REVIEW 5 major objections 5 minor 43 references
An Adaptive Framework for Multi-View Clustering Leveraging Conditional Entropy Optimization
T0 review · 5 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash
Pith's one-line read 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.
desk verdict 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. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
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.
What would settle it
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.
Extended reading notes
Core claim
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.
Load-bearing premise
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.
Editorial extensions
If this is right
- 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.
Reading between the lines
- 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.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
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.
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 (5)
- [§II-C, Eq. (4)] 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.
- [§II-C, Eq. (5)] 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.
- [§II-C, 'Asymptotic adaptive weighting'] 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.
- [§II-C, §II-D] 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.
- [§III-A and §III-B] 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).
minor comments (5)
- [§II-B, Eq. (1)] 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.
- [§II-C, Eq. (2)] 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.
- [§III-C, Table III] 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.
- [Throughout] 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.
- [References] 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]).
Circularity Check
No significant circularity: the adaptive weighting is a heuristic self-training loop, but the empirical evaluation is anchored to external ground-truth labels and no claim reduces to its inputs by construction.
full rationale
The paper's derivation chain contains no step in which a predicted quantity is equivalent to an input by definition or by a fitted parameter. Equation (4) labels a sum of pairwise conditional entropies as the conditional entropy of a view, and for V>2 this label is mathematically inaccurate unless an unstated conditional-independence condition holds; however, this is a correctness or assumption gap, not a circularity. The weighting rule in Eq. (5) is a heuristic schedule: it uses the model's own representations and soft labels, and those weights then reshape the representations used in the next iteration. That is an iterative self-training loop, but it is not a logical reduction of the output to the input by construction, and the final performance claim is validated against external ground-truth labels on DIGIT, COIL, RGB-D, and Caltech, so the empirical comparison is independently grounded. The self-citations in the reference list are contextual background items and are not load-bearing for the adaptive weighting or the parameter-decoupled architecture. No uniqueness theorem is imported from the authors' prior work, no ansatz is smuggled in by citation, and no known result is simply renamed as a new contribution. Therefore, while the theoretical justification of Eq. (4) deserves scrutiny as a validity concern, there is no circular step under the defined criteria.
Assumptions & free parameters
free parameters (5)
- lambda (Eq 8)
- KDE bandwidth
- number of iterations
- autoencoder architecture
- learning rate and optimizer
assumptions (4)
- ad hoc to paper Eq (4) sum of pairwise entropy differences equals conditional entropy of a view given all other views.
- domain assumption Low conditional entropy implies high complementarity and high conditional entropy implies a noisy view.
- domain assumption KDE-based entropy estimates in Eq (3) are reliable for the high-dimensional latent representations used.
- domain assumption Parameter-decoupled per-view training prevents the noisy-view drawback without a shared fusion module.
Cite this review
Pith. "Pith review of An Adaptive Framework for Multi-View Clustering Leveraging Conditional Entropy Optimization." pith.science (2026). https://pith.science/paper/D5X7AJSH
@misc{pith2026241217647,
author = {Pith},
title = {Pith review of: An Adaptive Framework for Multi-View Clustering Leveraging Conditional Entropy Optimization},
year = {2026},
howpublished = {\url{https://pith.science/paper/D5X7AJSH}},
note = {Machine review of arXiv:2412.17647}
}
read the original abstract
Multi-view clustering (MVC) has emerged as a powerful technique for extracting valuable insights from data characterized by multiple perspectives or modalities. Despite significant advancements, existing MVC methods struggle with effectively quantifying the consistency and complementarity among views, and are particularly susceptible to the adverse effects of noisy views, known as the Noisy-View Drawback (NVD). To address these challenges, we propose CE-MVC, a novel framework that integrates an adaptive weighting algorithm with a parameter-decoupled deep model. Leveraging the concept of conditional entropy and normalized mutual information, CE-MVC quantitatively assesses and weights the informative contribution of each view, facilitating the construction of robust unified representations. The parameter-decoupled design enables independent processing of each view, effectively mitigating the influence of noise and enhancing overall clustering performance. Extensive experiments demonstrate that CE-MVC outperforms existing approaches, offering a more resilient and accurate solution for multi-view clustering tasks.
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