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REVIEW 3 major objections 5 minor 47 references

Approximate Borderline Sampling using Granular-Ball for Classification Tasks

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read GBABS is a granular-ball sampling method that targets borderline samples, removes class noise during ball generation, and claims linear-time compression with higher classifier accuracy than existing GB-based and representative baselines.

desk verdict A genuine new GB-based borderline sampler with a real design flaw: its noise detector deletes clean boundary points, so the noise-robustness story needs rework, but the paper deserves peer review. read the letter →

arxiv 2506.02366 v1 pith:4AJKRFRB submitted 2025-06-03 cs.CV cs.LG

Qin Xie , Qinghua Zhang , Shuyin Xia This is my paper
classification cs.CVcs.LG
keywords granular-ballcomputingborderlinesamplingclassnoisedataundersamplingimbalancedclassificationgeneration
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 tries to establish that borderline sampling and class-noise cleaning can be done together by one general, classifier-agnostic sampling method. It proposes RD-GBG, a granular-ball generation procedure that builds pure, non-overlapping balls by restricted diffusion, along with GBABS, which samples only the samples adjacent to class boundaries. If the claim holds, training-data compression, robustness to label noise, and imbalanced-class performance all improve without tuning a purity threshold. The reported experiments support the claim on 13 datasets, with GBABS-based classifiers outperforming GB-based sampling and representative baselines, especially at high noise ratios.

What carries the argument

The carrying mechanism is restricted diffusion-based granular-ball generation (RD-GBG) paired with dimension-wise borderline detection. A granular ball is a ball with center $c$, radius $r$, label $l$, and the sample set $O$ it covers; RD-GBG makes every ball pure by expanding from a local-density center until the $\omega$-th nearest neighbor is homogeneous and the $(\omega+1)$-th is heterogeneous, then caps the radius at the conflict radius $r_{\mathrm{conf}}(c)$ if the ball would overlap an earlier one. This builds a non-overlapping cover of the data whose boundaries match the class structure, avoiding the blurred or shrunken boundaries that overlapping balls cause. For sampling, the centers of all balls are ordered along each feature; a center is borderline if a left or right neighbor in any dimension belongs to a different class, and the samples adjacent to those centers in the corresponding dimension are collected. Local-density center detection, which counts heterogeneous neighbors $h(c,l)$ among the $\rho$ nearest neighbors, acts as the built-in noise filter: it labels candidate centers or their nearest neighbors as class noise and returns low-density samples to the undivided set.

What would settle it

Take a synthetic two-class dataset with known injected label flips, run RD-GBG with a fixed $\rho$, and compare the samples flagged as class noise under the $h(c,l)=\rho$ rule against the ground-truth flips. If precision on the flips is no better than random selection, or if most flagged samples are actually boundary points, the claimed noise robustness without a purity threshold collapses.

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Extended reading notes

Core claim

On its own terms, the paper claims that a granular-ball sampling method can do two things existing general samplers do not: keep the samples that carry class-boundary information and remove class noise from the training set, with no purity threshold to tune. The method first runs RD-GBG, which grows pure, non-overlapping granular balls from local-density centers by restricted diffusion: each ball expands until it meets a heterogeneous sample or a previously generated ball, and if the locally consistent radius $\mathrm{CR}(c)$ would collide with an existing ball, the radius is truncated to the restricted maximum consistent radius $r_{\max}(c)$. Then GBABS projects the ball centers onto each feature dimension and marks as borderline any ball whose left or right neighbor in that dimension has a different label; the samples just across those boundaries form the sampled set. On 13 datasets with injected class noise from 5% to 40%, the authors report that classifiers trained on GBABS samples beat GB-based GGBS, simple random sampling, and the unsampled data, and that the advantage grows as noise rises. The paper also reports lower sampling ratios than GGBS and stable behavior as the density tolerance $\rho$ ranges from 3 to 19, which it reads as evidence that no optimal purity threshold is required.

Load-bearing premise

The load-bearing premise is that a fixed rule on nearest-neighbor counts can tell genuine class noise from useful borderline points: if all $\rho$ nearest neighbors are foreign the center is noise, if exactly one is foreign that neighbor is noise, and otherwise the center is a low-density sample, with no theoretical or held-out justification for those cutoffs.

