RHEA: Reliability-Harmonized Reconstruction and Assignment for Robust Multimodal-Attributed Graph Clustering

# Reliability-Harmonized Reconstruction and Assignment for Robust Multimodal-Attributed Graph Clustering
Source: [https://arxiv.org/html/2608.00621](https://arxiv.org/html/2608.00621)
Yinlin Zhu1, Di Wu1, Ziyu Han2, Zekai Chen3, Wang Luo1, Miao Hu1, Guocong Quan1

###### Abstract

Multimodal\-attributed graphs \(MAGs\), whose nodes carry heterogeneous attributes such as text and images over a relational structure, have become a fundamental substrate for label\-free entity grouping tasks, including community discovery and product segmentation\. Existing MAG clustering methods effectively integrate complementary modalities when attributes are clean and complete, but degrade substantially under noisy or missing attributes because they implicitly assume equal modality reliability across all nodes\. In practice, modality reliability is inherently node\-specific: images may be corrupted or absent, while textual descriptions are incomplete or noisy\. We argue that, under attribute homophily, graph neighborhoods naturally provide supervision\-free evidence for estimating node\-specific modality reliability\. Based on this insight, we propose RHEA, a reliability\-aware framework for MAG clustering that estimates node\-specific modality reliability from neighborhood consensus and propagates this signal throughout the clustering pipeline\. RHEA reconstructs unreliable or missing modalities from graph neighborhoods, adaptively weights modalities during reliability\-aware fusion, and performs topology\-aware optimal transport clustering with reliability\-aware transport assignment and neighbor\-consensus assignment distillation\. Furthermore, the confidence of reconstructed representations is incorporated into the clustering objective, allowing uncertain reconstructions to contribute proportionally during optimization\. Experiments on four MAG benchmarks under five attribute conditions show that RHEA consistently outperforms the strongest baseline, with NMI gains increasing as attribute quality deteriorates\.

## 1Introduction

Multimodal\-attributed graphs \(MAGs\), in which nodes are associated with heterogeneous attributes such as text and images over relational structures, have become a fundamental data model for recommendation systems, e\-commerce catalogs, citation networks, and social communities\(Guoet al\.[2025](https://arxiv.org/html/2608.00621#bib.bib2); Zhenget al\.[2025](https://arxiv.org/html/2608.00621#bib.bib1); Penget al\.[2021](https://arxiv.org/html/2608.00621#bib.bib11)\)\. A fundamental task on MAGs is node clustering, which aims to discover semantically coherent node clusters without manual annotation for applications such as community discovery, product segmentation, and cold\-start taxonomy construction\. Recent multimodal graph clustering methods learn node representations by jointly modeling graph topology and multimodal attributes, achieving strong performance when attributes across all modalities are clean and complete\(Guoet al\.[2025](https://arxiv.org/html/2608.00621#bib.bib2); Zhenget al\.[2025](https://arxiv.org/html/2608.00621#bib.bib1)\)\.

However, this assumption rarely holds in real\-world MAGs\. Product images may be corrupted or missing, textual descriptions are often noisy or incomplete, and the most informative modality can vary substantially across nodes\. Existing methods\(Guoet al\.[2025](https://arxiv.org/html/2608.00621#bib.bib2); Zhenget al\.[2025](https://arxiv.org/html/2608.00621#bib.bib1)\)nevertheless implicitly assume that each modality is equally reliable for all nodes during representation learning\. As a result, corrupted modalities contaminate fused representations, missing modalities cannot be effectively compensated, and clustering performance deteriorates as attribute quality declines\. The problem is particularly challenging in the unsupervised setting, where modality reliability cannot be inferred from labels\. This raises a fundamental question:*how can node\-specific modality reliability be estimated without supervision to support robust multimodal\-attributed graph clustering?*

We argue that the graph structure itself provides the answer\. Under the widely observed principle of attribute homophily\(McPhersonet al\.[2001](https://arxiv.org/html/2608.00621#bib.bib41)\), neighboring nodes tend to exhibit similar semantic attributes\. Therefore, a modality that is consistent with its neighborhood is more likely to be reliable than one that persistently deviates from local consensus\. This observation enables supervision\-free estimation of node\-specific modality reliability directly from the graph\. Instead of treating reliability as a modality\-level property shared across all nodes, we model it as a latent variable that varies across both nodes and modalities, providing a unified signal for robust multimodal representation learning\.

