Pith. sign in

REVIEW 3 major objections 5 minor 43 references

On the Impact of Downstream Tasks on Sampling and Reconstructing Noisy Graph Signals

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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

Pith's one-line read For noisy partial observations of graph signals, the expected classification loss of a linearized graph convolutional network equals a sum of arc-cosine correlations, and this identity can be used to design sampling that minimizes…

desk verdict The classification-loss formula for linearized GCNs is a genuine new result, but Corollary 1.1 has a dimensional error in the stated proof and needs a correct rewrite before this is publishable. read the letter →

arxiv 2509.10874 v1 pith:UY7W2VUG submitted 2025-09-13 eess.SP cs.LG

Baskaran Sripathmanathan , Xiaowen Dong , Michael Bronstein This is my paper · ORCID
classification eess.SPcs.LG
keywords graphsignalprocessingsamplingreconstructionclassificationlossconvolutionalnetworksGaussianfeaturesnodefeaturepropagation
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

Most graph signal processing work chooses where to sample nodes by minimizing how well the unobserved signal is reconstructed, even when the actual task is node classification. This paper asks whether that mismatch matters and shows it does: for binary classification with a linearized graph convolutional network whose labels are generated by $f(X)=GXw$ and whose features are jointly Gaussian, the per-node misclassification probability is exactly $\frac{1}{\pi}\arccos$ of the correlation between the clean and reconstructed outputs. The paper proves this identity, uses it to build a greedy sampling scheme that directly minimizes classification loss, and reports that reconstruction-optimal sampling can underperform random sampling when judged by classification error. A sympathetic reader takes away a closed-form language for task-aware sampling on graphs, one in which the downstream loss, not the reconstruction loss, becomes the objective.

What carries the argument

The load-bearing identity is Lemma 1, $P(\operatorname{sign}(X)\neq\operatorname{sign}(Y)) = \arccos(\rho)/\pi$ for zero-mean jointly Gaussian $(X,Y)$ with correlation $\rho$. Theorem 1 extends it node-by-node: because $f(X)=GXw$ and $f(\hat{X})$ are linear transformations of jointly Gaussian features, each pair $(f(X)_i, f(\hat{X})_i)$ inherits joint Gaussianity, and the node's misclassification probability is exactly the arc-cosine of the correlation $\rho_i(G)$. This correlation is the object that couples the graph filter $G$, the feature covariance, the sampling set $S$, the reconstruction operator $R_S$, and the noise level, and it is what allows classification loss to be optimized directly without running the classifier.

What would settle it

Take a real graph dataset whose features are visibly non-Gaussian (for example heavy-tailed fMRI signals or discrete attributes), fix a sample set, fit $G$ and $w$, and compare the closed-form prediction $\sum_i \frac{1}{\pi}\arccos(\rho_i(G))$ to the empirical misclassification rate of the linearized GCN over many noise draws; a substantial systematic gap would show the Gaussian assumption is necessary, not incidental.

Watch

Extended reading notes

Core claim

The central object is Theorem 1. Under zero-mean jointly Gaussian feature columns with covariance $\Sigma$ and labels $\operatorname{sign}(f(X))$ with $f(X)=GXw$, the classification loss over sample set $S$ equals $\sum_{i\in V} \frac{1}{\pi}\arccos(\rho_i(G))$, where $\rho_i(G)$ is the correlation between the clean output $f(X)_i$ and the reconstructed output $f(\hat{X})_i$ built from noisy observations on $S$. The proof hinges on Lemma 1: two zero-mean jointly Gaussian scalars with correlation $\rho$ have opposite signs with probability $\arccos(\rho)/\pi$, which follows from rotational invariance of the standard bivariate Gaussian. Since both outputs are linear functions of the Gaussian features, their correlation is computable from $G$, the reconstruction operator $R_S$, the covariance of $Xw$, and the noise variance $\eta^2$. The same correlation geometry gives a reconstruction-loss formula for scalar features and, for graph filters $G$ that are polynomials of the normalized augmented adjacency matrix, a bound in which reconstruction loss controls the summed normalized output error through $\|G\|^2$.