Editorial extensions

If this is right

  • GBABS should keep classifiers accurate under class noise: the reported average accuracy at 40% noise is higher for GBABS than for GGBS, SRS, or the full dataset on every tested classifier.
  • GBABS should compress more aggressively than GGBS on almost all datasets, and the gap widens as noise increases, because noise removal and borderline-only sampling both cut samples.
  • On imbalanced data, GBABS should rank at or near the top in G-mean among eight sampling methods, particularly on noisy imbalanced datasets, because it undersamples the majority more aggressively near boundaries.
  • The density tolerance $\rho$ should be an insensitive hyperparameter: sampling ratio and decision-tree accuracy stay roughly flat for $\rho$ from 3 to 19.
  • The total runtime should stay roughly linear in the number of samples, $O(tqN + p m \log m)$, so the method scales to large datasets.

Reading between the lines

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

  • A natural extension is to lift RD-GBG's local-density center detection out of sampling and use it as a standalone label-noise filter, since it requires only class-specific nearest-neighbor counts.
  • The boundary-focused selection could also serve as a preprocessing step for active learning or large-scale support-vector training, where only points near the decision surface matter.
  • At high noise ratios on small datasets, pure borderline undersampling may remove too many minority samples; pairing GBABS with a constrained oversampling step is a testable extension that its own G-mean rankings hint at.
  • One direct check of the method's geometric claim is to compare the samples GBABS selects with the support vectors of a support-vector machine trained on the same data; high overlap would confirm that the ball centers approximate the true decision boundary.
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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 / 5 minor

Summary. The paper proposes a two-stage sampling method for classification: RD-GBG, a restricted-diffusion granular-ball generation algorithm that avoids ball overlap and includes a local-density center detection rule for noise elimination, and GBABS, a granular-ball-based approximate borderline sampling method that selects samples near class boundaries. The authors claim that this is the first general sampling method that simultaneously performs borderline sampling and improves class-noise robustness, with linear time complexity and no need for an optimal purity threshold. Experiments on 13 datasets, with added class noise at 5%–40%, compare GBABS against GGBS, IGBS, SRS, SMOTE variants, and Tomek Links across five classifiers.

Significance. If the algorithm performs as claimed, it would be a practically useful contribution: it provides a general, compression-oriented sampling method that targets borderline points, and it comes with publicly available source code and a fairly broad experimental comparison. The RD-GBG overlap-avoidance mechanism is a reasonable idea, and the empirical evaluation spans multiple classifiers, datasets, and noise levels. However, the central noise-detection rule has a problematic behavior that undermines the boundary-preservation claim, and several experimental claims are stronger than the reported results support.

