{"id":"edaaae85-7dad-4537-9568-eb8212f36903","arxiv_id":"1908.04766","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"MV-Co-VH clusters multi-view data by jointly using original views and an NMF-derived shared hidden view, and it achieves higher NMI than seven baselines on eight two-view benchmark datasets.","lead":"This paper introduces MV-Co-VH, a multi-view clustering algorithm that combines information from the original data views with a shared hidden view extracted by non-negative matrix factorization. It reports better clustering accuracy than seven baselines on eight multi-view datasets, although one of its broadest claims is contradicted by its own tables.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Reuters results contradict the claim of best NMI, RI and Precision on all eight datasets; MultiNMF (and MVKSC for RI) beat MV-Co-VH in Table X.","rationale":"The reader's verdict is CONDITIONAL with moderate confidence, and their rationale explicitly notes that 'Reuters RI and Precision contradict the all-metrics claim.' However, the reader's formal weakest_assumption focuses on the shared hidden-space assumption in Eq. (6) and the two-stage extraction of H. In my reading, the most load-bearing concern is the internal contradiction between the headline empirical claim and the paper's own Table X. A false or overbroad central claim directly undermines the paper's main message, even if the underlying algorithm could be valuable after the claim is corrected. The hidden-space assumption is important, but the reported experiments provide some empirical support for it (Tables V-XI generally show improvement with hidden information), whereas the Reuters results provide direct counterevidence to the strongest claim. Since the reader already assigned CONDITIONAL and flagged the Reuters issue in the rationale, my read does not change the verdict; it sharpens the reason. The concrete test I propose is the natural one: verify Table X's rankings and, if necessary, rerun the Reuters experiment to distinguish a typo from a genuine counterexample. No ad hominem is intended; the issue is with the precision of the empirical claim in the paper, not with the authors' integrity.","tokens_in":17541,"tokens_out":7938,"duration_ms":82394,"concrete_test":"Recompute per-dataset, per-metric rankings from Tables III-X. If the Reuters RI and Precision values remain as printed, the claim of 'best on all eight datasets in NMI, RI and Precision' is false. To further test whether this is a data-entry error, obtain the authors' implementation (or rerun the Reuters experiment with the grid-searched parameters reported in Section IV) and compare RI and Precision against MultiNMF and MVKSC; if MultiNMF or MVKSC still ranks higher, the paper must be revised to claim best NMI on all datasets and best overall average, not best RI and Precision on all eight.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's strongest claim, stated in Section IV-B and echoed in the abstract and conclusion, is that MV-Co-VH shows the best performance in terms of NMI, RI and Precision on all eight multi-view datasets. This claim is internally contradicted by Table X (Reuters). In Table X, MV-Co-VH achieves NMI 0.3211 (best), but RI 0.7430, lower than MVKSC (0.7450) and MultiNMF (0.7587), and Precision 0.2964, lower than MultiNMF (0.3058). Thus MV-Co-VH is not the best on RI or Precision on that dataset. The Friedman and Holm analyses in Section IV-E are computed using NMI only (\"the statistical analysis is presented only with NMI as an example\"), so they do not support the all-metrics claim. If the all-metrics-all-datasets statement is the central empirical contribution, it is false as written; the strongest defensible version is that MV-Co-VH has the best average rank and the best NMI on every dataset. Because the authors provide no code or raw results, it is impossible to verify whether the Reuters table is a typo or the true outcome; as printed, the paper overstates its results in a directly falsifiable way.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":17804,"tokens_out":4681,"duration_ms":50172,"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":[{"comment":"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.","section":"Section IV-B, Table X (and Abstract/Conclusion)"},{"comment":"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.","section":"Section IV-E, Tables XII and XIII"},{"comment":"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.","section":"Section IV-A and IV-C (parameter selection)"}],"minor_comments":[{"comment":"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.\"","section":"Section IV-B"},{"comment":"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.","section":"Section IV-E, Table XII"},{"comment":"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.","section":"Section III-A, Algorithm SHD-NMF"},{"comment":"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.","section":"Section III-B, Eq. (14)"},{"comment":"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.","section":"Section II-B, Eqs. (5a)-(5b)"},{"comment":"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).","section":"Section IV-E"},{"comment":"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.","section":"Section IV-C, Convergence Analysis"},{"comment":"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.","section":"Section IV-D, Table XI"}],"recommendation":"major_revision","confidential_remarks":"The paper's algorithmic derivation is sound and the NMI results are consistently strong, but the overstatement in Section IV-B is a serious issue that must be fixed before publication. The authors should either correct the table(s), revise the claim to reflect the actual results, and add statistical analysis for RI and Precision, or weaken the conclusions accordingly. The contribution is within the scope of the journal, and with a careful revision of the empirical claims and a sensitivity analysis, the paper could become acceptable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: the method is a reasonable incremental contribution, and the paper's strongest claim is overstated. The idea is to extract a shared hidden view from multi-view data via NMF, then cluster on visible views plus that hidden view with entropy-weighted view weights. Eq. (13) is genuinely new relative to the cited MultiNMF and Co-FKM. The derivations are standard block-coordinate updates, and the convergence argument via Zangwill is plausible. The ablation in Table XI, showing that adding the hidden view improves NMI on all eight datasets, is the cleanest evidence for the central claim and I take it seriously.