Building upon this insight, we proposeReliability\-Harmonized rEconstruction andAssignment \(RHEA\), a reliability\-aware framework for MAG clustering\. RHEA estimates node\-specific modality reliability from neighborhood consensus and leverages it to reconstruct unreliable modalities, adaptively fuse multimodal representations, and guide topology\-aware optimal transport clustering\. A unified reliability signal connects these components, enabling robust representation learning under both attribute corruption and missingness\. Extensive experiments on four benchmark datasets under five attribute conditions show that RHEA consistently outperforms existing methods, with improvements becoming larger as attribute quality deteriorates\. Moreover, the learned reliability estimates accurately recover synthetically injected attribute corruption, with AUROC consistently exceeding0\.950\.95across all datasets, validating the effectiveness of the proposed reliability modeling\.

Our contributions\.\(1\)Valuable Insights\.We identify*node\-specific modality reliability*as the missing ingredient for robust multimodal\-attributed graph clustering, and show that graph neighborhoods provide supervision\-free evidence for estimating this reliability\. \(2\)Novel Method\.We propose RHEA, a unified reliability\-aware framework in which a shared neighborhood\-consensus reliability signal simultaneously guides graph\-based modality reconstruction, adaptive multimodal fusion, and topology\-aware optimal transport clustering\. \(3\)State\-of\-the\-Art Performance\.Extensive experiments on four benchmark datasets demonstrate consistent improvements over state\-of\-the\-art methods across diverse corruption and missingness settings\.

## 2Related Work

#### Attributed Graph Clustering\.

Attributed graph clustering has been extensively studied for graphs with a single attribute modality\. Early methods couple graph autoencoders with clustering objectives, progressively improving structural\-feature fusion through dual\-branch architectures, attention mechanisms, or refined graph encoders\(Boet al\.[2020](https://arxiv.org/html/2608.00621#bib.bib9); Tuet al\.[2021](https://arxiv.org/html/2608.00621#bib.bib10); Penget al\.[2021](https://arxiv.org/html/2608.00621#bib.bib11); Wanget al\.[2019](https://arxiv.org/html/2608.00621#bib.bib12); Liuet al\.[2022b](https://arxiv.org/html/2608.00621#bib.bib13); Cuiet al\.[2020](https://arxiv.org/html/2608.00621#bib.bib14); Liuet al\.[2023a](https://arxiv.org/html/2608.00621#bib.bib15),[2022a](https://arxiv.org/html/2608.00621#bib.bib16)\)\. More recent approaches instead rely on self\-supervised objectives, including contrastive learning\(Zhuet al\.[2021](https://arxiv.org/html/2608.00621#bib.bib24); Youet al\.[2020](https://arxiv.org/html/2608.00621#bib.bib25); Xiaet al\.[2022](https://arxiv.org/html/2608.00621#bib.bib26); Liuet al\.[2023b](https://arxiv.org/html/2608.00621#bib.bib19); Yanget al\.[2023](https://arxiv.org/html/2608.00621#bib.bib20); Liuet al\.[2024b](https://arxiv.org/html/2608.00621#bib.bib21)\)and differentiable graph partitioning based on modularity optimization\(Tsitsulinet al\.[2023](https://arxiv.org/html/2608.00621#bib.bib23); Newman[2006](https://arxiv.org/html/2608.00621#bib.bib36); Liuet al\.[2024a](https://arxiv.org/html/2608.00621#bib.bib22)\)\. Extending clustering to multimodal attributed graphs remains comparatively underexplored\. Existing methods mainly improve cross\-modal representation learning through disentanglement\(Guoet al\.[2025](https://arxiv.org/html/2608.00621#bib.bib2)\), graph filtering and contrastive alignment\(Zhenget al\.[2025](https://arxiv.org/html/2608.00621#bib.bib1)\), feature fusion\(Linet al\.[2024](https://arxiv.org/html/2608.00621#bib.bib3); Pan and Kang[2021](https://arxiv.org/html/2608.00621#bib.bib4); Keet al\.[2023](https://arxiv.org/html/2608.00621#bib.bib7)\), or more expressive multimodal architectures\(Zhuet al\.[2026](https://arxiv.org/html/2608.00621#bib.bib5); Liet al\.[2025b](https://arxiv.org/html/2608.00621#bib.bib6),[a](https://arxiv.org/html/2608.00621#bib.bib8),[2026](https://arxiv.org/html/2608.00621#bib.bib46); Lin and Hu[2022](https://arxiv.org/html/2608.00621#bib.bib33)\)\. Despite their differences, these methods employ a shared fusion strategy across all nodes, implicitly assuming that every modality contributes equally regardless of local modality quality in real\-world scenarios\.

