Pith. sign in

REVIEW 3 major objections 5 minor 59 references

Attributed Graph Clustering in Collaborative Settings

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read This paper claims that vertical collaborative attributed graph clustering can match centralized accuracy by building virtual nodes from intersections of local clusters, and proves a misclassification bound under a restricted proximity…

desk verdict A genuinely new vertical collaborative graph clustering protocol with honest experiments, but the proof of Theorem 1 rests on a false inequality, so the main theoretical guarantee is unproven. read the letter →

arxiv 2411.12329 v2 pith:RVQGMSM6 submitted 2024-11-19 cs.LG cs.SI

Rui Zhang , Xiaoyang Hou , Zhihua Tian , Yan he , Enchao Gong , Jian Liu , Qingbiao Wu , Kui Ren This is my paper · ORCID
classification cs.LGcs.SI MSC 62H3068T0568R10
keywords attributedgraphclusteringcollaborativelearningverticalfederatedk-meanssecureaggregationfilterproximityconditioncommunicationefficiency
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 is trying to establish that attributed graph clustering can be done collaboratively when each participant holds different features of the same nodes, without ever pooling the data. The method's central bet is that global clusters appear at the intersections of local clusters: if each participant can cluster its own feature block, the overlap patterns of those local clusters reveal where the global clusters are. The paper proves a theorem to this effect under a "restricted proximity condition," and supports it with experiments showing accuracy close to centralized methods while cutting the number of expensive secure aggregations from depending on the number of nodes to depending only on the number of clusters and participants.

What carries the argument

The central object is the intersection of local clusters: each participant's k-means output partitions the shared node set into $\hat{k}$ local clusters, and the protocol intersects these partitions across participants to produce candidate groups whose centers become weighted "virtual nodes." The restricted proximity condition is the paper's assumption that these intersections align with the global target clusters closely enough that the virtual nodes inherit the classic proximity condition used in centralized spectral-norm clustering analyses, so the centralized misclassification lemma can be applied to them unchanged.

What would settle it

Construct a two-participant dataset with $k=2$ global clusters in $\mathbb{R}^2$ where participant 1 sees only x-coordinates and participant 2 only y-coordinates, arranged so each participant's local k-means with $\hat{k}=2$ puts half of each global cluster into the same local cluster; running kCAGC with $\hat{k}=k$ then should produce intersections containing both global clusters, so if the misclassification rate drops far below the centralized k-means rate on the full 2D data, the alignment premise behind Theorem 1 has failed.

Watch

Extended reading notes

Core claim

The paper claims that in a vertically partitioned collaborative setting, the global clustering problem can be solved almost as accurately as centralized clustering by communicating only local-cluster memberships rather than raw features. Each participant runs k-means on its own filtered feature block, the intersections of these local cluster families form a small weighted set of virtual nodes, and secure aggregation over those virtual nodes reproduces the centralized k-means result. Theorem 1 states that with 10-approximate initialization, local center separation, and the restricted proximity condition, at most $(L\epsilon + O(1)Lc^{-4})n$ nodes are misclassified when each participant has $\epsilon n$ local 1-bad nodes, and all nodes are correctly assigned when $\epsilon = 0$. The paper also claims this reduces secure aggregations from $O(nk)$ per iteration to $O((Q+1)L\hat{k}^3)$, and experiments show accuracy comparable to centralized attributed-graph clustering and better than baselines trained on isolated data subsets.

Load-bearing premise

Every global cluster must be nearly an exact intersection of one local cluster from each participant; if local clusters cut across global cluster boundaries, the virtual nodes mix different global clusters and the weighted k-means on virtual nodes cannot recover the central partition.

Editorial extensions

If this is right

  • Communication complexity becomes independent of dataset size: kCAGC needs $O((Q+1)L\hat{k}^3)$ secure aggregations instead of $O(Qnk)$, so large-sample datasets train in seconds to minutes.
  • If each participant's local clustering has no 1-bad nodes, Theorem 1 says all nodes are assigned correctly; with $\epsilon n$ local 1-bad nodes per participant, at most $(L\epsilon + O(1)Lc^{-4})n$ nodes are misclassified.
  • Participants never share raw features: the protocol exchanges only node IDs within local clusters and securely aggregated sums of virtual-node centers.
  • Experiments on four public attributed graphs show accuracy comparable to centralized clustering and better than semi-supervised baselines trained on isolated data subsets.
  • Training time depends on the number of participants and local clusters rather than on the number of nodes, so a nearly ten-times-larger dataset trains in roughly the same time as smaller ones.

