{"id":"a33dfdf2-74c2-4067-9cbd-cf397c7a3c1a","arxiv_id":"2505.11182","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"FreeCSL performs incomplete multi-view clustering by learning shared semantic prototypes across views and enhancing them with within-view graph structure, avoiding explicit imputation and alignment.","lead":"This paper introduces FreeCSL, a clustering method for multi-view data with missing entries that learns a shared set of cluster prototypes to group observations without first filling in missing values. It reports large accuracy gains over existing incomplete multi-view clustering methods on several benchmarks, especially when many entries are missing.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 1's proof is not established: Eq. (17) miscounts negative pairs as 2r(1-r)N(N-1) (pairs with exactly one missing observation) instead of (1-r)^2N(N-1) observed pairs, and Eq. (26) sets the semantic-level false-negative rate to ~0 by assumption.","rationale":"The reader's weakest assumption is the same one I identify as most load-bearing: the proof of Theorem 1 depends on an asserted statistical model and sets the key error to zero by construction. I agree with the CONDITIONAL verdict. My read sharpens the concern with a specific, checkable algebraic error: N_in in Eq. (17) counts pairs with exactly one missing observation, whereas observed negative pairs number (1-r)^2 N(N-1). This is not a missing derivation but a miscount that invalidates Eq. (18). I also note that the proof analyzes a generic pairwise objective that does not match the implemented swapped-distillation loss of Eq. (6), so even a corrected counting would not directly establish the theorem for FreeCSL. Because Theorem 1 is cited as the design basis for the method, the theoretical claim should be demoted to motivation or removed; the empirical comparison remains the main evidence. Code release and error bars would be needed to fully assess the empirical claim. Thus the reader's CONDITIONAL verdict remains appropriate, and no adjustment is needed.","tokens_in":26641,"tokens_out":9028,"duration_ms":91720,"concrete_test":"Re-derive Eq. (17) under MCAR missingness with per-view rate r: the expected number of observed ordered cross-view negative pairs (i != j, both available) is (1-r)^2 N(N-1), not 2r(1-r)N(N-1). Substitute the corrected count into Eq. (18) and check whether the claimed (1+epsilon) amplification of the negative-pair penalty and the stated growth with r still follow; if not, Theorem 1's conclusion is unsupported even before considering Eq. (26), which assumes the conclusion.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central theoretical claim (Theorem 1, Appendix B) is not supported by the proof as written. In Eq. (17), N_in is defined as the expected number of instance-level negative pairs and computed as 2r(1-r)N(N-1). Under missing-completely-at-random with rate r, the expected number of observed ordered cross-view negative pairs (i != j, both available) is (1-r)^2 N(N-1); 2r(1-r)N(N-1) counts pairs in which exactly one of the two observations is missing, which do not appear in any contrastive loss. Consequently, Eq. (18)'s E[f_ic] with the (1+epsilon) amplification term does not follow. Separately, epsilon = P(C=1|I=0) = 1/K + beta*r is an unproven ansatz with unspecified beta, and Eq. (26) sets the semantic-level false-negative rate to approximately zero by invoking shared prototypes, effectively assuming the theorem's conclusion. Moreover, the proof analyzes the generic pairwise objective Eq. (15), while the actual L_cc in Eq. (6) is a swapped-distillation loss over paired observations only, so the theorem does not directly apply to the implemented loss. Thus the 'more confident and robust' guarantee has no rigorous foundation; the paper's contribution currently rests on the empirical tables.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes FreeCSL, an incomplete multi-view clustering method that avoids explicit imputation and cross-view alignment. It learns consensus semantic prototypes from all available observations via a prototypical contrastive clustering objective, and it adds a modularity-based within-view graph clustering module to sharpen cluster structure. The authors state two theorems: consensus semantic learning yields more confident and robust assignments than instance- and cluster-level paradigms (Theorem 1), and paired observations can reach semantic consensus through shared prototypes (Theorem 2). The experimental section compares FreeCSL against seven prior IMVC methods on six datasets at missing rates 0.1-0.7, with ablations, imputation control groups, similarity-matrix visualizations, and parameter sensitivity analyses.","tokens_in":26965,"tokens_out":2943,"duration_ms":31143,"significance":"If the empirical results are representative, FreeCSL is a practically strong contribution: it achieves large accuracy gains on multi-cluster and large-scale benchmarks, degrades gracefully as the missing rate increases, and is competitive without imputation or alignment. The paper also ships a substantial experimental study, including ablations of every module, imputation control groups, and visual evidence of