#### Incomplete Multimodal Learning\.

Our work is closely related to learning under missing or unreliable modalities\. Existing incomplete multi\-view methods typically recover missing views through contrastive prediction, feature alignment, or generative completion\(Linet al\.[2021](https://arxiv.org/html/2608.00621#bib.bib27); Xuet al\.[2023](https://arxiv.org/html/2608.00621#bib.bib28)\), while others adaptively weight modalities using evidential learning, information bottlenecks, or optimal transport\(Hanet al\.[2023](https://arxiv.org/html/2608.00621#bib.bib30); Yanet al\.[2024b](https://arxiv.org/html/2608.00621#bib.bib31); Cuturi[2013](https://arxiv.org/html/2608.00621#bib.bib32); Peyré and Cuturi[2019](https://arxiv.org/html/2608.00621#bib.bib43); Xueet al\.[2025](https://arxiv.org/html/2608.00621#bib.bib29)\)\. On graphs, recent approaches extend these ideas via graph propagation\(Malitestaet al\.[2026](https://arxiv.org/html/2608.00621#bib.bib49); Rohet al\.[2025](https://arxiv.org/html/2608.00621#bib.bib50)\), graph denoising\(Zhou and Shen[2023](https://arxiv.org/html/2608.00621#bib.bib52)\), diffusion\-based modality generation\(Jianget al\.[2024](https://arxiv.org/html/2608.00621#bib.bib51)\), or uncertainty\-aware aggregation\(Shimet al\.[2019](https://arxiv.org/html/2608.00621#bib.bib53); Wang and others[2025](https://arxiv.org/html/2608.00621#bib.bib54); Chenet al\.[2025](https://arxiv.org/html/2608.00621#bib.bib55)\)\. In contrast, we neither train a dedicated generative completion model nor assume a globally shared, modality\-level reliability estimate\. Instead, we study multimodal graph clustering under heterogeneous modality quality, where reliability is node\-specific and unreliable modalities are repaired directly from graph neighborhoods\. Our evaluation follows the standardized protocols of MAGB and OpenMAG\(Yanet al\.[2024a](https://arxiv.org/html/2608.00621#bib.bib44); Wanet al\.[2026](https://arxiv.org/html/2608.00621#bib.bib45)\); broader discussions of incomplete graph learning can be found in surveys\(Xiaet al\.[2025](https://arxiv.org/html/2608.00621#bib.bib47); Wuet al\.[2024](https://arxiv.org/html/2608.00621#bib.bib48)\)\.

