Dual-Center Graph Clustering with Neighbor Distribution

Enhao Cheng; Jianhua Yin; Li Jin; Liqiang Nie; Shoujia Zhang

REVIEW 4 major objections 5 minor 43 references

Dual-Center Graph Clustering with Neighbor Distribution

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper proposes Dual-Center Graph Clustering (DCGC), claiming that neighbor distributions—computed from a node's neighbors' cluster pseudo-labels—are a reliable supervision signal that consistently outperforms state-of-the-art…

desk verdict A genuinely new dual-center idea, but the core loss has a sign error that inverts the neighbor-distribution alignment and the baselines are unreliable; reject as written, worth revising. read the letter →

arxiv 2507.13765 v1 pith:25YSLROG submitted 2025-07-18 cs.LG

Enhao Cheng , Shoujia Zhang , Jianhua Yin , Li Jin , Liqiang Nie This is my paper

classification cs.LG

keywords graphclusteringcontrastivelearningneighbordistributionpseudo-labelreliabilityheterophilyhardnegativeminingdual-centeroptimizationdeep

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 argues that the distribution of cluster labels among a node's neighbors—the neighbor distribution—is a more reliable supervision signal for unsupervised graph clustering than the node's own pseudo-label, and that using it in two places improves clustering. First, it is used to reweight negative pairs in contrastive learning so hard negatives get more attention. Second, it defines a second clustering center, alongside the feature center, so the model is pulled toward two target distributions rather than one. If the paper is right, graph clustering can be made substantially more accurate without labels, with the largest gains on heterophilic graphs (where connected nodes often belong to different classes), such as Wisconsin, where accuracy rises from about 50 to 64.5 percent. The method, called DCGC, is tested on ten datasets and compared with nine baselines.

What carries the argument

The load-bearing object is the neighbor distribution vector $e_i = \frac{1}{|N_i|} \sum_{j \in N_i} y_j$, where $y_j$ is the one-hot K-means pseudo-label of neighbor $j$. It enters twice: in the contrastive weight $M(i,j) = |K_{ij} - \mathrm{Norm}(S(z_i,z_j))|$, which compares neighbor-distribution similarity with embedding similarity and up-weights pairs where they disagree, and as a second center $\pi_k$ obtained by averaging the $e_i$ of the cluster, which defines a soft assignment $F$ and a sharpened target $G$ alongside the feature-center assignment $Q$ and target $P$. The dual-center loss $L_d = \sum_i \sum_j (\lambda p_{ij}\log(p_{ij}/q_{ij}) + (1-\lambda)g_{ij}\log(g_{ij}/f_{ij}))$ forces the encoder to satisfy both centers, and the total objective $L = \beta L_c + (1-\beta)L_r + \gamma L_d$ couples representation learning with clustering.

What would settle it

Corrupt the K-means pseudo-labels on a heterophilic benchmark (for example, Wisconsin or Squirrel) by randomly flipping 30 percent of labels before computing neighbor distributions, then compare DCGC's accuracy against the same run with clean pseudo-labels; if accuracy drops by more than a few points, the claimed insensitivity to pseudo-label error fails.

Watch

Extended reading notes

Core claim

DCGC's central claim is that neighbor distribution, the average of the one-hot pseudo-labels of a node's neighbors, carries two useful properties for clustering: intra-class consistency (same-class nodes have similar neighbor distributions, even in heterophilic graphs) and reliability (neighbor distributions stay informative when individual pseudo-labels are wrong). The method converts these properties into a contrastive loss with a weight $M(i,j)=|K_{ij}-\mathrm{Norm}(S(z_i,z_j))|$ that up-weights pairs whose neighbor-distribution similarity disagrees with embedding similarity, and into a dual-center KL-divergence loss that aligns soft assignments with both a feature-center target $P$ and a neighbor-distribution-center target $G$. On ten benchmark graphs spanning homophilic, mixed, and heterophilic structure, the paper reports that DCGC consistently outperforms previous contrastive and goal-directed clustering methods across ACC, NMI, ARI, and F1, with the largest margins on heterophilic datasets.