block-structured consensus representations. The main weakness is theoretical: the proof of Theorem 1 in Appendix B is not a valid derivation, and Theorem 2's proof is partly circular. Because the abstract and Section 1 present Theorem 1 as the motivation for the method, the theoretical claim needs to be either rigorously repaired or explicitly downgraded to a heuristic; the empirical contribution itself remains meaningful.","major_comments":[{"comment":"The expression for the expected number of instance-level negative pairs is incorrect. Under missing-completely-at-random with rate r, the expected number of observed ordered cross-view negative pairs (i ≠ j, both views available) is (1-r)^2 N(N-1), not 2r(1-r)N(N-1). The expression used in Eq. (17) counts pairs in which exactly one of the two observations is missing, and such pairs do not enter any contrastive loss. Consequently, the amplified penalty term (1+ε)E[ρ⁻] in Eq. (18) is not derived from the model, and the subsequent comparison between paradigms is not quantitatively supported.","section":"Appendix B, Eq. (17)"},{"comment":"The false-negative probability ε = P(C=1|I=0) = 1/K + βr is an unproven ansatz with an unspecified coefficient β. No data-generating mechanism or derivation is given for this linear form, and the proof later sets the semantic-level false-negative rate ε_sc to approximately zero in Eq. (26) by invoking shared prototypes. This effectively assumes the conclusion of Theorem 1 rather than establishing it. If the theorem is retained, the authors need to derive both quantities from a concrete statistical model or state them as assumptions and validate them empirically.","section":"Appendix B, Eqs. (17) and (26)"},{"comment":"The proof of Theorem 1 analyzes a generic pairwise objective Eq. (15) with positive/negative pairs, but the implemented loss L_cc in Eq. (6) is a swapped-distillation loss computed over paired observations X^{m,n} only; it does not explicitly construct negative pairs over all observed cross-view instance pairs. Therefore the expected objective E[f_sc] in Eq. (27) does not directly correspond to the objective actually optimized in the paper. The authors should state explicitly which loss is being analyzed and prove the theorem for that loss, or reformulate the theoretical claim as a property of an idealized surrogate model.","section":"Section 2.3 and Appendix B, Eq. (15)"},{"comment":"The proof of Theorem 2 is partly circular. Condition 2 assumes that because x_i^m and x_i^n belong to the same cluster (CC), their nearest prototype under the shared set C must be the same prototype c_k. But this is exactly the semantic consensus property that the theorem is supposed to establish; cluster-level consistency across views does not, by itself, guarantee the same argmax under a single prototype set. The proof needs an additional argument, for example a guarantee on prototype alignment or a statement of the conditions under which the swapped-distillation objective would recover that property.","section":"Appendix B, Proof of Theorem 2"}],"minor_comments":[{"comment":"Theorems are numbered 1 and 2 in the main text but appear as Theorems 3 and 4 in Appendix B; the numbering should be aligned.","section":"Appendix B, Theorem numbering"},{"comment":"The Student's t-distribution kernel introduces a parameter γ, but γ is not defined or given a value anywhere in the paper.","section":"Section 2.4, Eq. (12)"},{"comment":"The notation Q^m and H^m is not defined before Eq. (7); it should be clarified that these are matrices of pseudo-labels and semantic representations for the paired observations in view m.","section":"Section 2.3, Eq. (7)"},{"comment":"The competitor name 'DIVC' appears in the YouTubeFace10 block; elsewhere the same method is called 'DIVIDE'.","section":"Table 2, YouTubeFace10 row"},{"comment":"Reference citations appear as '[49?]' and '[12, 49?]' in the related-work section; these should be corrected.","section":"Appendix A, Section 5.1"},{"comment":"The definitions of N_cp and N_cn use the same prefactor (1-r)^2 N^2 and differ only in the same-cluster probability; if these are intended to be pair counts, the i≠j restriction and the N(N-1) factor should be made explicit.","section":"Appendix B, Eq. (22)"}],"recommendation":"major_revision","confidential_remarks":"The theoretical apparatus is the main obstacle. The empirical study is extensive and the method appears competitive, but the proof of Theorem 1 is not valid as written, and the proof of Theorem 2 relies on an assumption that is close to the claim. If the authors revise the paper to either provide a correct, model-based derivation or explicitly present the theoretical statements as intuitive motivations rather than proven guarantees, the manuscript could become acceptable. The scope of the journal and the practical contribution are fit; the issue is internal consistency of the theoretical section."