Load-bearing premise

The features $X$ are jointly Gaussian with known covariance (for example bandlimited), and the labels are generated by a known linear map $f(X)=GXw$; if the real feature distribution or label function departs from this, the exact classification-loss formula and the sampling scheme built on it lose their theoretical guarantee.

Editorial extensions

If this is right

  • For any sample set $S$, the expected classification loss of a linearized GCN can be computed in closed form from the graph filter, feature covariance, and noise level, without Monte Carlo simulation or running the classifier.
  • Greedy sample selection can be driven by the true classification objective rather than by a reconstruction proxy; the paper derives such a scheme and shows it beats random and reconstruction-optimal sampling in synthetic and real-data experiments.
  • Reconstruction-optimal sampling can be worse than random sampling for classification, so the common practice of using reconstruction loss as a proxy is not harmless.
  • For polynomial graph filters with independent feature columns, the classification loss does not depend on the weight vector $w$, only on the filter's depth and the covariance model.
  • Reconstruction loss upper-bounds the summed normalized output error, but the nonlinear angle-to-error geometry shows that optimizing reconstruction loss is a poor proxy for per-node misclassification.

Reading between the lines

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

  • The same arc-cosine correlation mechanism should apply to any linear reconstruction operator whose output covariance can be written down; least-squares and feature propagation are the two worked examples, but the identity is not tied to them.
  • A natural plug-in extension would replace the Gaussian covariance with an empirical covariance estimated from data and use the same formula as an approximate classification-loss estimator; agreement on real data would show the identity is robust beyond its exact assumptions.
  • Because classification loss depends on correlations of clean versus reconstructed outputs, nodes where reconstruction is most uncertain (small correlation, large angle in the error triangle) are the natural targets for sampling, a principle that could transfer to active learning on graphs.
  • The triangle relation between output error, per-node variances, and misclassification probability suggests a geometric view of task-aware sampling: the sampling set should be chosen to shrink the angle, not just the magnitude, of the output error vector.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

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 graph signal sampling and reconstruction when the downstream task is binary node classification rather than reconstruction. The authors assume zero-mean Gaussian graph features with known covariance, linear reconstruction operators such as least-squares or feature propagation, and labels generated by a known linear function f(X)=GXw (a linearized GCN). Their main result (Theorem 1) gives an exact closed form for the expected classification loss—summed per-node misclassification probabilities—as (1/pi) arccos(rho_i(G)), where rho_i(G) is the correlation between the clean and reconstructed outputs at node i. Corollary 1.1 relates the corresponding output error to the classical reconstruction loss by an inequality and a claimed triangle relation. The paper then proposes a greedy sample selection scheme that directly minimizes the classification loss and compares it with random sampling and reconstruction-optimal (A-optimal) sampling on synthetic graphs and an FMRI dataset, finding that reconstruction-optimal sampling can underperform random sampling for classification.

Significance. Provided Theorem 1 is correct, this is a valuable contribution: it gives an exact, parameter-free characterization of how partial noisy observations affect a downstream linearized-GCN classifier, without running the classifier, and it applies to several reconstruction methods. The derivation is clean and internally consistent, and the assumptions are stated explicitly. The analytic curves in Figs. 3-6 are falsifiable predictions in the stated Gaussian model, and the empirical validation on synthetic data matches the analytic formula. The paper also makes a useful conceptual point that reconstruction loss and classification loss are different and can lead to very different sampling choices, and it supports this claim experimentally. However, the currently stated Corollary 1.1 contains mathematical errors, the 'optimal' sampling claim is stronger than what is proved, and the real-data experiment omits the specification of the label function f; these issues need correction before the paper is publishable.