## 3Preliminaries and Problem Formulation

#### Multimodal Attributed Graph \(MAG\)\.

We consider a MAG𝒢=\(𝐀,\{𝐗\(m\)\}m∈ℳ\)\\mathcal\{G\}=\(\\mathbf\{A\},\\\{\\mathbf\{X\}^\{\(m\)\}\\\}\_\{m\\in\\mathcal\{M\}\}\)overNNnodes\. Here𝐀∈\{0,1\}N×N\\mathbf\{A\}\\in\\\{0,1\\\}^\{N\\times N\}is the adjacency matrix andℳ\\mathcal\{M\}indexes the attribute modalities, in our case text and image \(\|ℳ\|=2\|\\mathcal\{M\}\|=2\)\. Each modality is associated with an attribute matrix𝐗\(m\)∈ℝN×dm\\mathbf\{X\}^\{\(m\)\}\\in\\mathbb\{R\}^\{N\\times d\_\{m\}\}whose row𝐱i\(m\)\\mathbf\{x\}^\{\(m\)\}\_\{i\}holds the modality\-mmattributes of nodeii, obtained from standard pretrained encoders\(Vaswaniet al\.[2017](https://arxiv.org/html/2608.00621#bib.bib37); Radfordet al\.[2021](https://arxiv.org/html/2608.00621#bib.bib42)\)\. We use𝐃\\mathbf\{D\}to denote the degree matrix,𝐀~=𝐃−1/2​𝐀𝐃−1/2\\tilde\{\\mathbf\{A\}\}=\\mathbf\{D\}^\{\-1/2\}\\mathbf\{A\}\\mathbf\{D\}^\{\-1/2\}for the symmetric\-normalized adjacency, and𝒩​\(i\)\\mathcal\{N\}\(i\)for the graph neighbors of nodeii\.

#### MAG Clustering\.

We consider MAG clustering under heterogeneous modality quality, where, for an unknown subset of nodes, a modality is either absent \(its absence is observable\) or present but uninformative \(its unreliability is latent and must be inferred\)\. The goal is to partition theNNnodes intoKKclusters without labels, producing a hard assignmenty^i∈\{1,…,K\}\\hat\{y\}\_\{i\}\\in\\\{1,\\dots,K\\\}for every nodeii\.

#### Reliability Field\.

We define a node\-specific*modality reliability field*ρi,m∈\[0,1\]\\rho\_\{i,m\}\\in\[0,1\]that captures how trustworthy modalitymmis for nodeii, normalized per node so that∑m∈ℳρi,m=1\\sum\_\{m\\in\\mathcal\{M\}\}\\rho\_\{i,m\}=1\. Notably, a larger value indicates higher reliability\.

## 4Methodology

![Refer to caption](https://arxiv.org/html/2608.00621v1/x1.png)Figure 1:Overview of RHEA\. RHEA consists of four stages: \(1\)Estimation: learning node\-specific modality reliability from neighbor consensus; \(2\)Representation: reconstructing unreliable modalities and performing reliability\-aware fusion; \(3\)Clustering: obtaining topology\-consistent assignments through reliability\-aware optimal transport; and \(4\)Optimization: jointly training clustering and representation objectives\. A unified reliability field connects all stages\.In this section, we present RHEA, a reliability\-aware framework for robust multimodal graph clustering\. As illustrated in Fig\.[1](https://arxiv.org/html/2608.00621#S4.F1), RHEA estimates node\-specific modality reliability from neighborhood consensus in a fully unsupervised manner, and propagates this reliability field throughout representation learning, fusion, and clustering\.

### 4\.1Neighbor\-Consensus Reliability Estimation

RHEA is built upon the observation that modality reliability is inherently node\-specific\. Rather than assuming that each modality is equally reliable across all nodes, we estimate a node\-specific modality reliability field based on neighborhood consensus\. Under attribute homophily, reliable modalities should be consistent with the semantic evidence provided by neighboring nodes, whereas corrupted modalities tend to deviate from this consensus\.

Specifically, let𝐳i\(m\)=fm​\(𝐗\(m\),𝐀\)∈ℝd\\mathbf\{z\}^\{\(m\)\}\_\{i\}=f\_\{m\}\(\\mathbf\{X\}^\{\(m\)\},\\mathbf\{A\}\)\\in\\mathbb\{R\}^\{d\}be theℓ2\\ell\_\{2\}\-normalized embedding of nodeiiin modalitymmfrom the per\-modality graph encoderfmf\_\{m\}\(e\.g\., GCN\(Kipf and Welling[2017](https://arxiv.org/html/2608.00621#bib.bib34)\)or GAT\(Veličkovićet al\.[2018](https://arxiv.org/html/2608.00621#bib.bib35)\)\)\. For nodeiiand modalitymm, we measure the intra\-modal neighbor agreement, which can be calculated as follows:

