{"id":"738162a8-e48f-4537-a6cb-b6f5a915d9a7","arxiv_id":"2412.17647","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"CE-MVC combines NMI-based and conditional-entropy-based view weighting with per-view autoencoders, and reports top clustering accuracy on DIGIT, COIL, RGB-D, and Caltech.","lead":"CE-MVC is a multi-view clustering framework that weights each view using normalized mutual information and a conditional entropy score, then trains a separate autoencoder per view. The authors report large accuracy gains over ten baselines on four image datasets, including synthetic noisy-view versions, but the central entropy formula is mathematically questionable.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (4) does not compute conditional entropy for V>2; without a stated independence condition or proof, the load-bearing weighting rationale in Eq. (5) is unsupported.","rationale":"The reader's weakest assumption correctly identifies Eq. (4) as the central load-bearing step. The paper claims that conditional entropy quantifies complementary information and uses it to weight views, but for V>2 the pairwise sum is not the conditional entropy. This is not a minor typo: the entire weighting formula Eq. (5) and the ablation study comparing 'CE' vs. 'NMI' depend on this quantity having the claimed monotone behavior. I agree with the reader's assessment that this is a high-correctness-risk issue. I also note additional problems that reinforce the same verdict without changing it: the normalization in Eq. (5) is undefined, no code or hyperparameters are provided, and no error bars are reported. However, the single most load-bearing concern remains the invalidity of Eq. (4) as a conditional entropy. The proposed test — a small three-view example with known ground-truth distributions — would settle whether the monotonicity claim holds; if it fails, the theoretical foundation of the method collapses, regardless of reported empirical performance. Since the reader already rejected the paper, my independent analysis leaves the verdict unchanged.","tokens_in":9782,"tokens_out":2133,"duration_ms":33858,"concrete_test":"Construct a three-view synthetic dataset with known generative distributions, e.g., cluster label Y ~ Bernoulli(0.5); view 1: R1 = Y + noise; view 2: R2 = Y + independent noise; view 3: R3 = Y XOR independent Bernoulli(0.1) (or a continuous analog). Compute exactly (or by Monte Carlo with very large samples) the true conditional entropy H(Rv | R_u, R_w) for each view and compare it with the pairwise sum in Eq. (4). If the ranking of views by Eq. (4) differs from the ranking by the true conditional entropy, or if the monotonic claim 'noisy view has highest score' fails on this example, then the theoretical rationale for Eq. (5) is refuted. Also compute the actual weights w_v from Eq. (5) with any reasonable normalization to check whether the undefined 'N orm' changes the relative ordering.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central novelty is the claim that Eq. (4) quantifies the complementary information of view v via conditional entropy, and Eq. (5) uses that quantity to amplify views with low conditional entropy. But Eq. (4) sums pairwise differences E(Rv,Ru)-E(Ru), which equals H(Rv|Ru) for each other view u. For V>2, this sum is generally not the true conditional entropy H(Rv | {Ru}_{u≠v}); the latter is H(Rv, {Ru}_{u≠v}) - H({Ru}_{u≠v}). In fact, by the chain rule, sum_{u≠v} H(Rv|Ru) ≥ H(Rv | {Ru}_{u≠v}), with equality only under a conditional-independence condition that the paper never states or proves. The paper also asserts that 'if the current view contains complementary information ... its conditional entropy will be relatively low' and that a noisy view 'will be the highest,' but this monotonic ordering is not established for the pairwise sum. Redundancy among the other views can inflate or deflate the sum relative to the true conditional entropy, so a view that is truly complementary can receive a higher score than a noisy view. Moreover, Eq. (5) uses 'N orm(repräsentation)' with no definition of normalization; the exponential-NMI numerator is also not derived. These are not mere presentational gaps: if Eq. (4) is not a valid conditional entropy or a monotone complementarity measure, the adaptive weighting mechanism does not do what the paper claims, even if the empirical numbers are reproducible. The parameter-decoupled architecture and the experimental results may stand on their own, but the stated theoretical foundation of CE-MVC is the load-bearing part being challenged.