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REVIEW 3 major objections 5 minor 49 references

Multi-view Granular-ball Contrastive Clustering

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Multi-view contrastive clustering works better when the contrast units are granular balls—compact local groups of samples—rather than individual instances, and the paper supports this with strong results on seven benchmarks.

desk verdict Granular-ball contrastive clustering has a promising intermediate-scale idea, but Eq. (12) is missing its negative sign and log, so the printed loss repels associated balls and attracts unrelated ones, inverting the paper's central claim. read the letter →

arxiv 2412.13550 v2 pith:MMUAGX4R submitted 2024-12-18 cs.LG

Peng Su , Shudong Huang , Weihong Ma , Deng Xiong , Jiancheng Lv This is my paper · ORCID
classification cs.LG
keywords multi-viewclusteringcontrastivelearninggranular-ballcomputingdeeprepresentationunsupervisedlocalstructure
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that multi-view contrastive clustering should operate at an intermediate scale between individual instances and whole clusters: on 'granular balls,' or compact groups of similar samples. The authors propose MGBCC, a deep clustering method that first constructs these balls in each view's learned latent space, then links balls within a view if they overlap and across views if they share enough of the same samples. A contrastive loss then pulls linked balls together and pushes unlinked balls apart, so the shared representation learns both local topology and cross-view agreement. On seven standard multi-view datasets, the method reports accuracy, normalized mutual information, and purity that are best or second-best in most cases, and it substantially improves on instance-level contrastive baselines such as SURE on three datasets.

What carries the argument

The load-bearing objects are granular balls: local clusters of latent-space representations with a center and radius, obtained by a direct $k$-means partition with a granularity parameter $p$ rather than the classical recursive splitting. The mechanism is a dual-association contrastive step: intra-view associations come from an overlap matrix $A^v$ (two balls overlap if their center distance minus the sum of radii is below a threshold related to their overlap counts), and cross-view associations come from a matrix $P^{(m,n)}$ (two balls in different views are linked if the fraction of common sample indices over the smaller ball's size exceeds $\tau$). These are merged into a unified mask matrix $M$ that feeds a contrastive loss on ball centers, so that the shared latent space preserves within-view topology and cross-view agreement at the ball level.

What would settle it

One can settle the central claim by training MGBCC with the loss exactly as written in Eq. (12) and measuring whether the average cosine similarity between associated granular-ball pairs increases or decreases over training; if it decreases, the stated objective implements the opposite of the claimed contrastive behavior.

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Extended reading notes

Core claim

MGBCC claims that contrastive learning at the granular-ball level yields highly discriminative multi-view representations. Instead of pairing individual samples across views (which creates false negatives) or aligning whole cluster assignments (which ignores local structure), the method segments each view's latent space into a number of granular balls set by a granularity parameter $p$ (roughly $N/p$ balls) via $k$-means, computes intra-view overlap from ball center distances and radii, and computes inter-view overlap from the fraction of shared sample indices. The resulting association masks are combined into a unified mask matrix, and a contrastive loss on ball centers encourages associated balls to attract and unassociated balls to repel in a shared space. The paper demonstrates on BBCSport, Cora, MNIST-USPS, and other benchmarks that this intermediate-scale contrastive objective matches or exceeds state-of-the-art instance-level and cluster-level methods, and an ablation on Caltech101-20 shows granular-ball contrast ($p=2$) far outperforms instance-level contrast ($p=1$) when both are added to the reconstruction loss.

Load-bearing premise

The method relies on the printed contrastive loss actually pulling associated granular balls together and pushing unassociated ones apart, and on the overlap definition being computable rather than circular; if either assumption fails, the claimed feature learning would not follow from the stated objective.

Editorial extensions

If this is right

  • The granular-ball construction can be added to any multi-view contrastive pipeline that uses instance-level negatives, because it only requires computing ball centers and masks from the latent representation.
  • Because negatives are defined between whole balls rather than individual samples, the method reduces the impact of false negative pairs that come from putting two samples of the same class into a negative pair.
  • The granularity parameter $p$ provides a continuous interpolation between instance-level contrast ($p=1$) and cluster-level contrast (large $p$), so a single framework covers both existing regimes.
  • The reported Cora accuracy (65.44%) against the best baseline (49.07%) suggests ball-level contrast is especially effective when views are high-dimensional and sparse.

Reading between the lines

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

  • The same granular-ball idea could be transplanted to single-view contrastive learning, where augmentations of the same image could define ball membership and negative pairs could be drawn from other balls; the paper does not test this, but it follows directly from the mechanism.
  • Because the contrastive loss operates on ball centers rather than all $N$ samples, memory use scales with the number of balls $k$, opening the way to very large datasets when $p$ is chosen moderately; this scaling is not demonstrated in the paper.
  • The parameter $p$ sensitivity suggests an adaptive granularity schedule: starting with large balls early in training and refining to smaller $p$ later could give a curriculum that the paper does not explore.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper proposes MGBCC, a multi-view clustering method that performs contrastive learning at the granular-ball level. Granular balls are formed in each view's latent space via k-means, intra-view associations are defined by a geometric overlap criterion, cross-view associations are defined by the proportion of shared sample indices, and a contrastive loss over granular-ball centers is minimized jointly with reconstruction losses. Experiments on seven multi-view datasets report state-of-the-art or competitive ACC/NMI/PUR, and an ablation on Caltech101-20 is used to argue that granular-ball-level contrastive learning outperforms instance-level contrastive learning.