Reading between the lines

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

  • A direct extension would be to verify the restricted proximity condition empirically on real datasets, since the paper's experiments do not measure the fraction of local 1-bad nodes that the theorem's bound depends on.
  • The one-time exchange of node IDs could be made fully private with private set intersection; the paper notes record linkage can be done this way but does not analyze the combined protocol.
  • Because accuracy is non-monotonic in the number of local clusters, an adaptive selector for $\hat{k}$ would likely improve both accuracy and communication cost in practice.
  • The intersection-of-local-clusters mechanism is not inherently graph-specific and may transfer to other center-based clustering problems in vertical collaborative settings.
Share X Bluesky LinkedIn Reddit HN

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. This paper studies vertically partitioned attributed graph clustering: L participants share a graph but hold different feature blocks of the same n nodes, and they want to cluster the nodes without sharing raw features. The authors propose kCAGC, which first runs a local k-means procedure (Protocol 1) on each participant's filtered features, then intersects the local clusters across participants to form a set of virtual nodes, and finally runs a secure-aggregation k-means (Protocol 2) on those virtual nodes with cluster sizes as weights. The paper claims a communication reduction from O(nk) secure aggregations to O((Q+1)L k^3) for a tree variant, and it states Theorem 1 asserting that, under a 'restricted proximity condition' plus local and global center separation, at most (L epsilon + O(1)L c^{-4})n nodes are misclassified when each participant has epsilon n local 1-bad nodes, with exact recovery when epsilon = 0. Experiments on Cora, Citeseer, Pubmed, and Wiki compare accuracy with the centralized methods AGC and GCC and with a basic kCAGC baseline, and report training times in LAN and WAN settings.

Significance. If the theoretical claim were established, this would be a useful contribution: it addresses a relatively unexplored vertical unsupervised graph-clustering setting, it gives a concrete protocol for reducing the number of expensive secure aggregations, and it provides a fairly complete experimental evaluation, including a comparison with semi-supervised GraphSAGE models and a privacy-leakage measurement. The implementation is described in detail, with experiments run on real datasets under multiple participant counts and local cluster counts. These empirical strengths are real. However, the central Theorem 1 is not proven as stated: the proof in Appendix B contains a false norm inequality and an unstated alignment assumption between global target clusters and intersections of local clusters. The experimental results may still justify the algorithmic contribution, but the advertised theoretical guarantee needs substantial repair before the abstract and contribution statements are supported.

