Locally adaptive metric nearest-neighbor classification,”IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 9, pp. 1281–1285, 2002

    2002

  8. [16]

    An affinity-based new local distance function and similarity measure for knn algorithm,

    G. Bhattacharya, K. Ghosh, and A. S. Chowdhury, “An affinity-based new local distance function and similarity measure for knn algorithm,” Pattern Recognition Letters, vol. 33, no. 3, pp. 356–363, 2012

    2012

  9. [17]

    Reverse nearest neighbors search in ad hoc subspaces,

    M. L. Yiu and N. Mamoulis, “Reverse nearest neighbors search in ad hoc subspaces,”IEEE Transactions on Knowledge and Data Engineering, vol. 19, no. 3, pp. 412–426, 2007

    2007

  10. [18]

    A geometric-based clustering method using natural neighbors,

    S. Pourbahrami and M. Hashemzadeh, “A geometric-based clustering method using natural neighbors,”Information Sciences, vol. 610, pp. 694–706, 2022

    2022

  11. [19]

    Natural neighbor: A self-adaptive neighborhood method without parameter k,

    Q. Zhu, J. Feng, and J. Huang, “Natural neighbor: A self-adaptive neighborhood method without parameter k,”Pattern Recognition Letters, vol. 80, pp. 30–36, 2016

    2016

  12. [20]

    Gnan: A natural neighbor search algorithm based on universal gravita- tion,

    J. Yang, L. Yang, J. Zhang, Q. Liang, W. Wang, D. Tang, and T. Liu, “Gnan: A natural neighbor search algorithm based on universal gravita- tion,”Pattern Recognition, vol. 146, p. 110063, 2024

    2024

  13. [21]

    Granular ball computing classifiers for efficient, scalable and robust learning,

    S. Xia, Y . Liu, X. Ding, G. Wang, H. Yu, and Y . Luo, “Granular ball computing classifiers for efficient, scalable and robust learning,” Information Sciences, vol. 483, pp. 136–152, 2019

    2019

  14. [22]

    An efficient and adaptive granular-ball generation method in classification problem,

    S. Xia, X. Dai, G. Wang, X. Gao, and E. Giem, “An efficient and adaptive granular-ball generation method in classification problem,” IEEE Transactions on Neural Networks and Learning Systems, vol. 35, no. 4, pp. 5319–5331, 2022

    2022

  15. [23]

    Mgnr: A multi- granularity neighbor relationship and its application in knn classification and clustering methods,

    J. Xie, X. Xiang, S. Xia, L. Jiang, G. Wang, and X. Gao, “Mgnr: A multi- granularity neighbor relationship and its application in knn classification and clustering methods,”IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024

    2024

  16. [24]

    Lightweight-yet-efficient: Revitalizing ball- tree for point-to-hyperplane nearest neighbor search,

    Q. Huang and A. K. Tung, “Lightweight-yet-efficient: Revitalizing ball- tree for point-to-hyperplane nearest neighbor search,” in2023 IEEE 39th International Conference on Data Engineering (ICDE). IEEE, 2023, pp. 436–449

    2023

  17. [25]

    Lan: Learning-based approximate k-nearest neighbor search in graph databases,

    Y . Peng, B. Choi, T. N. Chan, and J. Xu, “Lan: Learning-based approximate k-nearest neighbor search in graph databases,” in2022 IEEE 38th International Conference on Data Engineering (ICDE), 2022, pp. 2508–2521

    2022

  18. [26]

    Joint evidential k-nearest neighbor classification,

    C. Gong, Y . Li, Y . Liu, P.-h. Wang, and Y . You, “Joint evidential k-nearest neighbor classification,” in2022 IEEE 38th International Conference on Data Engineering (ICDE). IEEE, 2022, pp. 2113–2126

    2022

  19. [27]

    Connec- tivity of the mutual k-nearest-neighbor graph in clustering and outlier detection,

    M. R. Brito, E. L. Ch ´avez, A. J. Quiroz, and J. E. Yukich, “Connec- tivity of the mutual k-nearest-neighbor graph in clustering and outlier detection,”Statistics & Probability Letters, vol. 35, no. 1, pp. 33–42, 1997

    1997

  20. [28]

    Adaptive learning-basedk- nearest neighbor classifiers with resilience to class imbalance,

    S. S. Mullick, S. Datta, and S. Das, “Adaptive learning-basedk- nearest neighbor classifiers with resilience to class imbalance,”IEEE Transactions on Neural Networks and Learning Systems, vol. 29, no. 11, pp. 5713–5725, 2018