Significance. If the method were correctly specified, the proposal of an intermediate granularity between instances and clusters for multi-view contrastive learning would be a useful contribution, and the experimental suite is broad. The paper is also among the first to connect granular-ball computing to deep multi-view contrastive clustering. However, the central objective as printed in Eq. (12) does not do what the text claims: minimizing it repels associated granular balls and relatively attracts unrelated ones. Because this equation is the defining mechanism of the method, the theoretical description, the ablation, and the interpretation of the experimental results are not supported as written. The circularity in Eq. (2) further means that the overlap matrix used to build the contrastive mask is not well defined.

major comments (3)
  1. [Granular-ball Contrastive Learning, Eq. (12)] Equation (12) defines the granular-ball contrastive loss as L(m,n) = (1/k) sum_i sum_{j in Omega_i} exp(cos(c_i,c_j)) / sum_{z in Phi_i} exp(cos(c_i,c_z)), with no negative sign and no logarithm. Since every term in the numerator is positive, the partial derivative of the summand with respect to the cosine similarity of an associated pair is exp(cos(c_i,c_j)) / sum_{z in Phi_i} exp(cos(c_i,c_z)) > 0. Gradient descent therefore makes associated granular balls less similar, while the denominator makes non-associated balls relatively more similar. This is exactly the opposite of the objective stated in the text and in Figure 2. As a result, Table 2, Figure 3, and Table 3 cannot be interpreted as evidence for granular-ball contrastive learning unless the actual loss used in the experiments is different from Eq. (12) and is stated explicitly.
  2. [Within-view Granular-ball Generation, Eq. (2)] Equation (2) defines the overlap criterion using omega = min(ri, rj) / min(pi, pj), where pi and pj are described as the total numbers of overlaps with adjacent granular balls for GBi and GBj. Whether two balls overlap is precisely the relation being defined, so pi and pj are not available before the overlap matrix Av is computed. The manuscript provides no fixed-point iteration, initialization rule, or alternative definition. Therefore Av in Eq. (6), the mask M in Eq. (11), and the contrastive loss in Eq. (12) are not well defined for an arbitrary input.
  3. [Ablation Studies, Table 3] The ablation compares Lrec, Lrec + Lcon with p=1, and Lrec + Lcon with p=2, and uses the improvement of the p=2 setting to conclude that granular-ball contrastive learning is effective. This conclusion is load-bearing for the paper's central claim. Because Eq. (12) is not a contrastive objective, the difference between the two settings cannot be attributed to the claimed mechanism. The authors need to specify the actual loss minimized in the experiments and provide the corrected equation; otherwise the ablation cannot support the granular-ball hypothesis.
minor comments (5)
  1. [Methodology heading] The heading contains a typo: 'granular-ball asociation' should be 'granular-ball association'.
  2. [Experimental Results] The text says 'classical multi-view constrastive learning methods'; 'constrastive' should be 'contrastive'.
  3. [Equation (13)] The coefficient in Eq. (13) is rendered as '2 V (V - 1)'; it should be written as 2 / (V(V - 1)) to avoid ambiguity.
  4. [Equation (12)] The sum symbol in Eq. (12) appears as 'P' in the rendering; it should be a proper summation symbol (\sum) over z in Phi_i.
  5. [Implementation Details] For BBCSport and Cora, lambda is set to 0, so the reconstruction loss is disabled; the manuscript should clarify what prevents the encoder from collapsing or drifting when the only loss is the contrastive term.

Circularity Check

1 steps flagged · score 4.0 of 10

One self-referential definition in the overlap matrix, but the central empirical claim is independently grounded.

  1. self definitional [Section 'Within-view Granular-ball Generation', Eq. (2) and Eq. (6)]
    "Two balls are considered overlapping if they satisfy following conditions ∥ci − cj∥2 − (ri + rj) < ω, ω= min(ri, rj) min(pi, pj) . (2) where pi and pj denote the total number of overlaps with adjacent granular balls for GBi and GBj."