major comments (3)
  1. [Appendix B, Eq. (19)] The proof of Theorem 1 asserts that for i = argmin_i ||X_i - mu_q_hat|| and u the indicator vector of T_q, n_q ||X_i - mu_q_hat|| <= ||(X - C_hat) u||, and hence ||X_i - mu_q_hat|| <= (1/sqrt(n_q)) ||X - C_hat||. This inequality is false. The right-hand side is the norm of the sum of the within-cluster residual vectors, while the left-hand side is n_q times the smallest residual norm; the sum can vanish through cancellation even when every individual residual is large. For example, take L = 1, T_q = {[1,0],[0,1],[-1,0],[0,-1]}, mu_q_hat = [0,0], and C_hat_j = mu_q_hat for all j in T_q. Then n_q = 4, ||(X - C_hat)u|| = 0, and ||X_i - mu_q_hat|| = 1 for every i, so the claimed inequality reads 4 <= 0. Shifting the configuration by a small vector shows the failure is not degenerate. Because Eqs. (19)-(20) are the only bridge from the virtual-node construction to the restricted proximity margin in Eq. (21), Theorem 1 is not established by this proof.
  2. [Theorem 1 and Appendix B, Eqs. (17)-(20)] The proof silently assumes an alignment between global target clusters and intersections of local clusters: it treats C_hat_i as equal to mu_q_hat for every i in T_q, which requires that all members of T_q fall into the same local cluster in every participant, i.e., T_q is exactly an intersection of local clusters of the form intersection_l T^l_{r_l}. This condition is not stated in Theorem 1, and it is not shown to follow from local center separation or from the restricted proximity condition in Definition 1. If a local cluster cuts across two global clusters, the virtual node for that intersection combines points from different target clusters, and Protocol 3 line 17 assigns the whole intersection to one output cluster, causing unavoidable misclassifications. The theorem must either state this alignment explicitly as an assumption or bound the number of points contained in misaligned intersections.
  3. [Section 3.5, after Eq. (12)] The paper claims that ||X - C_hat|| <= ||X - C|| for k_hat >= k 'since C_hat is the local optimal centers'. This does not follow for the spectral norm. k-means optimality is a statement about the Frobenius norm of the residual matrix, and a finer local clustering can reduce the sum of squared residuals while increasing the largest singular value of the residual matrix. This step is used to argue that the restricted proximity condition is a compromise between Definition 2 and the Kumar-Kannan condition, so the comparison needs either a corrected norm argument or a different definition of the quantities in Definition 1.
minor comments (5)
  1. [Section 1 and Section 3.4] The contribution bullet and the abstract state that the communication cost drops from O(n) to O(k^3), but Protocol 3 as written produces k_hat^L intersections; the O((Q+1)L k_hat^3) bound is for the tree variant described later in Section 3.4. Please qualify the complexity claim consistently.
  2. [Throughout] There are several typos and notation inconsistencies: 'changeling' in Section 1, 'Effenciency' in the Appendix E.3 heading, 'garph' in the Table 8 and Table 9 captions, inconsistent use of 'k-CAGC' versus 'kCAGC', and 'security aggregation' versus 'secure aggregation'.
  3. [Protocol 2 and Protocol 3] In Protocol 2, line 26, d^m_{i,r} should be d^j_{i,r}; in Protocol 3, line 7, the participant performing the intersection should be P_L, not P_l.
  4. [Table 2] The Pubmed row for L = 4, k_hat = k reports 65.61 +/- 5.43, an order-of-magnitude larger standard deviation than the neighboring entries in the table; this outlier deserves a remark or a check.
  5. [Appendix D] The setting with split graph structures is described only for two participants; the text should state how the common graph filter G is computed when participants do not share the same Laplacian.

Circularity Check

0 steps flagged · score 1.0 of 10

No load-bearing circularity; Theorem 1 is a conditional analysis built on external proximity lemmas, with only a minor contextual self-citation.

full rationale

The central derivation chain is not circular. Theorem 1 states a conditional guarantee: under local center separation, the restricted proximity condition (Definition 1), and a 10-approximation initialization, the misclassification bound follows by applying Lemma 1 from Awasthi and Sheffet [36] to the virtual intersection nodes. The restricted proximity condition is a data assumption expressed through target cluster means and spectral norms; it is not fitted from the output and is not defined in terms of the algorithm's clusters. The proof does not rename a known result: it extends Definition 2 with an extra ||X−C_hat|| term and cites the external Lemma 1 for the final error bound. No free parameter is fit to the reported accuracies, and the empirical comparison to centralized AGC/GCC is self-contained. The only self-citation, [15] (federboost, sharing authors with this paper), is used in the introduction and the adversary model as background; it is not load-bearing for Theorem 1 or the efficiency claim. I do flag a correctness concern in Appendix B: inequality (19), || |T_q|(X_i−mu_hat_q)|| <= ||(X−C_hat)u||, is asserted with no derivation and is not a consequence of the stated definitions (the right side is a sum of residual vectors, which can be much smaller than n_q times a single residual). This threatens the proof of Theorem 1 if the inequality is indeed false, but an invalid step is a correctness gap, not circularity: the conclusion is not equivalent to the input, and the argument would fail rather than reduce to its assumptions. Accordingly the circularity score is 1, reflecting only a non-load-bearing self-citation.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claim rests on two strong data assumptions imported from prior clustering theory (center separation and proximity conditions) plus a new condition (restricted proximity) that the paper does not validate empirically. It also implicitly assumes that global clusters align with intersections of local clusters. The free parameters are experimental hyperparameters, not fitted to the target result, so they do not make the derivation circular.