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes CE-MVC, a deep multi-view clustering framework with two main components: (i) an adaptive view-weighting scheme that uses a quantity labeled 'conditional entropy' in Eq. (4) together with an NMI-based term in Eq. (5), and (ii) a parameter-decoupled autoencoder model in which each view has its own encoder, decoder, and clustering head to mitigate the Noisy-View Drawback. Experiments on six datasets (DIGIT, COIL, their noisy versions, RGB-D, and Caltech) report that CE-MVC outperforms ten prior methods, with a small ablation study on weighting strategies.","tokens_in":10116,"tokens_out":5787,"duration_ms":52375,"significance":"If the proposed weighting mechanism were theoretically sound and the empirical results reproducible, CE-MVC would offer a useful step toward robustness against noisy views in deep multi-view clustering, particularly through its parameter-decoupled architecture. The idea of complementing NMI-based consistency weighting with a separate measure of complementarity is reasonable, and the reported gains over strong baselines such as MVCAN on noisy datasets are substantial. However, the paper's central theoretical contribution is not supported as written: the quantity in Eq. (4) is not conditional entropy for V>2, no convergence or monotonicity analysis is given for the weighting iteration, and the experimental protocol lacks key details. The significance is therefore presently limited by these gaps, though the empirical direction may be salvageable with major revision.","major_comments":[{"comment":"Equation (4) defines E(Rv_t | {Ru_t}_{u≠v}) as the sum over u≠v of [E(Rv_t, Ru_t) − E(Ru_t)], which equals the sum of pairwise conditional entropies Σ_{u≠v} H(Rv_t | Ru_t). This is not equal to the true conditional entropy H(Rv_t | {Ru_t}_{u≠v}) unless a conditional-independence condition holds that is never stated. In general, Σ_{u≠v} H(Rv|Ru) ≥ H(Rv|{Ru}_{u≠v}), with equality only when Rv is conditionally independent of each Ru given the other views. The paper also claims, without proof, that a complementary view has relatively low conditional entropy and a noisy view has the highest; no monotonicity or ordering property is established for the pairwise sum. Because this quantity is the denominator in the weighting formula Eq. (5), the central weighting rationale is unsupported as written.","section":"§II-C, Eq. (4)"},{"comment":"Equation (5) contains an undefined normalization operator 'N orm' and an unexplained exponential-NMI numerator. The notation 'N orm(E(Rv_t | {Ru_t}_{u≠v}))' is never defined, making the formula non-reproducible. Moreover, the choice of exp(2M(SLv;SL(t))/(E(SLv)+E(SL(t)))) − 1 is simply a monotone transformation of NMI; no derivation or justification is given for why this specific form should balance consistency and complementarity. Without a precise definition of the normalization, the weights cannot be computed by a reader.","section":"§II-C, Eq. (5)"},{"comment":"The iterative weighting procedure is described as 'asymptotic' but no convergence analysis is provided. There is no theorem, no stopping criterion beyond a generic iteration count, and no discussion of whether the fixed-point iteration W(t+1) = K(...) can oscillate or fail to converge. In addition, Eq. (2) writes R(0) = O(W(0) | R(t), R1, ..., RV), but R(t) does not exist at t=0; this appears to be a typo that obscures the initialization step. The load-bearing claim that the algorithm learns a reliable target T while keeping model parameters fixed needs formal support.","section":"§II-C, 'Asymptotic adaptive weighting'"},{"comment":"There is a self-referential loop in the training procedure: the weights W(t+1) are computed from the same latent representations Rv and soft labels SLv that are produced by the model being trained, and those weights are then used to construct the weighted representation R(t) that generates the clustering target T(t), which in turn supervises the clustering loss in Eq. (6). Since the score and objective co-evolve, the weighting mechanism may simply reflect the model's own current state rather than a meaningful measure of view informativeness. The ablation in Table III compares weighting variants but does not test this circularity, e.g., by using a target derived from an independent source or by freezing the target.","section":"§II-C, §II-D"},{"comment":"The experimental reporting is incomplete. No dataset statistics (number of samples, dimensions, number of views, cluster count) are given; the construction of the noisy views is described only as 'randomly sampled noise' without details. Hyperparameters (λ in Eq. (8), KDE bandwidth, learning rate, optimizer, batch size, number of iterations) are not reported, and no standard deviations or significance tests over repeated runs are provided. No code is released. These omissions prevent verification of the claimed state-of-the-art results and are particularly important because the reported improvements over MVCAN are sometimes small (e.g., 49.6 vs 48.0 ACC on RGB-D).","section":"§III-A and §III-B"}],"minor_comments":[{"comment":"Equation (1) defines a common clustering objective but the notation FΘ(SLv | {Rv}_{v=1}^V) is confusing: the soft labels SLv are the output of F, not an input. The equation should be rewritten to show how the shared-parameter fusion takes representations as input