major comments (3)
  1. [III-B, Corollary 1.1 and Fig. 2] The stated expression for Error_out,i is incorrect. Using the definitions in Theorem 1, E[(f(X)_i - f(hat X)_i)^2]/||w||^2 = (sigma_i(G))^2 + (nu_i(G))^2 - 2 c_i(G) = (sigma_i(G))^2 + (nu_i(G))^2 - 2 rho_i(G) sigma_i(G) nu_i(G). The proof's formula d*((sigma_i(G))^2 + (nu_i(G))^2 - 2 rho_i(G)) both introduces a spurious factor d (the output f(X)_i is scalar even when d>1) and drops the sigma_i nu_i factor on the cross term; since rho_i is dimensionless, the written expression is not dimensionally consistent and can be negative. Thus the triangle in Fig. 2 does not follow as stated. In addition, the proof's claim that rho_i(G) is the misclassification probability is false: rho_i(G) is the correlation coefficient, and Theorem 1 gives the misclassification probability as arccos(rho_i(G))/pi. The corrected relationship is a triangle with sides sigma_i(G), nu_i(G), and sqrt(Error_out,i), with the angle opposite sqrt(Error_out,i) equal to arccos(rho_i(G)); the misclassification probability is that angle divided by pi. Inequality (14) and Theorem 1 are unaffected, but Corollary 1.1 and Fig. 2 need to be revised.
  2. [Abstract and III-C] The paper repeatedly calls the proposed sample-selection procedure 'optimal' (Abstract: 'derive new optimal sampling methods'; Section III-C: 'minimising mean classification loss'). What is actually proposed in Section III-C is greedy minimization of the set function in Eq. (6). No optimality, near-optimality, or approximation guarantee is provided for this greedy scheme, and the submodularity/supermodularity properties that underlie known guarantees for reconstruction-based objectives are not established for Eq. (6). Please either add an analysis of the greedy procedure or qualify the language to 'task-specific greedy sampling' / 'greedy sampling for the classification objective.' The greedy algorithm itself and its computational cost should also be described.
  3. [IV-A4-A5, Fig. 7] The real-world FMRI experiment is underspecified with respect to the label function f. Theorem 1 applies only when f(X)=GXw with a known G and w. Section IV-A4 constructs binary labels from the mean-subtracted signals, and Section IV-A5 states assumptions on the feature covariance and SNR, but it never states which G and w are used to compute the classification loss that the sampling schemes optimize. Without this, the experiment is not reproducible and it is not possible to verify that the analytic classification loss is being computed correctly. Please specify f (e.g., G=I and w equal to the averaging vector if labels are signs of the average signal, or a particular linearized GCN) and state the resulting C for the FMRI dataset.
minor comments (5)
  1. [III-A] The notation sigma_i is overloaded: in Theorem 1, sigma_i(M) is a standard deviation via (sigma_i(M))^2, but the interpretive paragraph after Theorem 1 treats sigma_i as a variance in expressions such as sqrt(c_i/sigma_i). Please make the notation consistent throughout.
  2. [Lemma 1, proof] The proof divides by sqrt(1-rho^2), so the edge cases rho = +/-1 should be handled separately or by a limiting argument.
  3. [Eq. (13)] In the definition of Error_out,i, the quantity (f(X))_i is a scalar, so the use of ||.||_2 is unnecessary and may confuse readers; please clarify that this is the squared scalar difference.
  4. [Fig. 2] The caption text 'Error_out,i * d^{-1}' is ambiguous; after correcting Corollary 1.1, please redraw the triangle and explicitly identify which side is sqrt(Error_out,i) and which angle is arccos(rho_i(G)).
  5. [IV-B] No error bars or number of Monte Carlo trials are reported, so the statement that the empirical and analytic losses 'largely agree' is not quantified; please add this information.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: Theorem 1 is a parameter-free derivation from the stated Gaussian and linear-model assumptions; self-citations are background and not load-bearing.