free parameters (3)
  • graph filter order psi = Cora=9, Citeseer=15, Pubmed=60, Wiki=2
    Chosen per dataset in Section 4.1; directly controls the feature smoothing before clustering and affects accuracy.
  • local cluster multiplier for hat_k = k, 2k, 4k, 8k; best selected per dataset
    Section 4.1 varies hat_k and highlights the best result; the optimum differs by dataset and participant count.
  • maximum Lloyd iterations Q = 10
    Set in Section 3.5; experiments converge in about 4 iterations, so this is a safe cap rather than a tuned parameter.
assumptions (6)
  • standard math Normalized Laplacian eigenvalues lie in [0,2]
    Used in Section 3.2 to design p(lambda) as a nonnegative decreasing filter; standard result from spectral graph theory (Chung).
  • domain assumption Nearby nodes in the graph have similar features
    Assumed in Section 3.2 to justify low-pass graph filtering; if false the graph filter does not help.
  • domain assumption Awasthi-Sheffet proximity and center separation conditions hold for local and global clusters
    Theorem 1 imports Lemma 1 from [36]; these conditions are strong and not validated on real data.
  • ad hoc to paper Restricted proximity condition (Definition 1) holds for the data
    Definition 1 is introduced solely for this analysis; the paper does not verify it empirically and even notes it is stronger than Definition 2.
  • ad hoc to paper Each global target cluster is an intersection of local clusters from each participant
    The proof in Appendix B requires hat_C_i = hat_mu_q for all i in T_q (equation (19)); this alignment is not proven and not stated as an assumption.
  • domain assumption Participants are honest-but-curious, do not drop out, and have a secure channel
    Section 3.1.2 states these to simplify secure aggregation; real deployments may not satisfy them.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Attributed Graph Clustering in Collaborative Settings." pith.science (2026). https://pith.science/paper/RVQGMSM6

@misc{pith2026241112329,
  author       = {Pith},
  title        = {Pith review of: Attributed Graph Clustering in Collaborative Settings},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RVQGMSM6}},
  note         = {Machine review of arXiv:2411.12329}
}
read the original abstract

Graph clustering is an unsupervised machine learning method that partitions the nodes in a graph into different groups. Despite achieving significant progress in exploiting both attributed and structured data information, graph clustering methods often face practical challenges related to data isolation. Moreover, the absence of collaborative methods for graph clustering limits their effectiveness. In this paper, we propose a collaborative graph clustering framework for attributed graphs, supporting attributed graph clustering over vertically partitioned data with different participants holding distinct features of the same data. Our method leverages a novel technique that reduces the sample space, improving the efficiency of the attributed graph clustering method. Furthermore, we compare our method to its centralized counterpart under a proximity condition, demonstrating that the successful local results of each participant contribute to the overall success of the collaboration. We fully implement our approach and evaluate its utility and efficiency by conducting experiments on four public datasets. The results demonstrate that our method achieves comparable accuracy levels to centralized attributed graph clustering methods. Our collaborative graph clustering framework provides an efficient and effective solution for graph clustering challenges related to data isolation.

Figures

Figures reproduced from arXiv: 2411.12329 by the authors.

Figure 1
Figure 1. An example of collaborative setting. Users sign in to [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. The visualization of the intuition. (a): [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. The t-SNE projection of the feature for “Cora” dataset according to the real (a) labels, (b) AGC, (c) Protocol 2, and [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Accuracy of kCAGC while increasing the proportion of shared graph data for “Cora” Dataset required to make our method comparable to the centralized method. We start with allocating 50% of the complete graph structure to each participant, and gradually increase the prop…
Figure 5
Figure 5. Figure 5: Different order of graph filter (ψ) for kCAGC E.1 Order of graph filter In our experiments, we set the number of participants to L = 2 and the number of clusters to ˆk = k. We compare the performance of our proposed method, denoted as kCAGC, with that of the AGC method…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

59 extracted references · 50 canonical work pages

  1. [1]

    Private hierarchical clustering in federated networks,

    A. Kolluri, T. Baluta, and P . Saxena, “Private hierarchical clustering in federated networks,” in Proceedings of the 2021 ACM CCS , 2021, pp. 2342–2360

    work page 2021

  2. [2]

    Collective classification in network data,

    P . Sen, G. Namata, M. Bilgic, L. Getoor, B. Galligher, and T. Eliassi- Rad, “Collective classification in network data,” AI magazine , vol. 29, no. 3, pp. 93–93, 2008

    work page 2008

  3. [3]

    Label informed attributed network embedding,

    X. Huang, J. Li, and X. Hu, “Label informed attributed network embedding,” in Proceedings of the tenth ACM international conference on web search and data mining , 2017, pp. 731–739

    work page 2017

  4. [4]