    2018

  21. [29]

    Knn classification with one-step computation,

    S. Zhang and J. Li, “Knn classification with one-step computation,” IEEE Transactions on Knowledge and Data Engineering, vol. 35, no. 3, pp. 2711–2723, 2021

    2021

  22. [30]

    Pl-k nn: A parameterless nearest neighbors classifier,

    D. S. Jodas, L. A. Passos, A. Adeel, and J. P. Papa, “Pl-k nn: A parameterless nearest neighbors classifier,” in2022 29th International Conference on Systems, Signals and Image Processing (IWSSIP). IEEE, 2022, pp. 1–4

    2022

  23. [31]

    Distributionally robust weighted k-nearest neighbors,

    S. Zhu, L. Xie, M. Zhang, R. Gao, and Y . Xie, “Distributionally robust weighted k-nearest neighbors,”Advances in Neural Information Processing Systems, vol. 35, pp. 29 088–29 100, 2022

    2022

  24. [32]

    Gene expression cancer classification using modified k-nearest neighbors technique,

    S. M. Ayyad, A. I. Saleh, and L. M. Labib, “Gene expression cancer classification using modified k-nearest neighbors technique,”Biosystems, vol. 176, pp. 41–51, 2019

    2019

  25. [33]

    Gbg++: A fast and stable granular ball generation method for clas- sification,

    Q. Xie, Q. Zhang, S. Xia, F. Zhao, C. Wu, G. Wang, and W. Ding, “Gbg++: A fast and stable granular ball generation method for clas- sification,”IEEE Transactions on Emerging Topics in Computational Intelligence, 2024

    2024

  26. [34]

    Gbsvm: an efficient and robust support vector machine framework via granular- ball computing,

    S. Xia, X. Lian, G. Wang, X. Gao, J. Chen, and X. Peng, “Gbsvm: an efficient and robust support vector machine framework via granular- ball computing,”IEEE Transactions on Neural Networks and Learning Systems, 2024

    2024

  27. [35]

    W-gbc: An adaptive weighted clustering method based on granular-ball structure,

    J. Xie, C. Hua, S. Xia, Y . Cheng, G. Wang, and X. Gao, “W-gbc: An adaptive weighted clustering method based on granular-ball structure,” in 2024 IEEE 40th International Conference on Data Engineering (ICDE). IEEE, 2024, pp. 914–925

    2024

  28. [36]

    Graph coarsening via supervised granular-ball for scalable graph neural network training,

    S. Xia, X. Ma, Z. Liu, C. Liu, S. Zhao, and G. Wang, “Graph coarsening via supervised granular-ball for scalable graph neural network training,” inProceedings of the AAAI Conference on Artificial Intelligence, vol. 39, no. 12, 2025, pp. 12 872–12 880

    2025

  29. [37]

    Gbrs: A unified granular-ball learning model of pawlak rough set and neighborhood rough set,

    S. Xia, C. Wang, G. Wang, X. Gao, W. Ding, J. Yu, Y . Zhai, and Z. Chen, “Gbrs: A unified granular-ball learning model of pawlak rough set and neighborhood rough set,”IEEE Transactions on Neural Networks and Learning Systems, 2023

    2023

  30. [38]

    Unlock the cognitive generalization of deep reinforcement learning via granular ball representation,

    J. Liu, H. Jianye, Y . Ma, and S. Xia, “Unlock the cognitive generalization of deep reinforcement learning via granular ball representation,” in Forty-first International Conference on Machine Learning, 2024

    2024

  31. [39]

    Never-ending learning for explainable brain computing,

    H. Kuai, J. Chen, X. Tao, L. Cai, K. Imamura, H. Matsumoto, P. Liang, and N. Zhong, “Never-ending learning for explainable brain computing,” Advanced Science, vol. 11, no. 24, p. 2307647, 2024

    2024

  32. [40]

    Circumspheres of sets of n+1 random points in the d- dimensional euclidean unit ball (1≤n≤d),

    G. Le Ca ¨er, “Circumspheres of sets of n+1 random points in the d- dimensional euclidean unit ball (1≤n≤d),”Journal of Mathematical Physics, vol. 58, no. 5, 2017

    2017

  33. [41]

    Hilbert space embeddings and metrics on probability measures,

    B. K. Sriperumbudur, A. Gretton, K. Fukumizu, B. Sch ¨olkopf, and G. R. Lanckriet, “Hilbert space embeddings and metrics on probability measures,”The Journal of Machine Learning Research, vol. 11, pp. 1517–1561, 2010

    2010

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.