full rationale

The derivation chain is self-contained. Lemma 1 is a standard Gaussian correlation identity proved in the paper, and Theorem 1 substitutes the covariance identities c_i(G), sigma_i(G), nu_i(G) into Lemma 1 with no fitted parameter or hidden identification: the classification-loss formula (6) is an exact re-expression of P(sign(f(X)_i) != sign(f(hat X)_i)) under the stated assumptions f(X)=GXw and Gaussian features. Corollary 1.1's inequality (14) follows by linearity and submultiplicativity. The sampling scheme in Section III-C is the optimization of the derived objective (6) over S, not a fitted quantity renamed as a prediction. Self-citations appear only as background or as part of the assumed signal model: [32] is cited for the smooth-signal model Sigma = Pi_bl(K), for the A-optimal reconstruction objective, and for interpreting the reconstruction-error spike in Fig. 5a; [29] defines the Feature Propagation reconstruction operator used as input; [42] supplies the fMRI dataset. None of these citations carries the proof of Theorem 1 or Corollary 1.1. The empirical validation uses synthetic data generated under the same model as the derivation, so it is a consistency check rather than evidence against an alternative model, but a consistency check is not circular reasoning. The dimensional inconsistency in the proof of Corollary 1.1 (Error_out,i = d*((sigma_i(G))^2 + (nu_i(G))^2 - 2*rho_i(G)) drops the sigma_i*nu_i factors on the cross term) is a correctness defect that should be corrected, but it does not make the derivation circular. No step in the paper reduces to its own input by construction.

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

The derivation of Theorem 1 is self-contained given the stated Gaussian and linearity assumptions; those assumptions are domain assumptions rather than free parameters. The principal hand-chosen numeric inputs are the noise variance eta^2 and the signal bandwidth k used in the experiments, both stated explicitly. The greedy sample-selection step, which the abstract calls optimal, is an unproved approximation. No new entities are introduced.

free parameters (2)
  • Noise variance eta^2 (20dB SNR) = 1e-3
    Chosen by hand in synthetic experiments (Section IV-A.2) and assumed for the FMRI experiment (Section IV-A.5) to define the observation model used in the sampling objectives. Not estimated from data; the sensitivity of results to this value is not tested.
  • Signal bandwidth k (fraction of nodes) = N/10 (k=36 for FMRI)
    Chosen in Section IV-A.2 (k=N/10) for synthetic signals and assumed in Section IV-A.5 (k=36) for FMRI to define the bandlimited covariance Sigma = Pi_bl(K). The sampling scheme and analytic loss depend on this choice.
assumptions (5)
  • domain assumption Features are jointly Gaussian: each column of X ~ N(0, Sigma) with Sigma = Pi_bl(K) (bandlimited) or L^dagger (smooth).
    Section II-D; required for the Gaussian correlation formula in Lemma 1 and Theorem 1.
  • domain assumption Observation noise is white Gaussian, independent of X, with variance eta^2.
    Section II-D; used in covariance expansions in Theorem 1.
  • domain assumption Labels are generated by a known linear function f(X) = GXw with w != 0; for experiments G is a linearized GCN with fixed random weights.
    Theorem 1's premise; the classification loss measures disagreement between this known f applied to clean vs reconstructed features.
  • ad hoc to paper Greedy selection of the sample set S to minimize equation (6) is a valid optimization for the classification loss.
    Section III-C proposes greedy selection without proof of near-optimality; the abstract refers to the result as optimal sampling, which is stronger than the greedy heuristic warrants.
  • standard math For SGC filters, norm(tilde A_gamma) <= 1 and hence the spectral norm bound in Corollary 1.1 holds.
    Used after Corollary 1.1, citing Gershgorin's disc theorem [39] and [34, Theorem 1].