    Deep attributed network embedding,

    H. Gao and H. Huang, “Deep attributed network embedding,” in Twenty-Seventh International Joint Conference on Artificial Intelligence (IJCAI)), 2018. JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 11 TABLE 4: Efficiency of k-CAGC in LAN. Training Time (s) Cora Citeseer Pubmed Wiki L 2 4 8 16 2 4 8 16 2 4 8 16 2 4 8 16 ˆk = k 1.16 3.43 7.86 16.6...

    work page 2018

  5. [5]

    Magnn: Metapath ag- gregated graph neural network for heterogeneous graph embed- ding,

    X. Fu, J. Zhang, Z. Meng, and I. King, “Magnn: Metapath ag- gregated graph neural network for heterogeneous graph embed- ding,” in Proceedings of The Web Conference, 2020, pp. 2331–2341

    work page 2020

  6. [6]

    Variational graph auto- encoders,

    Kipf, Thomas N and Welling, Max, “Variational graph auto- encoders,” NIPS Workshop on Bayesian Deep Learning , 2016

    work page 2016

  7. [7]

    Inductive representation learning on large graphs,

    W. Hamilton, Z. Ying, and J. Leskovec, “Inductive representation learning on large graphs,” NeurIPS, vol. 30, 2017

    2017

  8. [8]

    Semi-supervised classification with graph convolutional networks,

    T. N. Kipf and M. Welling, “Semi-supervised classification with graph convolutional networks,” In International Conference on Learning Representations, 2017

    work page 2017

Show all 59 references
  1. [9]

    Deeper insights into graph convo- lutional networks for semi-supervised learning,

    Q. Li, Z. Han, and X.-M. Wu, “Deeper insights into graph convo- lutional networks for semi-supervised learning,” in Proceedings of the AAAI conference on artificial intelligence , vol. 32, no. 1, 2018

    2018

  2. [10]

    Protecting privacy in knowledge graphs with personalized anonymization,

    A.-T. Hoang, B. Carminati, and E. Ferrari, “Protecting privacy in knowledge graphs with personalized anonymization,” IEEE Transactions on Dependable and Secure Computing, vol. 21, no. 4, pp. 2181–2193, 2024

    2024

  3. [11]

    A privacy mechanism for access controlled graph data,

    M. U. Arshad, M. Felemban, Z. Pervaiz, A. Ghafoor, and W. G. Aref, “A privacy mechanism for access controlled graph data,” IEEE Transactions on Dependable and Secure Computing, vol. 16, no. 5, pp. 819–832, 2019

    2019

  4. [12]

    Privacy-preserving graph neural network for node classifica- tion,

    J. Zhou, C. Chen, L. Zheng, X. Zheng, B. Wu, Z. Liu, and L. Wang, “Privacy-preserving graph neural network for node classifica- tion,” arXiv preprint arXiv:2005.11903, 2020

    2005 arXiv

  5. [13]

    Fedgnn: Federated graph neural network for privacy-preserving recommendation,

    C. Wu, F. Wu, Y. Cao, Y. Huang, and X. Xie, “Fedgnn: Federated graph neural network for privacy-preserving recommendation,” In Proceedings of ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD 2021), 2021

    2021

  6. [14]

    Locally private graph neural networks,

    S. Sajadmanesh and D. Gatica-Perez, “Locally private graph neural networks,” in Proceedings of the 2021 ACM CCS , 2021, pp. 2130– 2145

    2021

  7. [15]

    federboost: Private federated learning for gbdt,

    Z. Tian, R. Zhang, X. Hou, L. Lyu, T. Zhang, J. Liu, and K. Ren, “federboost: Private federated learning for gbdt,” IEEE Transac- tions on Dependable and Secure Computing , pp. 1–12, 2023

    2023

  8. [16]

    Tapfed: Threshold secure aggregation for privacy-preserving federated learning,

    R. Xu, B. Li, C. Li, J. B. D. Joshi, S. Ma, and J. Li, “Tapfed: Threshold secure aggregation for privacy-preserving federated learning,” IEEE Transactions on Dependable and Secure Computing, vol. 21, no. 5, pp. 4309–4323, 2024

    2024

  9. [17]

    Communication-efficient learning of deep networks from decentralized data,

    B. McMahan, E. Moore, D. Ramage, S. Hampson, and B. A. y Ar- cas, “Communication-efficient learning of deep networks from decentralized data,” in Artificial intelligence and statistics . PMLR, 2017, pp. 1273–1282