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my take on arXiv:2505.11182. The paper is a serious empirical contribution to incomplete multi-view clustering, but the theoretical guarantee they advertise does not hold as written. The consensus semantic-level paradigm—learning shared prototypes from available data and using them for swapped-distillation contrastive learning, enhanced by modularity-based graph clustering within each view—is a reasonable new combination. The experiments are a plus: six datasets, missing rates from 0.1 to 0.7, seven baselines, ablations, and imputation control groups. The gains on ALOI-100 and YouTubeFace10 are notable, and the method degrades gracefully at r=0.7. If the empirical results are reproducible, this is a useful method paper.\n\nThe main weakness is the proof of Theorem 1 in Appendix B. The stress-test analysis is correct: Eq. (17) miscounts the expected number of instance-level negative pairs as 2r(1-r)N(N-1), which actually counts pairs where exactly one observation is missing; observed negative pairs are (1-r)^2N(N-1). The false-negative probability epsilon = 1/K + beta*r is an unproven ansatz with beta unspecified. And Eq. (26) sets the semantic-level false-negative rate to approximately zero by invoking shared prototypes, which essentially assumes the conclusion. Additionally, the proof analyzes a generic pairwise objective (Eq. 15), while the implemented loss L_cc is a swapped-distillation loss over paired observations only, so the theorem does not directly apply. I'd drop the theorem from the main text and keep it as informal motivation, or rewrite it as an empirical observation.\n\nOther soft spots are minor but real: no code is released, and the main tables lack error bars. The convergence plot with five runs on Caltech-5V is good, but the headline numbers need similar treatment. These are addressable in revision.\n\nThe empirical comparison is against external baselines, so the main claim is not circular. The imputation control groups (ILR/ISR) are a nice way to test the 'imputation-free' claim directly. I found the paper honestly engaged with related work, and the method design is coherent. I'd send this to a serious referee, but with the expectation that the theoretical claim is removed or substantially weakened and the empirical evidence is made reproducible. It's a conditional accept for me, not a reject.","headline":"A solid empirical IMVC paper whose theoretical guarantee does not survive scrutiny; useful if treated as a method contribution.","tokens_in":27515,"tokens_out":2615,"would_cite":true,"duration_ms":24681,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that incomplete multi-view clustering can skip both imputation and alignment by learning consensus prototypes from all available observations, and that this yields more confident and robust cluster assignments than…","keywords":["incomplete multi-view clustering","imputation-free","alignment-free","consensus prototypes","prototypical contrastive clustering","modularity-based graph clustering","semantic-level consistency","deep clustering"],"falsifier":"On a labeled benchmark with known ground-truth clusters, measure the empirical false-negative rate $P(C=1\\mid I=0)$ among unpaired cross-view pairs under uniform random missingness and check whether it grows as $1/K+\\beta r$; then run FreeCSL against instance-level and cluster-level baselines under non-uniform missingness (for example, a fixed subset of instances missing in all but one view). If the empirical false-negative statistics deviate from the assumed form, or if the method's advantage shrinks or reverses under blockwise missingness, the paper's central guarantee is contradicted even if the reported benchmark numbers are reproduced.","tokens_in":26422,"feed_emoji":"🧩","tokens_out":10139,"duration_ms":91366,"temperature":0.7,"pith_summary":"Incomplete multi-view clustering has assumed that missing data must be repaired by imputation or that views must be aligned before clustering. This paper claims that both steps are unnecessary and often harmful, and that a shared set of consensus prototypes, learned from whatever observations are present, can pull every sample toward its correct semantic center regardless of which views it appears in. A companion within-view module uses spectral modularity to recover per-view cluster structure. If the claim holds, the payoff is a clustering method whose accuracy degrades gradually as missingness rises, where existing methods drop sharply; the paper reports that on six benchmarks it outperforms seven competing methods across missing rates $r=0.1$ to $r=0.7$.","feed_headline":"Imputation-free clustering wins on incomplete multi-view data","feed_subtitle":"It skips imputation and alignment, clustering six datasets at missing rates from 10 to 70 percent.","key_machinery":"The carrying object is the set of consensus prototypes $\\mathcal{C}=\\{c_k\\}_{k=1}^K$, obtained by $k$-means on consensus representations $Z=\\sum_v w_v Z_v$, where the fusion weights $w_i^v$ are completeness statistics: the indicator that instance $i$ is observed in view $v$, divided by the number of views in which $i$ appears. Each view's semantic representation $h_i^v$ is projected onto the prototypes to give soft assignments $p_{i,k}=\\exp(h_i^{\\top}c_k/\\tau)/\\sum_{k'}\\exp(h_i^{\\top}c_{k'}/\\tau)$, and paired views supervise each other through swapped knowledge distillation. A second module maximizes spectral modularity $\\operatorname{Tr}((P^v)^{\\top}B^vP^v)$ on per-view $k$-NN graphs, regularized by KL divergence toward self-supervised pseudo-labels from a Student's $t$-distribution, to inject within-view cluster structure. Together these create a shared semantic space in which unpaired but semantically similar observations pull together instead of being treated as false negatives, and within-view structure counteracts the coarseness of cluster-level consistency.","core_discovery":"The central claim is Theorem 1: consensus semantic learning, which assigns all available observations to a common set of consensus prototypes, yields more confident and robust cluster assignments than either instance-level or cluster-level consistency learning. Theorem 2 adds that paired cross-view observations, which already satisfy instance- and cluster-level consistency, automatically reach semantic consensus in the shared prototype space, so no explicit imputation or alignment is needed. The reported experiments support this with accuracy gains on six datasets against seven state-of-the-art methods: on ALOI-100 (100 clusters) the ACC advantage over the best competitor is 15.12, 26.38, 23.91, and 26.21 percentage points at $r=0.1, 0.3, 0.5, 0.7$, and on Caltech-5V at $r=0.7$ accuracy remains 83.64 percent while competitors fall to 60–80 percent.","pith_inferences":["The theoretical argument assumes missingness is uniform-random across views; a natural stress test is blockwise or view-correlated missingness, under which the completeness-weighted fusion could be dominated by the most complete views and the claimed robustness may not persist. The paper does not test this setting.","The consensus-prototype recipe is generic: any partially observed multi-view task, such as retrieval, few-shot classification, or multimodal representation learning, could replace missing-data recovery with prototype-anchored contrasting over all available observations. This is an extension the paper does not make.","The modularity term is doing the work of an intra-view clustering objective; one could test whether spectral modularity specifically is essential, or whether any within-view contrastive grouping gives the same enhancement.","The proof of the main theorem rests on asserted false-negative statistics; a tightening would derive $P(C=1\\mid I=0)$ from a concrete generative model of cluster structure and missingness, making the confidence-and-robustness claim checkable in closed form rather than by construction."],"forward_implications":["At high missing rates ($r=0.5$ and $0.7$), the model degrades gradually because it does not depend on the shrinking pool of paired complete observations; reported ACC on Caltech-5V stays at 88.36 and 83.64 percent, and on NoisyMNIST at 96.04 and 92.19 percent.","The claimed advantage grows on many-cluster, large-scale tasks: on ALOI-100 with 100 clusters the reported ACC gains over the best competitor are 15.12, 26.38, 23.91, and 26.21 percentage points as $r$ goes from 0.1 to 0.7.","Because no imputation or alignment is performed, the method avoids error accumulation from graph-structure transfer and prototype alignment; the paper's control experiments (ILR and ISR) show that injecting $k$-NN imputation does not help and can hurt at high missing rates.","The two modules are synergistic: ablations show the consensus semantic learning module contributes the most, but the modularity-based enhancement improves both reconstruction and semantic learning when added.","Final cluster labels come from $k$-means on the consensus semantic representation, with no balancing weights and no imputation step, which the paper argues makes the framework simple to deploy end-to-end."],"supporting_citations":[{"why":"Supplies the prototype-based imputation baseline (ProImp) and the motivation that semantic consistency should integrate within-view and cross-view information; it is the prior approach FreeCSL explicitly avoids with imputation-free learning.","marker":"[24]"},{"why":"Contrastive clustering, the direct ancestor of the prototype-contrastive mechanism that FreeCSL extends from cluster-level logic to a consensus prototype space across incomplete views.","marker":"[27]"},{"why":"Defines network modularity, the objective behind the spectral modularity term that the cluster semantic enhancement module maximizes to recover within-view cluster structure.","marker":"[35]"},{"why":"Supplies the notion that a consensus prototype or anchor comprehensively captures the semantic information of all data, which justifies learning prototypes from the fused consensus representation.","marker":"[63]"},{"why":"Cluster-level contrastive competitor (SURE) that detects false negatives with an adaptive threshold; the main cluster-level paradigm FreeCSL claims to supersede in Theorem 1.","marker":"[62]"},{"why":"Cluster-level competitor (DIVIDE) that uses high-order random walks to handle false negatives; a key baseline in the reported comparisons.","marker":"[34]"},{"why":"Instance-level contrastive baseline (COMPLETER) and the source of the NoisyMNIST dataset; represents the imputation-based paradigm that FreeCSL is compared against.","marker":"[29]"},{"why":"Instance-level consistency baseline with assignment alignment (DIMVC); represents the alignment-based paradigm FreeCSL claims to avoid.","marker":"[53]"},{"why":"Generative imputation baseline (CPM-Nets) using adversarial common representations; a representative of the imputation-based paradigm in the comparison.","marker":"[66]"}],"fun_headline_variants":["Consensus semantic learning beats imputation in incomplete views","Skip imputation and alignment: consensus prototypes rule","No imputation, no alignment: consensus semantics wins","Incomplete views? FreeCSL clusters without imputation","Consensus prototypes: the imputation-free fix for missing views"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The main theorem assumes a specific statistical model of how missing data creates false-negative pairs — that the false-negative probability is $P(C=1\\mid I=0)=1/K+\\beta r$ and that the expected negative-pair count is $N_{in}=2r(1-r)N(N-1)$ — and then treats the semantic-level false-negative rate as approximately zero by construction in Eq. (26); these assertions are assumed rather than derived from a data-generating process, so the theorem's guarantee falls if the assumed missingness pattern does not hold.","fun_headline_variants_meta":{"raw":{"variants":["Consensus semantic learning beats imputation in incomplete views","Skip imputation and alignment: consensus prototypes rule","No imputation, no alignment: consensus semantics wins","Incomplete views? FreeCSL clusters without imputation","Consensus prototypes: the imputation-free fix for missing views"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000549,"raw_usage":{"total_tokens":2640,"prompt_tokens":980,"completion_tokens":1660,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":596,"completion_tokens_details":{"reasoning_tokens":1582}},"tokens_in":596,"tokens_out":1660,"duration_ms":12159,"temperature":1.0,"reasoning_tokens":1582,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T20:56:30.527774+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"On a labeled benchmark with known ground-truth clusters, measure the empirical false-negative rate $P(C=1\\mid I=0)$ among unpaired cross-view pairs under uniform random missingness and check whether it grows as $1/K+\\beta r$; then run FreeCSL against instance-level and cluster-level baselines under non-uniform missingness (for example, a fixed subset of instances missing in all but one view). If the empirical false-negative statistics deviate from the assumed form, or if the method's advantage shrinks or reverses under blockwise missingness, the paper's central guarantee is contradicted even if the reported benchmark numbers are reproduced.","supporting_citations":[{"cited_title":"Contrastive clustering","cited_arxiv_id":null,"evidence_quote":"Contrastive clustering, the direct ancestor of the prototype-contrastive mechanism that FreeCSL extends from cluster-level logic to a consensus prototype space across incomplete views."},{"cited_title":"Modularity and community structure in networks.Proceedings of the national academy of sciences, 103(23):8577–8582, 2006","cited_arxiv_id":null,"evidence_quote":"Defines network modularity, the objective behind the spectral modularity term that the cluster semantic enhancement module maximizes to recover within-view cluster structure."},{"cited_title":"Sparse low- rank multi-view subspace clustering with consensus anchors and unified bipartite graph.IEEE Transactions on Neural Networks and Learning Systems, 2023","cited_arxiv_id":null,"evidence_quote":"Supplies the notion that a consensus prototype or anchor comprehensively captures the semantic information of all data, which justifies learning prototypes from the fused consensus representation."},{"cited_title":"Robust multi-view clustering with incom- plete information.IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022","cited_arxiv_id":null,"evidence_quote":"Cluster-level contrastive competitor (SURE) that detects false negatives with an adaptive threshold; the main cluster-level paradigm FreeCSL claims to supersede in Theorem 1."},{"cited_title":"Decoupled contrastive multi-view cluster- ing with high-order random walks","cited_arxiv_id":null,"evidence_quote":"Cluster-level competitor (DIVIDE) that uses high-order random walks to handle false negatives; a key baseline in the reported comparisons."},{"cited_title":"Completer: Incomplete multi-view clustering via contrastive prediction","cited_arxiv_id":null,"evidence_quote":"Instance-level contrastive baseline (COMPLETER) and the source of the NoisyMNIST dataset; represents the imputation-based paradigm that FreeCSL is compared against."},{"cited_title":"Deep incomplete multi- view clustering via mining cluster complementarity","cited_arxiv_id":null,"evidence_quote":"Instance-level consistency baseline with assignment alignment (DIMVC); represents the alignment-based paradigm FreeCSL claims to avoid."},{"cited_title":"Deep partial multi-view learning.IEEE transactions on pattern analysis and machine intelligence, 44(5):2402–2415, 2020","cited_arxiv_id":null,"evidence_quote":"Generative imputation baseline (CPM-Nets) using adversarial common representations; a representative of the imputation-based paradigm in the comparison."}],"review_version":1}