and computes labels.","section":"§II-B, Eq. (1)"},{"comment":"The operator O is not defined; it is unclear whether it represents concatenation, a weighted sum, or another aggregation. Also, as noted, the appearance of R(t) in the definition of R(0) is a typo.","section":"§II-C, Eq. (2)"},{"comment":"The ablation table compares only NMI, ENMI, and ENMI+CE. There is no condition with NMI+CE alone, so the individual contribution of the conditional-entropy term relative to the exponential transform is not isolated. Also, the table header does not clearly indicate which metric is used in each row.","section":"§III-C, Table III"},{"comment":"There are many typographical errors, e.g., 'N orm(repräsentation)' in Eq. (5), 'can’t' in place of 'cannot', and inconsistent use of λ vs. lambda. The paper should be carefully proofread.","section":"Throughout"},{"comment":"Several references in the text, such as [26] for Noisy-View Drawback, are cited in a way that does not clearly connect to the definition. The reference list also contains a mixed style and a few entries with missing page numbers (e.g., [12], [13]).","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper's central idea is interesting and the empirical results are suggestive, but the theoretical flaw in Eq. (4) is not a mere wording issue—it is the mechanism that the entire weighting scheme rests on. The authors could plausibly repair this by redefining the quantity in Eq. (4) as a heuristic 'multi-view complementarity score' rather than conditional entropy, and by providing a convergence analysis or at least a more careful iterative scheme. However, given the lack of experimental details and the self-referential nature of the weighting, I would want to see a substantially revised manuscript before considering publication. The novelty relative to existing weighting-based MVC methods may also need clearer positioning."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper combines a parameter-decoupled autoencoder architecture with an adaptive weighting scheme that mixes NMI and an entropy-based complementarity score, and it reports solid gains over MVCAN on standard benchmarks. The ablation shows both weighting terms help. That part is real and worth pursuing.\n\nThe soft spot is large and it sits at the center. Equation (4) claims to compute the conditional entropy of view v given all other views by summing pairwise terms H(Rv,Ru)-H(Ru). For three or more views, that sum is not the true conditional entropy H(Rv | {Ru}_{u≠v}) unless you add an independence assumption you don't state or prove. The chain rule gives sum_{u≠v} H(Rv|Ru) ≥ H(Rv | R_{-v}), so the score can rank a noisy view above a complementary one. The paper also asserts without proof that complementary views have low conditional entropy and noisy views have high conditional entropy. That monotonicity is exactly what the weighting formula (5) depends on, and it isn't established for the pairwise sum. On top of that, Eq (5) contains an undefined 'N orm(...)' term, and the denominator normalization is never specified. There is no convergence analysis for the iterative weighting, no error bars, and no code or hyperparameters. So the experimental numbers are unverifiable, and the method's stated foundation is not sound.\n\nWhat's salvageable: the idea of training each view with separate parameters to avoid the noisy-view drawback is sensible, and the NMI/entropy pairing is a reasonable heuristic even if the entropy part is mislabeled. A corrected version with a proper definition of the complementarity score, a proof of the monotonicity claim (or a replacement metric), and a reproducible release could be a decent incremental contribution.\n\nI would not send this out as is. The central derivation is wrong and the missing details preclude checking the results. I'd suggest a reject, but with an encouragement to resubmit after fixing the math and releasing code. This is a paper for readers in deep MVC who care about robust fusion; for them the ideas are relevant, but the current form doesn't support the claims.","headline":"Promising empirical combination, but Eq (4) mislabels a pairwise sum as conditional entropy; the paper needs a corrected metric and a reproducible release before it merits serious review.","tokens_in":10661,"tokens_out":3444,"would_cite":false,"duration_ms":31149,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims CE-MVC, a multi-view clustering framework, outperforms ten existing methods by weighting views with a conditional-entropy score and keeping each view's parameters separate.","keywords":["multi-view clustering","conditional entropy","normalized mutual information","adaptive weighting","noisy-view drawback","parameter-decoupled deep model","deep autoencoder","clustering robustness"],"falsifier":"A synthetic experiment with three or more views whose dependencies are controlled: choose two informative views that share private information and a third noisy view, compute