    2017

  10. [18]

    Federated learning on non-iid graphs via structural knowledge sharing,

    Y. Tan, Y. Liu, G. Long, J. Jiang, Q. Lu, and C. Zhang, “Federated learning on non-iid graphs via structural knowledge sharing,” in Proceedings of the AAAI conference on artificial intelligence , vol. 37, no. 8, 2023, pp. 9953–9961

    2023

  11. [19]

    Fedgraph: Federated graph learning with intelligent sampling,

    F. Chen, P . Li, T. Miyazaki, and C. Wu, “Fedgraph: Federated graph learning with intelligent sampling,” IEEE Trans. Parallel Distributed Syst., vol. 33, no. 8, pp. 1775–1786, 2022

    2022

  12. [20]

    Personalized subgraph federated learning,

    J. Baek, W. Jeong, J. Jin, J. Yoon, and S. J. Hwang, “Personalized subgraph federated learning,” in International Conference on Ma- chine Learning. PMLR, 2023, pp. 1396–1415

    2023

  13. [21]

    Fedgcn: Convergence and communication tradeoffs in federated training of graph con- volutional networks,

    Y. Yao, W. Jin, S. Ravi, and C. Joe-Wong, “Fedgcn: Convergence and communication tradeoffs in federated training of graph con- volutional networks,” arXiv preprint arXiv:2201.12433, 2022

    2022 arXiv

  14. [22]

    Subgraph federated learning with missing neighbor generation,

    K. Zhang, C. Yang, X. Li, L. Sun, and S. M. Yiu, “Subgraph federated learning with missing neighbor generation,” NeurIPS, vol. 34, pp. 6671–6682, 2021

    2021

  15. [23]

    Vertical federated graph neural network for recommender system,

    P . Mai and Y. Pang, “Vertical federated graph neural network for recommender system,” arXiv preprint arXiv:2303.05786, 2023

    2023 arXiv

  16. [24]

    Your labels are selling you out: Relation leaks in vertical federated learning,

    P . Qiu, X. Zhang, S. Ji, T. Du, Y. Pu, J. Zhou, and T. Wang, “Your labels are selling you out: Relation leaks in vertical federated learning,” IEEE Transactions on Dependable and Secure Computing , vol. 20, no. 5, pp. 3653–3668, 2023

    2023

  17. [25]

    Dynamic user clustering for efficient and privacy-preserving federated learning,

    Z. Liu, J. Guo, W. Yang, J. Fan, K.-Y. Lam, and J. Zhao, “Dynamic user clustering for efficient and privacy-preserving federated learning,” IEEE Transactions on Dependable and Secure Computing , pp. 1–12, 2024

    2024

  18. [26]

    Vertically federated graph neural net- work for privacy-preserving node classification,

    C. Chen, J. Zhou, L. Zheng, H. Wu, L. Lyu, J. Wu, B. Wu, Z. Liu, L. Wang, and X. Zheng, “Vertically federated graph neural net- work for privacy-preserving node classification,” in Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence (IJCAI...

    2022

  19. [27]

    A vertical feder- ated learning framework for graph convolutional network,

    X. Ni, X. Xu, L. Lyu, C. Meng, and W. Wang, “A vertical feder- ated learning framework for graph convolutional network,” arXiv preprint arXiv:2106.11593, 2021

    2021 arXiv

  20. [28]

    Graph clustering,

    S. E. Schaeffer, “Graph clustering,” Computer science review, vol. 1, no. 1, pp. 27–64, 2007

    2007

  21. [29]

    Attributed graph clustering: a deep attentional embedding ap- proach,

    C. Wang, S. Pan, R. Hu, G. Long, J. Jiang, and C. Zhang, “Attributed graph clustering: a deep attentional embedding ap- proach,” in International Joint Conference on Artificial Intelligence 2019, 2019, pp. 3670–3676

    2019

  22. [30]

    Adaptive graph encoder for attributed graph embedding,

    G. Cui, J. Zhou, C. Yang, and Z. Liu, “Adaptive graph encoder for attributed graph embedding,” in Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, 2020, pp. 976–985

    2020

  23. [31]

