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REVIEW 3 major objections 8 minor 43 references

Multi-view Clustering with the Cooperation of Visible and Hidden Views

T0 review · 3 major / 8 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Clustering improves when visible views are joined by a shared hidden view learned by non-negative matrix factorization, and the resulting algorithm beats seven baselines on all eight test datasets.

desk verdict Reasonable incremental idea, but the paper's own Table X contradicts its all-datasets all-metrics claim; needs a correction rather than a desk reject. read the letter →

arxiv 1908.04766 v1 pith:2LUFYSM7 submitted 2019-08-12 cs.LG cs.AIstat.ML

Zhaohong Deng , Ruixiu Liu , Te Zhang , Peng Xu , Kup-Sze Choi , Bin Qin , Shitong Wang This is my paper · ORCID
classification cs.LGcs.AIstat.ML
keywords multi-viewclusteringnon-negativematrixfactorizationsharedhiddenviewcollaborativelearningvisibleandviewsentropyweightingK-meansevaluationmetrics
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

Multi-view data describe the same objects through several feature sets, and this paper argues that clustering improves when those visible views are joined by a hidden view: a low-dimensional shared representation that all views are assumed to be generated from. The proposed algorithm, MV-Co-VH, first extracts that shared representation with non-negative matrix factorization, then runs K-means-style collaborative clustering over both the visible views and the hidden view, with a tunable parameter balancing the two sources. The paper's central claim is that visible views supply otherness information and the hidden view supplies consistency information, so using both together outperforms methods that exploit only one. Experiments on eight UCI and real-world image and text datasets report the best normalized mutual information, Rand index and precision against seven baselines, with statistical tests supporting the difference. If the claim holds, MV-Co-VH offers a simple, label-free way to make more use of multi-view data.

What carries the argument

The central object is the shared hidden view $H$, obtained by weighted non-negative matrix factorization, which approximates each visible view as $X_k \approx W_k H$ with nonnegative factors. The objective that carries the argument is Eq. (13): it sums the squared distances of samples to cluster centers in the hidden space and in each visible space, weights the visible terms by learnable view weights, combines the two sources with coefficient $\beta$, and regularizes the weights by their Shannon entropy. Alternating minimization over the partition matrix, visible centers, hidden centers, and view weights yields closed-form updates, including a softmax-like closed form for the view weights. This machinery is what lets the method exploit otherness, through different per-view centers, and consistency, through the single shared $H$, at the same time.

What would settle it

On a multi-view dataset, randomly permute the features of one view independently so that within-view cluster signal survives but cross-view consistency is destroyed; if MV-Co-VH no longer beats its own visible-only version ($\beta=0$), the reported gains come from genuine shared structure rather than from extra model capacity.

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Extended reading notes

Core claim

On its own terms, the paper establishes that the shared hidden space assumption can be turned into a working clustering objective. For each visible view $X_k$, SHD-NMF solves a minimization over mapping matrices $W_k$, the shared hidden view $H$, and view weights $q$, so that $H$ is the common hidden view. MV-Co-VH then minimizes a combined objective: the within-cluster dispersion of the hidden view plus the weighted within-cluster dispersions of the visible views, balanced by a collaboration coefficient $\beta$ and regularized by the Shannon entropy of the visible-view weights. The update rules assign each sample to the cluster with the smallest combined distance, recompute visible and hidden centers, and set each visible-view weight by a softmax-type formula in which high-dispersion views receive less weight. The paper reports that on all eight datasets this joint procedure achieves the highest mean NMI, RI and precision among the eight compared methods, that including the hidden view improves NMI on every dataset, and that Friedman and Holm tests reject performance equality with each baseline.

Load-bearing premise

The paper's entire gain depends on the assumption that all visible views are generated from one shared hidden space ($X_k \approx W_k H$), so the matrix factorization extracts meaningful common structure before clustering; if the views lack such a common low-dimensional representation, the hidden view adds noise rather than information.