Eq. (4) for each, and compare the resulting CE-MVC weights and clustering accuracy with known ground-truth informativeness. If a view with high true conditional entropy receives a low score and a low weight, or a genuinely informative view receives a high score, the claim that Eq. (4) quantifies complementarity is refuted. A simpler check is to replace Eq. (4) with the true conditional entropy and see whether CE-MVC's reported margins disappear.","tokens_in":9559,"feed_emoji":"🧩","tokens_out":5998,"duration_ms":51286,"temperature":0.7,"pith_summary":"CE-MVC claims that the failure of multi-view clustering in the presence of noisy views can be repaired by treating view quality as a measurable quantity and by keeping each view's network parameters separate. The framework assigns each view a weight from a formula that combines normalized mutual information between the view's soft labels and the unified target with a conditional-entropy score of the view's representation given all other views. Views whose representations carry complementary information receive low conditional entropy and therefore high weight, while noisy views are down-weighted. The paper reports that this scheme beats ten existing clustering methods on DIGIT, COIL, RGB-D, and Caltech, with its largest margins on noise-contaminated versions, and its ablation attributes the gain to adding the conditional-entropy term to exponential NMI weighting.","feed_headline":"Entropy-weighted views beat noisy multi-view clustering baselines","feed_subtitle":"A new weight formula rewards views that carry complementary information and trains each view alone, limiting noise damage.","key_machinery":"The load-bearing object is the weight formula in Eq. (5) together with the conditional-entropy estimate in Eq. (4). Eq. (4) defines the conditional entropy of view $v$ as $\\sum_{u\\neq v} [E(R^v_t, R^u_t) - E(R^u_t)]$; it is the mechanism that is supposed to quantify complementary information. Eq. (5) turns that score into a weight by dividing an exponential NMI consistency term by the normalized conditional entropy, and the parameter-decoupled autoencoders with reconstruction loss $L^v_r$ and clustering loss $L^v_c$ are the machinery that keeps noisy views from corrupting shared parameters.","core_discovery":"At the heart of the paper is Eq. (5), which sets the weight of view $v$ to $$w^v_{(t+1)} = \\frac{\\exp\\!\\left(\\frac{2M(SL^v; SL_{(t)})}{E(SL^v)+E(SL_{(t)})}\\right) - 1}{\\mathrm{Norm}\\!\\left(E(R^v_t \\mid \\{R^u_t\\}_{u\\neq v})\\right)},$$ where $M$ is mutual information, $E$ is entropy, and the conditional entropy in the denominator is computed by Eq. (4) as the sum over other views $u$ of $E(R^v_t, R^u_t) - E(R^u_t)$. The author's claim is that this ratio simultaneously captures consistency (the NMI-like numerator) and complementarity (the conditional-entropy denominator): a view with information that other views lack has low conditional entropy and is up-weighted, while a mostly redundant or noisy view has high conditional entropy and is down-weighted. Around this weighting rule, CE-MVC trains one autoencoder per view with disjoint parameters, so that clustering and reconstruction losses for each view cannot interfere, and uses the weighted representation to produce the unified soft-label target $T$. The stated result is that this two-part design outperforms the compared methods and is particularly robust to the Noisy-View Drawback.","pith_inferences":["A testable consequence the paper does not state: Eq. (4) equals the true conditional entropy $H(R^v \\mid \\{R^u\\}_{u\\neq v})$ only if an independence condition holds across views, and for $V>2$ one can construct pairwise dependencies that make the sum a poor proxy; a Monte Carlo check with controlled dependencies would settle whether the empirical gains survive.","The same conditional-entropy weighting could be applied outside clustering, for example to feature fusion in classification or retrieval whenever per-modality representations are learned with separate encoders.","Because the weighting is iterative, it may generalize to streaming multi-view data where the set of views changes over time, though the paper does not test this.","If the robustness claim holds, the Noisy-View Drawback could be diagnosed in future work by inspecting the conditional-entropy term directly rather than only through final ACC and NMI values."],"forward_implications":["CE-MVC is claimed to be the best-performing method on the four tested datasets, with ACC and NMI above 99 percent on COIL and NoisyCOIL.","On NoisyDIGIT, CE-MVC improves ACC by 18.8 points and NMI by 20.2 over the best compared method.","The ablation study shows that combining exponential NMI with conditional entropy raises ACC on RGB-D from 47.6 to 49.6 and NMI from 40.8 to 42.6, and raises Caltech ACC from 92.5 to 93.8 and NMI from 86.6 to 89.1.","The parameter-decoupled design means each view's encoder, decoder, and clustering head are trained