how reviews work

0 comments
Cite this review

Pith. "Pith review of On the Impact of Downstream Tasks on Sampling and Reconstructing Noisy Graph Signals." pith.science (2026). https://pith.science/paper/UY7W2VUG

@misc{pith2026250910874,
  author       = {Pith},
  title        = {Pith review of: On the Impact of Downstream Tasks on Sampling and Reconstructing Noisy Graph Signals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UY7W2VUG}},
  note         = {Machine review of arXiv:2509.10874}
}
read the original abstract

We investigate graph signal reconstruction and sample selection for classification tasks. We present general theoretical characterisations of classification error applicable to multiple commonly used reconstruction methods, and compare that to the classical reconstruction error. We demonstrate the applicability of our results by using them to derive new optimal sampling methods for linearized graph convolutional networks, and show improvement over other graph signal processing based methods.

Figures

Figures reproduced from arXiv: 2509.10874 by the authors.

Figure 1
Figure 1. {rX′2 < X′Z ′ } Note that θ = arccos(ρ). The distribution of X′ Z′  is rotationally invariant, so for any positive integer m, if mπ θ ∈ Z, we can copy and rotate the shaded area mπ θ times to cover the plane m times (one covering of the plane corresponds to P (X ′ ∈ R, Z′ ∈ R) = 1). Thus the shaded area is P (X ′Y ′ < 0) = θ π . Otherwise let θm = mπ ⌈ mπ θ ⌉ and our argument applies if the shaded area were shrunk … view at source ↗
Figure 2
Figure 2. Relationship between misclassification probability (angle) and [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. LS Reconstruction, BA graph model, noiseless [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FP Reconstruction, BA graph model, noiseless [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: LS Reconstruction, BA graph model, Noisy ( [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 6
Figure 6. Figure 6: LS Reconstruction, SBM graph model, noiseless [PITH_FULL_IMAGE:figures/full_fig_p004_6.png]
Figure 7
Figure 7. Figure 7: FMRI dataset, LS reconstruction, sampled assuming [PITH_FULL_IMAGE:figures/full_fig_p004_7.png]

Review history (2 revisions) →

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

43 extracted references · 33 canonical work pages

  1. [32]

    On the impact of sample size in reconstructing noisy graph signals: A theoretical characterisation,

    B. Sripathmanathan, X. Dong, and M. Bronstein, “On the impact of sample size in reconstructing noisy graph signals: A theoretical characterisation,”arXiv preprint arXiv:2406.16816, 2024

    work page arXiv 2024

  2. [1]

    A graph signal processing framework for the classification of temporal brain data,

    S. Itani and D. Thanou, “A graph signal processing framework for the classification of temporal brain data,” in2020 28th European Signal Processing Conference (EUSIPCO). IEEE, 2021, pp. 1180–1184

    work page 2021

  3. [2]

    Big data+ big cities: Graph signals of urban air pollution [exploratory sp],

    R. K. Jain, J. M. Moura, and C. E. Kontokosta, “Big data+ big cities: Graph signals of urban air pollution [exploratory sp],”IEEE Signal Processing Magazine, vol. 31, no. 5, pp. 130–136, 2014

    work page 2014

  4. [3]

    Estimating political leanings from mass media via graph-signal restoration with negative edges,

    B. Renoust, G. Cheung, and S. Satoh, “Estimating political leanings from mass media via graph-signal restoration with negative edges,” in 2017 IEEE International Conference on Multimedia and Expo (ICME). IEEE, 2017, pp. 1009–1014

    work page 2017

  5. [4]

    String v11: protein–protein association networks with increased cov- erage, supporting functional discovery in genome-wide experimental datasets,

    D. Szklarczyk, A. L. Gable, D. Lyon, A. Junge, S. Wyder, J. Huerta- Cepas, M. Simonovic, N. T. Doncheva, J. H. Morris, P. Borket al., “String v11: protein–protein association networks with increased cov- erage, supporting functional discovery in genome-wide experimental datasets,”Nucleic acids research, vol. 47, no. D1, pp. D607–D613, 2019

    work page 2019

  6. [5]