Editorial extensions

If this is right

  • Because the ablation in Table XI shows NMI rising on every dataset when the hidden view is added, the paper's recipe says hidden information is not redundant with visible views and should be mined rather than ignored.
  • Because MultiNMF, which uses only hidden information, ranks lower than MV-Co-VH, the paper implies that discarding visible otherness sacrifices cluster signal.
  • Because visible-only collaborative baselines such as Co-FKM, WV-Co-FCM and MinimaxFCM also rank lower, the paper implies that consistency information is worth adding to visible cooperation.
  • Because the coefficient $\beta$ interpolates from visible-only to hidden-only, practitioners get a single dial for trading otherness against consistency; grid search found interior values that outperform both extremes on the tested datasets.
  • Because Friedman and Holm tests reject equality with each of the seven baselines at the 0.05 level, the paper implies the advantage is systematic across the dataset collection, not a single favorable benchmark.

Reading between the lines

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

  • A direct testable extension is to replace the NMF hidden view with a random low-rank projection or with per-view NMF coefficients; if the shared factorization is truly responsible, MV-Co-VH should lose its edge in that ablation.
  • The extracted hidden view $H$ could be reused beyond clustering, for example as a common feature space for cross-view retrieval or label transfer between views, uses the paper does not explore.
  • The softmax-like view weights suggest a built-in robustness mechanism, namely that views with larger within-cluster dispersion are down-weighted, which could help on datasets with one noisy view, though the paper does not test corrupted-view scenarios.
  • Because $\beta$ is chosen per dataset by grid search, an automatic selection rule, such as maximizing agreement between the visible and hidden partitions, would remove the main tuning burden and is left open by the paper.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 8 minor

Summary. The paper proposes MV-Co-VH, a multi-view clustering algorithm that first extracts a shared hidden view from the visible views via non-negative matrix factorization (the SHD-NMF procedure) and then performs collaborative K-means-style clustering on the visible views together with the hidden view. The objective function in Eq. (13) combines within-cluster dispersions of the hidden view and weighted visible views with an entropy regularizer over view weights; the authors derive alternating update rules for the partition matrix, visible-view centers, hidden-view centers, and view weights, including a Lagrange multiplier result in Theorem 1. Experiments on eight multi-view datasets compare MV-Co-VH with seven baselines using NMI, RI, and Precision, and the paper claims that MV-Co-VH achieves the best performance in all three metrics on all eight datasets, supported by Friedman and Holm tests based on NMI.

Significance. If the empirical claims were accurate, the paper would present a simple and effective way to exploit both view-specific (visible) and shared (hidden) information in multi-view clustering, with a derivation that is standard and easy to reproduce. The NMI results reported in Tables III–X are consistently favorable to MV-Co-VH, and Table XI provides direct evidence that adding hidden information improves NMI on every dataset, which is a meaningful empirical contribution. However, the flagship claim of being best in NMI, RI, and Precision on all eight datasets is contradicted by the paper's own Table X, and the statistical analysis covers only NMI. The algorithmic contribution is modest but defensible once the empirical conclusions are corrected to match the reported numbers.