Load-bearing premise

Everything rests on the claim that a neighbor distribution computed from the model's own K-means pseudo-labels stays reliable even when those pseudo-labels are wrong, so that it can safely supervise both hard-negative mining and the second clustering center.

Editorial extensions

If this is right

If neighbor distributions are as reliable as the paper claims, contrastive graph clustering no longer needs to treat every negative pair equally; hard negatives can be identified without labels.
The dual-center objective gives a principled way to inject structural information into the target distribution, so goal-directed clustering is not limited to the feature space.
Heterophilic graphs, where feature-similar nodes often belong to different classes, stand to gain the most from neighbor-distribution supervision; the reported Wisconsin and Texas results are the largest gaps over baselines.
Because the added cost over plain InfoNCE is only $O(BKd)$ time and $O(B^2)$ space, the same recipe can be attached to existing contrastive clustering pipelines without changing their memory footprint much.

Reading between the lines

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

If neighbor distributions inherit mistakes from pseudo-labels, the same errors could reinforce themselves through the dual-center loss; a direct test is to measure how accuracy changes as pseudo-label noise is added during pre-training, something the paper does not report.
The same neighbor-distribution signal could be used for unsupervised anomaly detection: nodes whose neighbor distribution strongly disagrees with their own feature-cluster assignment are natural boundary or outlier candidates.
A learnable confidence threshold $\tau$ would let the method adapt to datasets with different homophily levels; the paper's fixed-threshold analysis already shows the optimal $\tau$ varies across datasets.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Read the DCGC paper. Short version: there’s a real idea here—adding a neighbor-distribution center to the standard feature center, and weighting hard negatives by neighbor-distribution similarity—but the loss that is supposed to implement it, Eq. (15), has the neighbor term’s sign backwards. With λ=10 (their own setting), (1−λ)=−9, so minimizing Ld maximizes KL(g‖f). That pushes soft assignments away from the neighbor centers, not toward them. The text says the opposite. Either the equation is wrong or the implementation is different. Either way, the reported experiments don’t demonstrate the claimed dual-center mechanism.

Credit where it’s due: the neighbor-distribution idea is new relative to the DEC/SDCN/DFCN line, and the motivation from intra-class consistency—especially on heterophilic graphs—is reasonable. The ablation study tries to isolate the contributions of representation learning and dual-center optimization, and the paper spans a broader set of datasets than most, including low-homophily ones.

The soft spots are serious. First, the sign issue: λ is described as learnable in Sec. 3.4 but fixed to 10 in Sec. 4.5. Second, baseline numbers are far off published values—SDCN on Cora at 35.6% ACC versus ~70% in the original paper—so the comparison isn’t apples-to-apples. Third, code isn’t provided despite the claim, so we cannot verify the intended loss or check whether some other term compensates. Fourth, hyperparameters τ and β are selected on the test sets, which inflates the gains. The claim that neighbor distributions are reliable despite noisy pseudo-labels is also illustrated but never measured; that matters for the hard-negative weighting.

The core idea may be salvageable. If the sign is corrected (e.g., λ in [0,1]), the dual-center alignment would work as claimed. But as written, the paper doesn’t give a reliable signal of whether the method works.

Who benefits: people working on deep graph clustering, especially heterophilic graphs, may get a useful idea from the neighbor-distribution center. But they shouldn’t treat the reported numbers as evidence for the mechanism.

Recommendation: send to review rather than desk reject—the idea is non-obvious and the flaw is specific and fixable. But I would reject as written. The authors need to fix the loss, rerun experiments, use published baseline numbers or official code, and release the code.