independently, so noisy views cannot overfit shared parameters.","The weight formula can up-weight a view with low NMI when its conditional entropy is low, addressing the failure mode the paper attributes to NMI-only weighting."],"supporting_citations":[{"why":"Supplies the DEC baseline whose BestV and WorstV results frame the Noisy-View Drawback.","marker":"[40]"},{"why":"Closest robust competitor targeting noisy-view side effects; CE-MVC is compared against it on all datasets.","marker":"[43]"},{"why":"Deep safe incomplete multi-view clustering with contrastive learning; a key baseline on noisy datasets.","marker":"[11]"},{"why":"Deep safe multi-view clustering that reduces degradation from adding views; provides context for weighting strategies.","marker":"[10]"},{"why":"Self-supervised discriminative deep MVC baseline used in the comparison tables.","marker":"[39]"},{"why":"Generative partial MVC with adaptive fusion and cycle consistency; baseline for the weighting and fusion design.","marker":"[36]"},{"why":"Deep incomplete MVC via cluster complementarity; supplies the notion of complementarity the paper builds on.","marker":"[42]"}],"fun_headline_variants":["CE-MVC: conditional entropy weights views against noise","Entropy-based weighting boosts multi-view clustering under noise","Adaptive entropy weights reward complementary views in clustering","CE-MVC rewards complementary views, punishes noisy ones","CE-MVC: adaptive entropy weights tame noisy multi-view clustering"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The weighting scheme assumes that summing pairwise conditional entropies over the other views, as in Eq. (4), faithfully measures how much complementary information a view contributes; for more than two views this is not the true conditional entropy unless an unstated independence condition holds.","fun_headline_variants_meta":{"raw":{"variants":["CE-MVC: conditional entropy weights views against noise","Entropy-based weighting boosts multi-view clustering under noise","Adaptive entropy weights reward complementary views in clustering","CE-MVC rewards complementary views, punishes noisy ones","CE-MVC: adaptive entropy weights tame noisy multi-view clustering"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000731,"raw_usage":{"total_tokens":3292,"prompt_tokens":983,"completion_tokens":2309,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":599,"completion_tokens_details":{"reasoning_tokens":2231}},"tokens_in":599,"tokens_out":2309,"duration_ms":17109,"temperature":1.0,"reasoning_tokens":2231,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T05:18:30.528038+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A synthetic experiment with three or more views whose dependencies are controlled: choose two informative views that share private information and a third noisy view, compute Eq. (4) for each, and compare the resulting CE-MVC weights and clustering accuracy with known ground-truth informativeness. If a view with high true conditional entropy receives a low score and a low weight, or a genuinely informative view receives a high score, the claim that Eq. (4) quantifies complementarity is refuted. A simpler check is to replace Eq. (4) with the true conditional entropy and see whether CE-MVC's reported margins disappear.","supporting_citations":[{"cited_title":"Girshick, and Ali Farhadi","cited_arxiv_id":null,"evidence_quote":"Supplies the DEC baseline whose BestV and WorstV results frame the Noisy-View Drawback."},{"cited_title":"Investigating and mitigating the side effects of noisy views for self-supervised clustering algorithms in practical multi-view scenarios","cited_arxiv_id":null,"evidence_quote":"Closest robust competitor targeting noisy-view side effects; CE-MVC is compared against it on all datasets."},{"cited_title":"Deep safe incomplete multi-view clustering: Theorem and algorithm","cited_arxiv_id":null,"evidence_quote":"Deep safe incomplete multi-view clustering with contrastive learning; a key baseline on noisy datasets."},{"cited_title":"Deep safe multi-view clustering: Reducing the risk of clustering performance degradation caused by view increase","cited_arxiv_id":null,"evidence_quote":"Deep safe multi-view clustering that reduces degradation from adding views; provides context for weighting strategies."},{"cited_title":"Yu, and Lifang He","cited_arxiv_id":null,"evidence_quote":"Self-supervised discriminative deep MVC baseline used in the comparison tables."},{"cited_title":"Generative partial multi-view clustering with adaptive fusion and cycle consistency","cited_arxiv_id":null,"evidence_quote":"Generative partial MVC with adaptive fusion and cycle consistency; baseline for the weighting and fusion design."},{"cited_title":"Deep incomplete multi-view clustering via mining cluster complementarity","cited_arxiv_id":null,"evidence_quote":"Deep incomplete MVC via cluster complementarity; supplies the notion of complementarity the paper builds on."}],"review_version":1}