major comments (3)
  1. [Section IV-B, Table X (and Abstract/Conclusion)] The statement that "the proposed MV-Co-VH algorithm shows the best performance in terms of NMI, RI and Precision on all the eight multi-view datasets" is contradicted by Table X on the Reuters dataset. In that table, MV-Co-VH achieves NMI 0.3211 (best), but RI 0.7430 is lower than both MVKSC (0.7450) and MultiNMF (0.7587), and Precision 0.2964 is lower than MultiNMF (0.3058). The central empirical claim is therefore false as written; the strongest defensible claim is that MV-Co-VH achieves the best NMI on every dataset and the best average performance, or the authors must correct the reported numbers and re-evaluate the claim.
  2. [Section IV-E, Tables XII and XIII] The Friedman test and Holm post-hoc analysis are performed only on NMI, with the justification that "the performance trends in terms of the three performance indices NMI, RI, and Precision are similar." No evidence is provided for this assertion, and no significance analysis is reported for RI or Precision. Since the paper claims superiority on all three metrics, the statistical support for the RI and Precision improvements is missing and must either be supplied or the claims limited to NMI.
  3. [Section IV-A and IV-C (parameter selection)] The regularization parameters β, η, r, and λ are tuned per dataset by grid search (Table I), and the reported means are obtained from ten runs at the best parameter configuration. This constitutes selection on the test data, and the paper does not report how sensitive the final ranking is to the choice of β or whether a single default parameter setting preserves the observed improvements. Because the conclusion that "the cooperation of visible and hidden information can enhance clustering performance" is demonstrated only at the per-dataset optimized β, the manuscript should include a sensitivity analysis or an explicit discussion of this limitation.
minor comments (8)
  1. [Section IV-B] The text states "By using these seven datasets, the performance of the proposed MV-Co-VH algorithm was evaluated," but eight datasets are used; this should read "eight datasets."
  2. [Section IV-E, Table XII] The p-value for MVKSC is reported as 0; this should be reported as a small positive value (e.g., <0.0001) to avoid implying an exactly zero probability under a continuous test statistic.
  3. [Section III-A, Algorithm SHD-NMF] The normalization step that makes each view X_k non-negative is not specified; different normalization choices will change the extracted hidden view H, and the paper should state the exact normalization used.
  4. [Section III-B, Eq. (14)] The expression for D_s in Eq. (14) is typeset in a way that makes the roles of β, (1−β), and w_k ambiguous; the formula should be written explicitly, e.g., D_s = β||h_j − ṽ_s||² + (1−β) Σ_k w_k ||x_j^k − v_s^k||², to match the description in the text.
  5. [Section II-B, Eqs. (5a)-(5b)] The NMF update rules are cited to references [24] and [25] without distinguishing which algorithm each reference supports; the authors should cite the specific Lee and Seung paper that introduces the multiplicative updates for the Frobenius norm objective.
  6. [Section IV-E] Reference [36] is cited for the Friedman test, but that reference is not the standard source for the Friedman test; the paper should cite the original Friedman paper or a modern exposition such as Demšar (2006).
  7. [Section IV-C, Convergence Analysis] The claim that convergence "is guaranteed based on the Zangwill convergence theorem" is asserted without verifying the theorem's conditions (such as compactness and continuity of the objective and update maps); either provide a proof or soften the statement to empirical convergence.
  8. [Section IV-D, Table XI] Table XI reports only NMI for the comparison with and without hidden information; since the paper claims improvements in RI and Precision as well, the table should include those metrics or state that the trend is representative.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the method's derivations are self-contained and its claims are empirically testable, even though the stated all-metrics/all-datasets result is contradicted by its own Reuters table.

full rationale

The paper's derivation chain is not circular. The shared hidden view H is obtained by minimizing Eq. (6), a weighted NMF objective over the visible views; the clustering objective Eq. (13) then treats H as an additional input and jointly optimizes the partition, visible centers, hidden centers, and view weights. H is not defined in terms of the clustering output U, and U is not fed back into the extraction of H, so no quantity is being predicted from itself by construction. The view weights w_k in Eq. (17) are derived from within-cluster dispersions D^k and the entropy regularizer, not from the final reported NMI/RI/Precision, so the empirical comparison is a genuine out-of-sample-style evaluation rather than a fitted quantity renamed as a prediction. The only self-citations are to prior baseline or notation sources (e.g., WV-Co-FCM in the comparison, and a reference for NMI definitions), and none carries the proof of the central claim. The strongest stated conclusion, that MV-Co-VH is best in NMI, RI, and Precision on all eight datasets, is internally contradicted by Table X on Reuters, where MultiNMF has higher RI and Precision; however, this is a factual/correctness defect in the reported experiments, not a circularity in the derivation. The statistical analysis is explicitly NMI-only, so it does not repair the overbroad claim, but it also does not make the method circular. No step reduces an output to an input by equation identity, fitted-parameter renaming, or a load-bearing self-citation chain, so the appropriate circularity score is 0.