    Graph signal processing: Overview, challenges, and applications,

    A. Ortega, P. Frossard, J. Kova ˇcevi´c, J. M. Moura, and P. Vandergheynst, “Graph signal processing: Overview, challenges, and applications,”Pro- ceedings of the IEEE, vol. 106, no. 5, pp. 808–828, 2018

    2018

  7. [6]

    A-optimal sampling and robust reconstruction for graph signals via truncated neumann series,

    F. Wang, Y . Wang, and G. Cheung, “A-optimal sampling and robust reconstruction for graph signals via truncated neumann series,”IEEE Signal Processing Letters, vol. 25, no. 5, pp. 680–684, 2018

    work page 2018

  8. [7]

    Low-complexity graph sampling with noise and signal reconstruction via neumann series,

    F. Wang, G. Cheung, and Y . Wang, “Low-complexity graph sampling with noise and signal reconstruction via neumann series,”IEEE Trans- actions on Signal Processing, vol. 67, no. 21, pp. 5511–5526, 2019

    work page 2019

Show all 43 references
  1. [8]

    Signals on graphs: Uncertainty principle and sampling,

    M. Tsitsvero, S. Barbarossa, and P. Di Lorenzo, “Signals on graphs: Uncertainty principle and sampling,”IEEE Transactions on Signal Processing, vol. 64, no. 18, pp. 4845–4860, 2016

    2016

  2. [9]

    Graph sampling with determinantal processes,

    N. Tremblay, P.-O. Amblard, and S. Barthelm ´e, “Graph sampling with determinantal processes,” in2017 25th European Signal Processing Conference (EUSIPCO). IEEE, 2017, pp. 1674–1678

    2017

  3. [10]

    Practical graph signal sampling with log- linear size scaling,

    A. Jayawant and A. Ortega, “Practical graph signal sampling with log- linear size scaling,”Signal Processing, vol. 194, p. 108436, 2022

    2022

  4. [11]

    Random sampling of bandlimited signals on graphs,

    G. Puy, N. Tremblay, R. Gribonval, and P. Vandergheynst, “Random sampling of bandlimited signals on graphs,”Applied and Computational Harmonic Analysis, vol. 44, no. 2, pp. 446–475, 2018

    2018

  5. [12]

    Graph-based signal sampling with adaptive subspace reconstruction for spatially-irregular sensor data,

    D. Pakiyarajah, E. Pavez, and A. Ortega, “Graph-based signal sampling with adaptive subspace reconstruction for spatially-irregular sensor data,” inICASSP 2025-2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2025, pp. 1–5

    2025

  6. [13]

    Fast graph sampling set selection using gershgorin disc alignment,

    Y . Bai, F. Wang, G. Cheung, Y . Nakatsukasa, and W. Gao, “Fast graph sampling set selection using gershgorin disc alignment,”IEEE Transactions on signal processing, vol. 68, pp. 2419–2434, 2020

    2020

  7. [14]

    Discrete signal processing on graphs: Sampling theory,

    S. Chen, R. Varma, A. Sandryhaila, and J. Kova ˇcevi´c, “Discrete signal processing on graphs: Sampling theory,”IEEE transactions on signal processing, vol. 63, no. 24, pp. 6510–6523, 2015

    2015

  8. [15]

    Pukelsheim,Optimal design of experiments

    F. Pukelsheim,Optimal design of experiments. SIAM, 2006

    2006

  9. [16]

    Graph learning from incomplete graph signals: From batch to online methods,

    X. Zhang and Q. Wang, “Graph learning from incomplete graph signals: From batch to online methods,”Signal Processing, vol. 226, p. 109663, 2025

    2025

  10. [17]