Referee Report

4 major / 5 minor

Summary. The paper proposes Dual-Center Graph Clustering (DCGC), an unsupervised graph clustering method that combines an adaptive filterbank with two MLP encoders, a contrastive loss weighted by neighbor-distribution similarity for hard-negative mining, and a 'dual-center' KL-divergence loss that aligns soft feature assignments and neighbor-distribution assignments with sharpened target distributions. Experiments are reported on ten datasets with different homophily levels, and the paper claims consistent state-of-the-art performance, with the largest gains on heterophilic graphs.

Significance. If the mechanism worked as described, the idea of using neighbor distribution as a more reliable pseudo-label signal in graph clustering would be a useful contribution, especially for heterophilic graphs. The paper includes extensive ablation studies, multiple benchmark datasets, and visualizations, which indicate effort in validating components. However, the central loss equation as written with the reported hyperparameter implements the opposite of the stated objective, the baseline numbers are inconsistent with published results, and no code is provided. The empirical claims therefore cannot currently be relied upon.

major comments (4)

[Section 3.4, Eq. (15), Section 4.5] With λ=10, the second term of L_d has coefficient (1−10)=−9, and because both p_ij/q_ij and g_ij/f_ij are KL divergences between probability vectors, minimizing the stated loss drives f_i away from g_i rather than aligning them. This contradicts the text in Section 3.4 ('encourage all samples to converge toward the neighbor distribution centers'). The same passage calls λ a learnable weight, while Section 4.5 fixes it to 10, so the formulation and the reported implementation are internally inconsistent. Since the alleged gains are attributed to dual-center optimization, this issue is load-bearing and must be resolved.
[Table 2, CORA rows] The reported SDCN ACC is 35.60±2.83 and DFCN ACC is 36.33±0.49, which are far below the values reported in the original SDCN and DFCN papers (typically above 80 for CORA). Because the paper claims consistent outperformance against these baselines, the comparison is not meaningful unless the baseline reproduction is explained; no code or configuration is provided to verify the experimental setup.
[Sections 1, 3.2, 3.4] The supervision signal is entirely self-generated: K-means on the model's own embeddings produces pseudo-labels, from which neighbor distributions e_i and centers π_k are computed, and then the model is optimized to match sharpened versions of those derived targets. The claimed reliability of neighbor distributions is supported only by the qualitative examples in Figure 1, not by a quantitative error-sensitivity analysis. This is a weak circularity issue for an unsupervised method, but it leaves the central assumption untested.
[Algorithm 1 and Section 4.2] The algorithm computes feature centers and class neighbor distributions once (Step 9) and updates only the target distributions every T iterations (Step 13), yet Section 3.4 states that the neighbor distribution center is 'updated jointly with the network.' Additionally, the coefficient γ in Eq. (16) is never given and no sensitivity analysis for γ is reported, so the actual optimized objective is not fully specified. The missing code makes these ambiguities unresolvable.

minor comments (5)

[Introduction, Contributions] The contribution bullet says 'Extensive experimental results on six datasets,' but Table 1 and the experiments cover ten datasets; this should be corrected.
[Eq. (5)] The normalization notation for Z^{v2}_j is corrupted in the text; the formula should be clearly expressed as division by the norm.
[Section 4.5] The paper states that DCGC is not sensitive to λ, but no experiment or figure for λ is shown; the claim needs supporting evidence if it is retained.
[Figure 2] Figure 2 contains unresolved '??' placeholders and the caption has an incomplete 'Unshared Parameters' label; the figure should be cleaned up.
[Section 4.7] The visualization analysis says dual-center optimization 'slightly increasing intra-cluster distance,' which seems to undercut the usual clustering goal; the authors should clarify what evidence Figure 3 provides and how this supports the method's superiority.