major comments (3)
  1. [Section IV-B1, Eq. (2) and Fig. 2] The local-density center detection rule deletes the nearest heterogeneous neighbor as class noise when h(c,l)=1. In a clean dataset, a nearest heterogeneous neighbor is typically a legitimate class-boundary point, not a mislabeled sample. The paper's own illustrative example in Fig. 2 is explicitly a noise-free dataset, yet for center (c3,l3) the nearest point (x1,y1) is removed as class noise. This behavior contradicts the paper's claim that the method preserves the class boundary while detecting noise, and it is load-bearing for both the borderline-sampling contribution and the noise-robustness claim. Please either revise the rule so that it can distinguish true label noise from genuine boundary structure, or provide direct evidence (e.g., on clean data with known boundaries) that this deletion does not degrade boundary fidelity.
  2. [Section V-C, Table II and Section V-D, Table IV] The claim that GBABS-based DT 'consistently achieves higher testingAccuracy' than plain DT is contradicted by Table II: plain DT has higher accuracy on S5 (0.8728 vs. 0.8709), S11 (0.9998 vs. 0.9994), and S12 (0.9750 vs. 0.9693). Similarly, Table IV shows GBABS-LightGBM at 5% and 10% noise (0.8660 and 0.8166) is worse than both GGBS-LightGBM (0.8690 and 0.8219) and plain LightGBM (0.8685 and 0.8222). The paper states only that GBABS 'generally performs better,' but the discussion in V-C and V-D conveys a stronger uniform superiority. Please analyze the datasets and settings where the method underperforms, and temper the claims accordingly.
  3. [Section IV-B3 and Section IV-C] The time-complexity claim that the total cost is O(tqN + p m log m) and 'still linear' is not justified as stated. The number of iterations t and the number of classes q are not bounded by constants in Algorithm 1; in the worst case t can be as large as O(N) and q as large as O(N). The text merely says the total is 'much lower than O(tqN),' which is not a formal bound. Please provide a rigorous worst-case analysis or clearly state the assumptions under which the method is linear in practice, supported by measured runtimes.
minor comments (5)
  1. [Section V-A1 and Section III-B] GGBS and IGBS are introduced in Section III-B as proposed in reference [23], but Section V-A1 cites [27] for these baselines; please correct the citation to avoid ambiguity.
  2. [Section V-A3] There is a typo in 'Accuray' that should be 'Accuracy'.
  3. [Section V-B] In the discussion of Fig. 6(a), the text says that for datasets with unclear class boundaries such as S3 the sampling ratio of GBABS is slightly higher than that of GGBS, but the figure appears to show GBABS with a lower ratio for S3; please verify the figure labels or the text.
  4. [Section VI] The conclusion states that 'the time complexity of the GBABS is not ideal when facing high-dimensional feature spaces,' which appears to contradict the earlier claim that the total complexity is linear; please reconcile these statements.
  5. [Algorithm 2, line 5] There is a typo in the notation: 'based on(c_j, l_i),(c_k, l_k)' should probably be 'based on(c_j, l_j),(c_k, l_k)'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: GBABS is validated by external benchmarks and the heuristic detection rules are assumptions, not reductions to the method's own outputs.

full rationale

The paper's central derivation is an algorithm construction, not a mathematical derivation from fitted constants. RD-GBG's local-density center detection (Section IV-B1) defines class noise via the rule h(c,l)=rho or h(c,l)=1; this is a heuristic assumption with rho as a tunable tolerance, and the sensitivity analysis (Section V-F) shows that the final accuracy is stable in rho. The 'without an optimal purity threshold' claim is therefore an empirical insensitivity claim, not a conclusion that follows from the definition. The borderline sampling step (Algorithm 2) is defined as collecting adjacent heterogeneous GBs, but the experimental evaluation compares against SRS, SMOTE, borderline-SMOTE, SMOTENC, and Tomek Links on 13 datasets and 5 classifiers, so the reported improvements do not reduce to the definition or to a fitted parameter. GGBS and IGBS are prior works by the same research group, but they are used as baselines, not as justifications for the soundness of the new method, and independent external baselines and public code provide corroboration. No uniqueness theorem is imported from the authors' prior work, and no equation is shown to equal an input by construction. The local-density heuristic could be criticized as arbitrary, but arbitrariness is a correctness or robustness concern, not circularity.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The method relies on several unproven modeling choices: the pure-ball diffusion radius rule, the density-tolerance noise rules, and the per-dimension heterogeneous-neighbor boundary criterion. These are ad hoc to the paper and are not derived from prior theory.

free parameters (2)
  • Density tolerance rho = Not reported in main experiments; sensitivity range 3-19
    Controls noise detection in Eq. (2) and local-density center classification. The paper does not state which value produced Tables II-IV.
  • Random seed
    Center selection, noise injection, and cross-validation repeats use randomness, but seeds are not reported, affecting exact reproduction.
assumptions (5)
  • domain assumption A granular ball with center c and radius r can represent the local data distribution well enough for sampling decisions.
    Adopted from granular-ball computing (Section III-A); the paper relies on it to derive borderline samples from ball centers and radii.
  • ad hoc to paper A sample whose rho nearest neighbors are all heterogeneous is class noise; a sample with 1 < h(c,l) < rho heterogeneous neighbors is low-density and should not seed a ball.
    These rules in Section IV-B1 are introduced without theoretical or empirical justification, and they control which samples are removed or deferred.
  • ad hoc to paper The nearest heterogeneous sample or previously generated ball defines the correct stopping boundary for a pure ball; Euclidean distance is the appropriate metric.
    Equations (3)-(6) assume this diffusion rule preserves class boundaries; the paper also states Euclidean distance fails in high dimensions (Section IV-C).
  • ad hoc to paper Centers that have heterogeneous neighbors along any feature dimension are exactly the borderline centers that matter for classification.
    Section IV-C defines borderline centers exclusively by per-dimension sorted-neighbor heterogeneity; no comparison against other boundary definitions is given.
  • ad hoc to paper The number of RD-GBG iterations t is small enough that O(tqN) is effectively linear.
    The complexity claim in Section IV-C depends on this; no bound on t is provided, and the conclusion admits high-dimensional inefficiency.