    Efficient graph learning from noisy and incomplete data,

    P. Berger, G. Hannak, and G. Matz, “Efficient graph learning from noisy and incomplete data,”IEEE Transactions on Signal and Information Processing over Networks, vol. 6, pp. 105–119, 2020

    2020

  11. [18]

    Towards joint graph learning and sampling set selection from data,

    S. N. Sridhara, E. Pavez, and A. Ortega, “Towards joint graph learning and sampling set selection from data,” in2024 58th Asilomar Conference on Signals, Systems, and Computers. IEEE, 2024, pp. 1168–1172

    2024

  12. [19]

    Sampling in paley-wiener spaces on combinatorial graphs,

    I. Pesenson, “Sampling in paley-wiener spaces on combinatorial graphs,” Transactions of the American Mathematical Society, vol. 360, no. 10, pp. 5603–5627, 2008

    2008

  13. [20]

    Near-optimality of greedy set selection in the sampling of graph signals,

    L. F. Chamon and A. Ribeiro, “Near-optimality of greedy set selection in the sampling of graph signals,” in2016 IEEE Global Conference on Signal and Information Processing (GlobalSIP). IEEE, 2016, pp. 1265–1269

    2016

  14. [21]

    Greedy sampling of graph signals,

    ——, “Greedy sampling of graph signals,”IEEE Transactions on Signal Processing, vol. 66, no. 1, pp. 34–47, 2017

    2017

  15. [22]

    Sampling large data on graphs,

    H. Shomorony and A. S. Avestimehr, “Sampling large data on graphs,” in2014 IEEE Global Conference on Signal and Information Processing (GlobalSIP). IEEE, 2014, pp. 933–936

    2014

  16. [23]

    Signal recovery on graphs: Fundamental limits of sampling strategies,

    S. Chen, R. Varma, A. Singh, and J. Kova ˇcevi´c, “Signal recovery on graphs: Fundamental limits of sampling strategies,”IEEE Transactions on Signal and Information Processing over Networks, vol. 2, no. 4, pp. 539–554, 2016

    2016

  17. [24]

    Learning with local and global consistency,

    D. Zhou, O. Bousquet, T. Lal, J. Weston, and B. Sch ¨olkopf, “Learning with local and global consistency,”Advances in neural information processing systems, vol. 16, 2003

    2003

  18. [25]

    Incomplete graph representation and learning via partial graph neural networks,

    B. Jiang and Z. Zhang, “Incomplete graph representation and learning via partial graph neural networks,”arXiv preprint arXiv:2003.10130, 2020

    2003 arXiv

  19. [26]

    Learning on attribute-missing graphs,

    X. Chen, S. Chen, J. Yao, H. Zheng, Y . Zhang, and I. W. Tsang, “Learning on attribute-missing graphs,”IEEE transactions on pattern analysis and machine intelligence, vol. 44, no. 2, pp. 740–757, 2020

    2020

  20. [27]

    Matrix completion on graphs,

    V . Kalofolias, X. Bresson, M. Bronstein, and P. Vandergheynst, “Matrix completion on graphs,”arXiv preprint arXiv:1408.1717, 2014

    2014 arXiv

  21. [28]

    Missing data imputation with adversarially-trained graph convolutional networks,

    I. Spinelli, S. Scardapane, and A. Uncini, “Missing data imputation with adversarially-trained graph convolutional networks,”Neural Networks, vol. 129, pp. 249–260, 2020

    2020

  22. [29]

    On the unreasonable effectiveness of feature propagation in learning on graphs with missing node features,

    E. Rossi, H. Kenlay, M. I. Gorinova, B. P. Chamberlain, X. Dong, and M. Bronstein, “On the unreasonable effectiveness of feature propagation in learning on graphs with missing node features,”arXiv preprint arXiv:2111.12128, 2021

    2021 arXiv

  23. [30]

    Graph convolutional networks for graphs containing missing features,

    H. Taguchi, X. Liu, and T. Murata, “Graph convolutional networks for graphs containing missing features,”Future Generation Computer Systems, vol. 117, pp. 155–168, 2021