Circularity Check

1 steps flagged · score 4.0 of 10

Neighbor-distribution supervision is a closed self-training loop: the target G is, by Eq. (14), a deterministic sharpening of the model's own assignment F, so the dual-center branch injects no information beyond the model's outputs and the fixed adjacency; external ground-truth evaluation keeps the empirical claim only partially circular.

self definitional [Section 3.2 (Eqs. 2–3) and Section 3.4 (Eqs. 13–15)]
"Here, we use the soft assignment qi as the label distribution, replacing the pseudo-label yi. This facilitates to derive the neighbor distribution ei of node i by Eq. (2), and the class neighbor distribution πk of cluster k by Eq. (3). Then, we compute a new set of soft assignments fij using neighbor distribution ... we introduce Eq. (14) to encourage all samples to converge toward the neighbor distribution centers ... the clustering loss compels the feature assignments Q and the neighbor distribution assignments F to align with the dual-target distributions."

By construction, the neighbor-distribution 'supervision' is a function of the model's own outputs: K-means on embeddings Z yields pseudo-labels Y; Eq. (2) gives neighbor distributions E as graph-smoothed Y; Eq. (3) gives centers π as class means of E; Eq. (13) gives assignments F from distances to π; and Eq. (14) defines the target G as a sharpening of F (g ∝ f², then normalized). Eq. (15) then trains the network to align F with its own sharpened image G, so the neighbor-distribution branch injects no information beyond Z and the fixed adjacency A. This is the pseudo-label self-training loop the paper itself criticizes ('pseudo-label as a supervision signal is unreliable'); the claimed reliability of the smoothed signal is asserted from Figure 1, not measured.

full rationale

Score 4: partial circularity. The neighbor-distribution center is not an external reference; its target G is, by Eq. (14), a deterministic sharpening of the model's own assignment F, and F is derived from pseudo-labels produced by K-means on the model's own embeddings (Eqs. 2–3, 13). Training the network to align F with G (Eq. 15) is therefore training the assignment toward a smoothed, sharpened version of itself — a DEC-style self-training loop that the paper frames as 'more reliable and robust clustering guidance' without external grounding. The central empirical claim (Tables 2–3) is nevertheless measured against ground-truth labels never used in training, so the reported superiority is not forced by construction; hence 4, not 6+. Self-citation is not load-bearing here: λ=10 is borrowed from [13] as a hyperparameter value, and no derivation rests on a result unique to the authors' prior work. Separate correctness flag (not circularity): Section 3.4 calls λ 'a learnable weight parameter' while Section 4.5 fixes λ=10; with λ=10, the second term of Eq. (15) has coefficient (1−λ)=−9, so minimizing Ld increases KL(g‖f), the opposite of the stated 'converge toward the neighbor distribution centers.' This internal inconsistency affects the described mechanism's validity but does not change the circularity assessment.

Assumptions & free parameters 5 free parameters · 6 assumptions · 1 invented entities

The method introduces a novel neighbor-distribution center but relies on several unmeasured assumptions about the reliability of pseudo-label-derived signals. The loss coefficients, especially λ, introduce free parameters that are inconsistently described and tuned on test data.

free parameters (5)

τ (confidence threshold) = 0.3 to 0.9 per dataset
Used in Eq. (8) as threshold for neighbor-distribution similarity; selected per dataset by test performance.
β (loss weight) = 0.2 or 0.3 per dataset
Weights contrastive loss in Eq. (16); chosen per dataset to maximize test accuracy.
γ (weight of Ld) = not reported
Coefficient for dual-center loss in Eq. (16); tuning procedure not described.
λ = 10
Coefficient in Eq. (15) balancing feature and neighbor centers. With λ=10, (1-λ) = -9, making the neighbor-distribution term negative, which contradicts the method's description.
t (filtering times) = not reported
Power of graph Laplacian filters in Eq. (4); value not specified in experimental setup.