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Cite this review

Pith. "Pith review of Approximate Borderline Sampling using Granular-Ball for Classification Tasks." pith.science (2026). https://pith.science/paper/4AJKRFRB

@misc{pith2026250602366,
  author       = {Pith},
  title        = {Pith review of: Approximate Borderline Sampling using Granular-Ball for Classification Tasks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4AJKRFRB}},
  note         = {Machine review of arXiv:2506.02366}
}
read the original abstract

Data sampling enhances classifier efficiency and robustness through data compression and quality improvement. Recently, the sampling method based on granular-ball (GB) has shown promising performance in generality and noisy classification tasks. However, some limitations remain, including the absence of borderline sampling strategies and issues with class boundary blurring or shrinking due to overlap between GBs. In this paper, an approximate borderline sampling method using GBs is proposed for classification tasks. First, a restricted diffusion-based GB generation (RD-GBG) method is proposed, which prevents GB overlaps by constrained expansion, preserving precise geometric representation of GBs via redefined ones. Second, based on the concept of heterogeneous nearest neighbor, a GB-based approximate borderline sampling (GBABS) method is proposed, which is the first general sampling method capable of both borderline sampling and improving the quality of class noise datasets. Additionally, since RD-GBG incorporates noise detection and GBABS focuses on borderline samples, GBABS performs outstandingly on class noise datasets without the need for an optimal purity threshold. Experimental results demonstrate that the proposed methods outperform the GB-based sampling method and several representative sampling methods. Our source code is publicly available at https://github.com/CherylTse/GBABS.

Figures

Figures reproduced from arXiv: 2506.02366 by the authors.

Figure 1
Figure 1. Architecture of GBABS based on RD-GBG method. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Example for detecting local-density centers. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Example for generation of GB. and x7. There is no previous GBs, then r3 = CR(c3), O3 = {(x, y) ∈ U | △(c3, x) ≤ r3}. As a result, the GB constructed on U centered around (c3, l3) is assembled as gb1 = {c3, r3, l3, O3}. Similarly, construct a new GB centered (c4, l4) on U − O3. The locally consistent radius CR(c4) is the distance between c4 and x6. In addition, there is a previous GB gb1, calculate the distance betwe… view at source ↗
Figures from the paper (7 more)
Figure 5
Figure 5. Figure 5: Visualization of several datasets. are unclear. However, retaining sufficient borderline samples for high-dimensional datasets or datasets with complex and blurred class boundaries is crucial to ensure effective clas￾sification. Besides, on a dataset with relatively cl…
Figure 6
Figure 6. Figure 6: Comparison of sampling ratio under different class noise ratios. [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: Distribution of testing Accuracy for XGBoost with different sampling methods at different noise ratios. Noise Ratio: 20% 0.4 0.5 0.6 0.7 0.8 0.9 Testing Accuracy Noise Ratio: 40% GBABS-RF GGBS-RF SRS-RF RF [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: Distribution of testing Accuracy for RF with different sampling methods at different noise ratios [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: Comparison on ranking of testing G − mean for DT with various sampling methods at each noise ratio. tion, so it still performs exceptionally well in scenarios with class imbalance and noise. F. Parameter Sensitivity Analysis This section primarily validates the impact …
Figure 10
Figure 10. Figure 10: Impact of density tolerance ρ on sampling ratio. 3 5 7 9 11 13 15 17 19 Density Tolerance 0.75 0.80 0.85 0.90 0.95 1.00 Testing Accuracy S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]
Figure 11
Figure 11. Figure 11: Impact of density tolerance ρ on testing Accuracy of DT. of existing GB-based sampling approaches by eliminating GB overlap and redefining GBs, ensuring a closer alignment be￾tween the generated GBs and the original dataset distribution. The GBABS method further advan…

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.