    Practical secure aggre- gation for privacy-preserving machine learning,

    K. Bonawitz, V . Ivanov, B. Kreuter, A. Marcedone, H. B. McMahan, S. Patel, D. Ramage, A. Segal, and K. Seth, “Practical secure aggre- gation for privacy-preserving machine learning,” in Proceedings of the 2017 ACM CCS. ACM, 2017, pp. 1175–1191

    2017

  24. [32]

    On the design of communication-efficient federated learning for health monitor- ing,

    D. Chu, W. Jaafar, and H. Yanikomeroglu, “On the design of communication-efficient federated learning for health monitor- ing,” in GLOBECOM 2022-2022 IEEE Global Communications Con- ference. IEEE, 2022, pp. 1128–1133

    2022

  25. [33]

    Socially-aware- clustering-enabled federated learning for edge networks,

    L. U. Khan, Z. Han, D. Niyato, and C. S. Hong, “Socially-aware- clustering-enabled federated learning for edge networks,” IEEE Transactions on Network and Service Management , vol. 18, no. 3, pp. 2641–2658, 2021

    2021

  26. [34]

    Efficient distribution similarity identification in clustered federated learning via principal angles between client data subspaces,

    S. Vahidian, M. Morafah, W. Wang, V . Kungurtsev, C. Chen, M. Shah, and B. Lin, “Efficient distribution similarity identification in clustered federated learning via principal angles between client data subspaces,” in Proceedings of the AAAI Conference on Artificial Intelligen...

    2023

  27. [35]

    Heterogeneity for the win: One- shot federated clustering,

    D. K. Dennis, T. Li, and V . Smith, “Heterogeneity for the win: One- shot federated clustering,” in International Conference on Machine Learning. PMLR, 2021, pp. 2611–2620

    2021

  28. [36]

    Improved spectral-norm bounds for clustering,

    P . Awasthi and O. Sheffet, “Improved spectral-norm bounds for clustering,” in Approximation, Randomization, and Combinatorial Op- timization. Algorithms and Techniques. Springer, 2012, pp. 37–49

    2012

  29. [37]

    Clustering with spectral norm and the k-means algorithm,

    A. Kumar and R. Kannan, “Clustering with spectral norm and the k-means algorithm,” in 2010 IEEE 51st Annual Symposium on Foundations of Computer Science. IEEE, 2010, pp. 299–308

    2010

  30. [38]

    Attributed graph clus- tering via adaptive graph convolution,

    X. Zhang, H. Liu, Q. Li, and X.-M. Wu, “Attributed graph clus- tering via adaptive graph convolution,” in Proceedings of the 28th International Joint Conference on Artificial Intelligence, 2019, pp. 4327– 4333

    2019

  31. [39]

    Efficient graph convolution for joint node representation learning and clustering,

    C. Fettal, L. Labiod, and M. Nadif, “Efficient graph convolution for joint node representation learning and clustering,” in Proceedings of the Fifteenth ACM International conference on web search and data mining, 2022, pp. 289–297

    2022

  32. [40]

    Spectral JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 12 embedding network for attributed graph clustering,

    X. Zhang, H. Liu, X.-M. Wu, X. Zhang, and X. Liu, “Spectral JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 12 embedding network for attributed graph clustering,” Neural Net- works, vol. 142, pp. 388–396, 2021

    2015

  33. [41]

    Secureml: A system for scalable privacy-preserving machine learning,

    P . Mohassel and Y. Zhang, “Secureml: A system for scalable privacy-preserving machine learning,” in 2017 IEEE Symposium on Security and Privacy (SP), May 2017, pp. 19–38

    2017

  34. [42]

    Oblivious neural network predictions via minionn transformations,

    J. Liu, M. Juuti, Y. Lu, and N. Asokan, “Oblivious neural network predictions via minionn transformations,” inProceedings of the 2017 ACM CCS, ser. CCS ’17, 2017, p. 619–631

    2017

  35. [43]

    Practical multi-party private set intersection from symmetric-key techniques,

    V . Kolesnikov, N. Matania, B. Pinkas, M. Rosulek, and N. Trieu, “Practical multi-party private set intersection from symmetric-key techniques,” in Proceedings of the 2017 ACM CCS, ser. CCS ’17, 2017, p. 1257–1272

    2017

  36. [44]

    F. R. Chung and F. C. Graham, Spectral graph theory . American Mathematical Soc., 1997, no. 92

    1997

  37. [45]