assumptions (6)

domain assumption Neighbor distribution exhibits intra-class consistency and is insensitive to pseudo-label errors.
Stated in Section 1 and illustrated in Figure 1, but no quantitative evidence is provided.
domain assumption K-means on node embeddings yields meaningful pseudo-labels.
Used as the source of neighbor distributions in Section 3.2 and Algorithm 1.
standard math Student's t-distribution is an appropriate kernel for soft assignment.
Adopted from DEC (Eq. 11); not rejustified for this setting.
domain assumption Sharpening the target distribution (Eq. 12) improves cluster confidence.
Borrowed from DEC self-training; no analysis of degenerate solutions in this dual-center setting.
domain assumption Adaptive filterbank with learnable weights can handle both homophilic and heterophilic graphs.
Core to the representation learning in Eq. (4); no theoretical or empirical validation beyond downstream accuracy.
domain assumption Dual-target distributions provide complementary and reliable guidance.
The basis for the dual-center loss in Section 3.4; supported only by ablation figures, not by a mechanism analysis.

invented entities (1)

Neighbor distribution center π_k
purpose: Acts as a second clustering center in the neighbor-distribution space, used to construct the target distribution g_ij in Eq. (14).
Introduced in Eqs. (13)-(14); no external validation beyond the paper's own experiments, and its benefit is asserted through ablation.

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Pith. "Pith review of Dual-Center Graph Clustering with Neighbor Distribution." pith.science (2026). https://pith.science/paper/25YSLROG

@misc{pith2026250713765,
  author       = {Pith},
  title        = {Pith review of: Dual-Center Graph Clustering with Neighbor Distribution},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/25YSLROG}},
  note         = {Machine review of arXiv:2507.13765}
}

read the original abstract

Graph clustering is crucial for unraveling intricate data structures, yet it presents significant challenges due to its unsupervised nature. Recently, goal-directed clustering techniques have yielded impressive results, with contrastive learning methods leveraging pseudo-label garnering considerable attention. Nonetheless, pseudo-label as a supervision signal is unreliable and existing goal-directed approaches utilize only features to construct a single-target distribution for single-center optimization, which lead to incomplete and less dependable guidance. In our work, we propose a novel Dual-Center Graph Clustering (DCGC) approach based on neighbor distribution properties, which includes representation learning with neighbor distribution and dual-center optimization. Specifically, we utilize neighbor distribution as a supervision signal to mine hard negative samples in contrastive learning, which is reliable and enhances the effectiveness of representation learning. Furthermore, neighbor distribution center is introduced alongside feature center to jointly construct a dual-target distribution for dual-center optimization. Extensive experiments and analysis demonstrate superior performance and effectiveness of our proposed method.

Figures

Figures reproduced from arXiv: 2507.13765 by the authors.

**Figure 1.** The neighbor distributions of samples from specific classes in the homophilic CORA and heterophilic SQUIRREL datasets. Each row vector represents the neighbor distribution of a node, which is defined as the class distribution aggregated from its neighbors and is expressed as a probability distribution over all classes. The intensity of the color in the visualization, along with each element of the neighbor distribut… view at source ↗

**Figure 2.** Illustration of our proposed dual-center graph clustering approach. Contrastive learning with neighbor distribution employs an adaptive filterbank and contrastive objectives to generate node representations Z. Then, K-means is applied to generate node neighbor distributions during neighbor distribution generation, which are utilized as supervision signals to mine hard negative samples in contrastive learning and to … view at source ↗

**Figure 3.** The 2D t-SNE visualization of six methods on the CORA dataset. ilar performances observed at the feature and neighbor distribution centers. 2) When comparing the proposed dual-center optimization with single-center optimization, the dual-center approach demonstrates improve performance across all datasets. This improvement is attributed to the complementarity of the dual-target distributions, resulting in superior … view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Ablation studies of the proposed representation learning with neighbor distribution on four datasets. (a) CORA (b) EAT [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: Ablation studies of the proposed dual-center optimization. (a) UAT (b) CITE [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 6.** Figure 6: Analysis of the hyper-parameter β. that DCGC is not sensitive to the hyperparameter λ. Therefore, following previous work [13], we set λ to 10. In this paper, the confidence is set to a fixed value, thus a possible future work is to design a learnable or dynamical co…

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

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