    Eq. (6) makes a_ij=1 exactly when Eq. (2) holds, so A^v is defined by whether the ball distance is below a threshold ω. But ω depends on p_i and p_j, which are defined as 'the total number of overlaps with adjacent granular balls' for balls i and j—i.e., the row/column sums of A^v itself. The mask matrix M in Eq. (11) is then built from A^v, so the intra-view association structure driving the contrastive loss is not well-defined as printed: no base case, fixed-point iteration, or existence argument is supplied, and p_i=p_j=0 makes the ratio undefined.

full rationale

The paper's central contribution—granular-ball-level contrastive learning improves multi-view clustering—is supported by external benchmarks and ablations, so it is not circular with respect to the method's equations. I found one genuine definitional circularity: Eq. (2) defines overlap via p_i and p_j, but p_i and p_j are themselves the overlap counts of the same matrix A^v defined by Eq. (2), leaving the intra-view mask (and hence part of Lcon) ill-defined as written. This is a load-bearing subcomponent rather than a minor citation issue, so the score is 4 rather than 0-2. I do not classify Eq. (12)'s missing negative sign/log as circularity; it is a serious correctness/sign error that inverts the stated contrastive objective, but it is not a reduction of a prediction to its inputs. Hyperparameter selection on Caltech101-20/Cora is in-sample tuning, not a circular 'prediction' in the sense of this review, and the self-citations (e.g., Su et al. 2024) are contextual, not load-bearing.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The method rests on four tuned hyperparameters (p, tau, lambda, d), on the assumption that k-means clusters behave as granular balls, on a well-defined overlap matrix that Eq. (2) does not actually define, and on a contrastive loss that as printed would do the opposite of the claimed behavior. No invented entities are introduced: granular balls are inherited from prior granular-ball computing literature.

free parameters (4)
  • p = 1, 2, or 4 per dataset
    Controls the number of granular balls via k = floor(N/p). The authors say p significantly impacts results and select it after parameter analysis on Caltech101-20 and Cora.
  • tau = 0.1 (uniform)
    Threshold in Eq. (9) for deciding whether two cross-view balls share enough samples. Set uniformly with no sensitivity analysis.
  • lambda = 1 generally; 0 for BBCSport and Cora
    Regularization weight balancing contrastive and reconstruction losses. Adjusted per dataset without a stated selection rule.
  • d = 64 generally; 128 in ablation
    Projection feature dimension shared by all views. The authors report a relatively minor impact and choose d = 64 for most experiments.
assumptions (4)
  • domain assumption k-means clusters can serve as granular balls preserving local topological structure
    Section 'Within-view Granular-ball Generation' sets k = floor(N/p) and treats each k-means cluster as a granular ball; no argument is given that this preserves local structure or handles outliers as claimed.
  • ad hoc to paper Minimizing Eq. (12) pulls associated granular balls together
    The text states that associated balls should be close, but Eq. (12) lacks a negative sign or log; as written, minimization drives positive pairs apart and negative pairs together.
  • ad hoc to paper The overlap matrix Av from Eq. (2) is well-defined and computable
    Eq. (2) defines overlap using pi and pj, which are the overlap counts with adjacent balls; these depend on Av itself, and no fixed-point iteration or existence proof is supplied.
  • domain assumption Centers and radii of k-means clusters are gradient-preserving
    Section 'Within-view Granular-ball Generation' states this without proof. Hard k-means cluster assignments are not differentiable with respect to the encoder parameters in the usual sense.

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Cite this review

Pith. "Pith review of Multi-view Granular-ball Contrastive Clustering." pith.science (2026). https://pith.science/paper/MMUAGX4R

@misc{pith2026241213550,
  author       = {Pith},
  title        = {Pith review of: Multi-view Granular-ball Contrastive Clustering},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MMUAGX4R}},
  note         = {Machine review of arXiv:2412.13550}
}
read the original abstract

Previous multi-view contrastive learning methods typically operate at two scales: instance-level and cluster-level. Instance-level approaches construct positive and negative pairs based on sample correspondences, aiming to bring positive pairs closer and push negative pairs further apart in the latent space. Cluster-level methods focus on calculating cluster assignments for samples under each view and maximize view consensus by reducing distribution discrepancies, e.g., minimizing KL divergence or maximizing mutual information. However, these two types of methods either introduce false negatives, leading to reduced model discriminability, or overlook local structures and cannot measure relationships between clusters across views explicitly. To this end, we propose a method named Multi-view Granular-ball Contrastive Clustering (MGBCC). MGBCC segments the sample set into coarse-grained granular balls, and establishes associations between intra-view and cross-view granular balls. These associations are reinforced in a shared latent space, thereby achieving multi-granularity contrastive learning. Granular balls lie between instances and clusters, naturally preserving the local topological structure of the sample set. We conduct extensive experiments to validate the effectiveness of the proposed method.

Figures

Figures reproduced from arXiv: 2412.13550 by the authors.

Figure 1
Figure 1. Examples of granular balls Given a dataset {xi} n i=1, let {GBi} k i=1 denote the set of granular balls generated based on it, where k represents the total number of balls. As illustrated in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. The framework of MGBCC. As shown, the overall loss function consists of two parts, e.g., reconstruction loss and [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. The t-SNE visualization of the clustering results on MNIST-USPS dataset. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: Loss vs. Metrics on Cora. Convergence Analysis We evaluated the convergence of the proposed method on Cora dataset by tracking the loss values and corresponding clustering performance over increasing epochs. As shown in [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 4
Figure 4. Figure 4: The clustering accuracy (%) with different param [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

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    Zhao, M.; Yang, W.; and Nie, F. 2023. Deep multi-view spectral clustering via ensemble. Pattern Recognition, 144: 109836

    2023

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.