    Hastie, R

    T. Hastie, R. Tibshirani, J. H. Friedman, and J. H. Friedman, The elements of statistical learning: data mining, inference, and prediction . Springer, 2009, vol. 2

    2009

  38. [46]

    A geometric understanding of deep learning,

    N. Lei, D. An, Y. Guo, K. Su, S. Liu, Z. Luo, S.-T. Yau, and X. Gu, “A geometric understanding of deep learning,” Engineering, vol. 6, no. 3, pp. 361–374, 2020

    2020

  39. [47]

    Federated machine learn- ing: concept and applications,

    Q. Yang, Y. Liu, T. Chen, and Y. Tong, “Federated machine learn- ing: concept and applications,” ACM Transactions on Intelligent Systems and Technology (TIST), vol. 10, no. 2, p. 12, 2019

    2019

  40. [48]

    Vertical federated learning: Challenges, methodologies and experiments,

    K. Wei, J. Li, C. Ma, M. Ding, S. Wei, F. Wu, G. Chen, and T. Ran- baduge, “Vertical federated learning: Challenges, methodologies and experiments,” arXiv preprint arXiv:2202.04309, 2022

    2022 arXiv

  41. [49]

    Visualizing data using t-sne,

    L. van der Maaten and G. Hinton, “Visualizing data using t-sne,” Journal of Machine Learning Research , vol. 9, no. 86, pp. 2579–2605, 2008

    2008

  42. [50]

    k-means++: The advantages of careful seeding,

    D. Arthur, S. Vassilvitskii et al. , “k-means++: The advantages of careful seeding,” in Soda, vol. 7, 2007, pp. 1027–1035

    2007

  43. [51]

    How fast is the k-means method?

    S. Har-Peled and B. Sadri, “How fast is the k-means method?” Algorithmica, vol. 41, pp. 185–202, 2005

    2005

  44. [52]

    Svd-based collaborative filtering with privacy,

    H. Polat and W. Du, “Svd-based collaborative filtering with privacy,” in Proceedings of the 2005 ACM symposium on Applied computing, 2005, pp. 791–795

    2005

  45. [53]

    Svd based data transformation methods for privacy preserving clustering,

    M. N. Lakshmi and K. S. Rani, “Svd based data transformation methods for privacy preserving clustering,” International Journal of Computer Applications, vol. 78, no. 3, 2013

    2013

  46. [54]

    Singular value decom- position based data distortion strategy for privacy protection,

    S. Xu, J. Zhang, D. Han, and J. Wang, “Singular value decom- position based data distortion strategy for privacy protection,” Knowledge and Information Systems, vol. 10, pp. 383–397, 2006

    2006

  47. [55]

    Network representation learning with rich text information,

    C. Yang, Z. Liu, D. Zhao, M. Sun, and E. Chang, “Network representation learning with rich text information,” in Twenty- fourth international joint conference on artificial intelligence , 2015

    2015

  48. [56]

    On the design and quantifi- cation of privacy preserving data mining algorithms,

    D. Agrawal and C. C. Aggarwal, “On the design and quantifi- cation of privacy preserving data mining algorithms,” in Proceed- ings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems, 2001, pp. 247–255

    2001

  49. [57]

    Svd-based privacy preserving data updat- ing in collaborative filtering,

    X. Wang and J. Zhang, “Svd-based privacy preserving data updat- ing in collaborative filtering,” in Proceedings of the World Congress on Engineering, vol. 1, 2012, pp. 377–384. Zhang Rui graduated from the School of Mathe- matics in Zhejiang University, Hangzhou China, in 2020...

    2012

  50. [59]

    nothing more

    c >100 will be sufficient Lemma 1. (Awasthi-Sheffet,2011) [36]. Let T = {T1, · · ·, Tk} be the target clusters. Assume that each pair of clusters Tr and Ts satisfy the center separation assumption. Then after constructing clusters Sr in Protocol 1, for every r, it holds that |...

    2011

  51. [2020]

    degree in the School of Cyber Science and Technol- ogy of Zhejiang University, Hangzhou, China

    Currently, he is pursuing a Ph.D. degree in the School of Cyber Science and Technol- ogy of Zhejiang University, Hangzhou, China. His research interests include machine learning, federated learning, and adversarial training algo- rithms. Enchao Gong Graduated with a master’s d...

    2012

Pith tools

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