Assumptions & free parameters 4 free parameters · 4 assumptions · 1 invented entities

The central claim rests on a shared latent representation extracted by NMF, standard K-means assumptions, and several hyperparameters selected per dataset. No code or external certificates are provided, so all axioms are assumed rather than independently verified.

free parameters (4)
  • beta = grid-searched per dataset in [0,1], step 0.1
    Controls balance between hidden-view and visible-view terms in Eq. (13); selected by grid search, not a priori.
  • eta = grid-searched over {2^-6, ..., 2^6}
    Controls strength of Shannon entropy weight term; an optimization hyperparameter.
  • r = grid-searched over [0.1d, 0.2d, ..., 1d] or [1,d] if d <= 10
    Rank of the NMF factorization for the shared hidden view; chosen per dataset.
  • lambda = unspecified
    Appears in Eq. (6) as the regularization coefficient for SHD-NMF, but is not listed in Table I parameter settings; experiments depend on an unstated choice.
assumptions (4)
  • domain assumption There exists a shared hidden space H from which all visible views can be generated as X_k approximately W_k H.
    Section III-A states this as a reasonable assumption; if false, the NMF-extracted hidden view does not represent true consistency and can hurt clustering.
  • standard math NMF multiplicative updates from Lee and Seung converge to a useful local solution for each subproblem.
    Updates (8) and (10) are adopted from [25]; the paper does not analyze initialization sensitivity or global optimality, and NMF is non-convex.
  • domain assumption The alternating optimization satisfies the conditions of the Zangwill convergence theorem.
    Section IV-C2 asserts convergence is guaranteed by the Zangwill theorem without verifying the point-to-set map conditions; this is invoked but not demonstrated.
  • domain assumption Euclidean distance in normalized visible and hidden spaces is a suitable similarity measure for clustering.
    The objective (13) uses K-means distances after normalization; no evidence is given that this distance is appropriate for all eight datasets.
invented entities (1)
  • Shared hidden view H
    purpose: Latent common representation of all visible views, used together with original views in the clustering objective.
    Postulated in Section III-A and Eq. (6). It has no falsifiable handle outside the paper's own benchmarks; it is a standard latent variable, not a confirmed physical or data-generating entity.

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Cite this review

Pith. "Pith review of Multi-view Clustering with the Cooperation of Visible and Hidden Views." pith.science (2026). https://pith.science/paper/2LUFYSM7

@misc{pith2026190804766,
  author       = {Pith},
  title        = {Pith review of: Multi-view Clustering with the Cooperation of Visible and Hidden Views},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2LUFYSM7}},
  note         = {Machine review of arXiv:1908.04766}
}
read the original abstract

Multi-view data are becoming common in real-world modeling tasks and many multi-view data clustering algorithms have thus been proposed. The existing algorithms usually focus on the cooperation of different views in the original space but neglect the influence of the hidden information among these different visible views, or they only consider the hidden information between the views. The algorithms are therefore not efficient since the available information is not fully excavated, particularly the otherness information in different views and the consistency information between them. In practice, the otherness and consistency information in multi-view data are both very useful for effective clustering analyses. In this study, a Multi-View clustering algorithm developed with the Cooperation of Visible and Hidden views, i.e., MV-Co-VH, is proposed. The MV-Co-VH algorithm first projects the multiple views from different visible spaces to the common hidden space by using the non-negative matrix factorization (NMF) strategy to obtain the common hidden view data. Collaborative learning is then implemented in the clustering procedure based on the visible views and the shared hidden view. The results of extensive experiments on UCI multi-view datasets and real-world image multi-view datasets show that the clustering performance of the proposed algorithm is competitive with or even better than that of the existing algorithms.

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Reference graph

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