\n\nThe soft spot is in the empirical headline. Section IV-B claims MV-Co-VH is best in NMI, RI and Precision on all eight datasets, but Table X contradicts that on Reuters: MultiNMF has higher RI (0.7587 vs 0.7430) and higher Precision (0.3058 vs 0.2964), and MVKSC also edges it on RI. The Friedman and Holm analyses are only run on NMI, so they don't rescue the all-metrics statement. The strongest defensible version is that MV-Co-VH has the best average rank and the best NMI on every dataset. That is still a decent result, but the paper should say it.\n\nTwo smaller issues: lambda is left unspecified in the SHD-NMF step, and beta is tuned per dataset by grid search. The tuning is acknowledged as an open problem, but it means part of the gain is selected post hoc; not fatal, but worth stating. No code or data is released, which makes the Reuters table impossible to verify as typo versus true outcome.\n\nCitation pattern looks fine; the self-citations are to the authors' prior fuzzy-clustering line and are relevant. Overall, this is a serious paper that deserves peer review rather than a desk reject. The math is sound, the ablation is useful, and the overclaim is fixable with a corrected table and a more careful conclusion. I'd want a revised version with code, but I'd engage with it.","headline":"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.","tokens_in":18345,"tokens_out":2080,"would_cite":false,"duration_ms":18459,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["multi-view clustering","non-negative matrix factorization","shared hidden view","collaborative learning","visible and hidden views","entropy weighting","K-means","clustering evaluation metrics"],"falsifier":"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.","tokens_in":17356,"feed_emoji":"🧩","tokens_out":8442,"duration_ms":87384,"temperature":0.7,"pith_summary":"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.","feed_headline":"Mining shared hidden views wins on all eight multi-view datasets","feed_subtitle":"MV-Co-VH clusters visible and hidden views together, outperforming the seven baselines that use only one kind of information.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"K-means; the base partition-and-centers framework that MV-Co-VH extends to visible and hidden views.","marker":"[1]"},{"why":"Entropy weighting k-means; source of the Shannon-entropy view-weight regularization used in the objective.","marker":"[2]"},{"why":"FCM; a single-view baseline constructed by concatenating features, one of the seven comparators.","marker":"[4]"},{"why":"Co-FKM; collaborative fuzzy clustering baseline that uses only visible views.","marker":"[16]"},{"why":"WV-Co-FCM; weighted collaborative fuzzy clustering baseline that uses only visible views.","marker":"[17]"},{"why":"MinimaxFCM; minimax fuzzy clustering baseline against which MV-Co-VH is compared.","marker":"[18]"},{"why":"MultiNMF; joint NMF multi-view clustering baseline that uses only shared hidden information.","marker":"[21]"},{"why":"NMF multiplicative update rules; the mechanism used by SHD-NMF to extract the shared hidden view H.","marker":"[25]"}],"fun_headline_variants":["Hidden views boost clustering on every dataset tested","MV-Co-VH merges visible and hidden views outranking 7 baselines","Shared hidden view unlocks consistent wins in multi-view clustering","All eight datasets: hidden plus visible beats visible-only","Cooperation of visible and hidden views wins eight benchmarks"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Hidden views boost clustering on every dataset tested","MV-Co-VH merges visible and hidden views outranking 7 baselines","Shared hidden view unlocks consistent wins in multi-view clustering","All eight datasets: hidden plus visible beats visible-only","Cooperation of visible and hidden views wins eight benchmarks"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000799,"raw_usage":{"total_tokens":3529,"prompt_tokens":978,"completion_tokens":2551,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":594,"completion_tokens_details":{"reasoning_tokens":2471}},"tokens_in":594,"tokens_out":2551,"duration_ms":19748,"temperature":1.0,"reasoning_tokens":2471,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T13:48:43.803523+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"K-means; the base partition-and-centers framework that MV-Co-VH extends to visible and hidden views."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Entropy weighting k-means; source of the Shannon-entropy view-weight regularization used in the objective."},{"cited_title":"The global partition matrix is then obtained by simple integration, such as weighting","cited_arxiv_id":null,"evidence_quote":"FCM; a single-view baseline constructed by concatenating features, one of the seven comparators."},{"cited_title":"Spectral learning,","cited_arxiv_id":null,"evidence_quote":"Co-FKM; collaborative fuzzy clustering baseline that uses only visible views."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"WV-Co-FCM; weighted collaborative fuzzy clustering baseline that uses only visible views."},{"cited_title":"On spectral clustering: Analysis and an algorithm,","cited_arxiv_id":null,"evidence_quote":"MinimaxFCM; minimax fuzzy clustering baseline against which MV-Co-VH is compared."},{"cited_title":"Multi-view k -means clustering on big data ,","cited_arxiv_id":null,"evidence_quote":"MultiNMF; joint NMF multi-view clustering baseline that uses only shared hidden information."},{"cited_title":"Multi-view fuzzy clustering with minimax optimization for effective clustering of data from multiple sources,","cited_arxiv_id":null,"evidence_quote":"NMF multiplicative update rules; the mechanism used by SHD-NMF to extract the shared hidden view H."}],"review_version":1}