    2021

  24. [31]

    Handling missing data with graph representation learning,

    J. You, X. Ma, Y . Ding, M. J. Kochenderfer, and J. Leskovec, “Handling missing data with graph representation learning,”Advances in Neural Information Processing Systems, vol. 33, pp. 19 075–19 087, 2020

    2020

  25. [33]

    Learning lapla- cian matrix in smooth graph signal representations,

    X. Dong, D. Thanou, P. Frossard, and P. Vandergheynst, “Learning lapla- cian matrix in smooth graph signal representations,”IEEE Transactions on Signal Processing, vol. 64, no. 23, pp. 6160–6173, 2016

    2016

  26. [34]

    Simplifying graph convolutional networks,

    F. Wu, A. Souza, T. Zhang, C. Fifty, T. Yu, and K. Weinberger, “Simplifying graph convolutional networks,” inInternational conference on machine learning. Pmlr, 2019, pp. 6861–6871

    2019

  27. [35]

    Convolutional neural networks on graphs with fast localized spectral filtering,

    M. Defferrard, X. Bresson, and P. Vandergheynst, “Convolutional neural networks on graphs with fast localized spectral filtering,”Advances in neural information processing systems, vol. 29, 2016

    2016

  28. [36]

    Graph neural networks with learnable and optimal polynomial bases,

    Y . Guo and Z. Wei, “Graph neural networks with learnable and optimal polynomial bases,” inProceedings of the 40th International Conference on Machine Learning, ser. Proceedings of Machine Learning Research, A. Krause, E. Brunskill, K. Cho, B. Engelhardt, S. Sabato, and J. Sca...

    2023

  29. [37]

    On manipulating signals of user-item graph: A jacobi polynomial-based graph collaborative filtering,

    J. Guo, L. Du, X. Chen, X. Ma, Q. Fu, S. Han, D. Zhang, and Y . Zhang, “On manipulating signals of user-item graph: A jacobi polynomial-based graph collaborative filtering,” inProceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 2023, pp. 602– 613

    2023

  30. [38]

    Bernnet: Learning arbitrary graph spectral filters via bernstein approximation,

    M. He, Z. Wei, H. Xuet al., “Bernnet: Learning arbitrary graph spectral filters via bernstein approximation,”Advances in Neural Information Processing Systems, vol. 34, pp. 14 239–14 251, 2021

    2021

  31. [39]

    R. A. Horn and C. R. Johnson,Matrix analysis. Cambridge university press, 2012

    2012

  32. [40]

    Classic GNNs are strong baselines: Reassessing GNNs for node classification,

    Y . Luo, L. Shi, and X.-M. Wu, “Classic GNNs are strong baselines: Reassessing GNNs for node classification,” inThe Thirty-eight Conference on Neural Information Processing Systems Datasets and Benchmarks Track, 2024. [Online]. Available: https://openreview.net/ forum?id=xkljKdGe4E

    2024

  33. [41]

    Understanding the difficulty of training deep feedforward neural networks,

    X. Glorot and Y . Bengio, “Understanding the difficulty of training deep feedforward neural networks,” inProceedings of the thirteenth international conference on artificial intelligence and statistics. JMLR Workshop and Conference Proceedings, 2010, pp. 249–256

    2010

  34. [42]

    Gaussian processes on graphs via spectral kernel learning,

    Y .-C. Zhi, Y . C. Ng, and X. Dong, “Gaussian processes on graphs via spectral kernel learning,”IEEE Transactions on Signal and Information Processing over Networks, vol. 9, pp. 304–314, 2023

    2023

  35. [43]

    Inductive representation learning on large graphs,

    W. Hamilton, Z. Ying, and J. Leskovec, “Inductive representation learning on large graphs,”Advances in neural information processing systems, vol. 30, 2017

    2017

Pith tools

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