ai,m=1\|𝒩​\(i\)\|​∑j∈𝒩​\(i\)⟨𝐳i\(m\),𝐳j\(m\)⟩,a\_\{i,m\}\\;=\\;\\frac\{1\}\{\|\\mathcal\{N\}\(i\)\|\}\\sum\_\{j\\in\\mathcal\{N\}\(i\)\}\\big\\langle\\mathbf\{z\}^\{\(m\)\}\_\{i\},\\,\\mathbf\{z\}^\{\(m\)\}\_\{j\}\\big\\rangle,\(1\)where⟨⋅,⋅⟩\\langle\\cdot,\\cdot\\rangleis cosine similarity on theℓ2\\ell\_\{2\}\-normalized embeddings\. The agreement score measures how consistently modalitymmof nodeiialigns with its local neighborhood under structural homophily\.

Subsequently, we convert the per\-modality agreements into a per\-node reliability, which is formulated as:

ρi,m=exp⁡\(ai,m/τ\)∑m′∈ℳexp⁡\(ai,m′/τ\),\\rho\_\{i,m\}\\;=\\;\\frac\{\\exp\(a\_\{i,m\}/\\tau\)\}\{\\sum\_\{m^\{\\prime\}\\in\\mathcal\{M\}\}\\exp\(a\_\{i,m^\{\\prime\}\}/\\tau\)\},\(2\)whereτ\\tauis a temperature,ρi,m∈\[0,1\]\\rho\_\{i,m\}\\in\[0,1\]and∑mρi,m=1\\sum\_\{m\}\\rho\_\{i,m\}=1\. The resultingρi,m\\rho\_\{i,m\}defines a probability distribution over modalities for each node, which serves as the unified reliability field for downstream learning\.

### 4\.2Reliability\-Aware Representation Learning

The estimated reliability identifies modalities that cannot be reliably used for representation learning\. RHEA first reconstructs unreliable modalities from their graph neighborhoods, allowing neighborhood consensus to compensate for missing or corrupted observations before multimodal fusion\.

Without loss of generality, we describe the reconstruction procedure for the image modality; the same process is applied symmetrically to all modalities \(Appendix[B](https://arxiv.org/html/2608.00621#A2.SS0.SSS0.Px2)\)\. Reconstruction is triggered under two conditions: \(1\) the modality is missing, or \(2\) the modality is observed but assigned low reliability\. Accordingly, the reconstruction set is defined as:

ℛ=\{i:oi=0∨ρi,img<γ\},\\mathcal\{R\}=\\\{i:o\_\{i\}=0\\;\\vee\\;\\rho\_\{i,\\mathrm\{img\}\}<\\gamma\\\},\(3\)whereoi∈\{0,1\}o\_\{i\}\\in\\\{0,1\\\}indicates whether the image modality of nodeiiis observed andγ\\gammadenotes the reliability threshold\.

For every nodei∈ℛi\\in\\mathcal\{R\}, the unreliable image representation is reconstructed by aggregating image embeddings from neighboring nodes with available observations:

𝐳^i\(img\)=∑j∈𝒩\+​\(i\)𝐀~i​j​𝐳j\(img\)∑j∈𝒩\+​\(i\)𝐀~i​j,i∈ℛ,\\hat\{\\mathbf\{z\}\}^\{\(\\mathrm\{img\}\)\}\_\{i\}=\\frac\{\\sum\_\{j\\in\\mathcal\{N\}^\{\+\}\(i\)\}\\tilde\{\\mathbf\{A\}\}\_\{ij\}\\,\\mathbf\{z\}^\{\(\\mathrm\{img\}\)\}\_\{j\}\}\{\\sum\_\{j\\in\\mathcal\{N\}^\{\+\}\(i\)\}\\tilde\{\\mathbf\{A\}\}\_\{ij\}\},\\qquad i\\in\\mathcal\{R\},\(4\)where𝒩\+​\(i\)=\{j∈𝒩​\(i\):oj=1\}\\mathcal\{N\}^\{\+\}\(i\)=\\\{j\\in\\mathcal\{N\}\(i\):o\_\{j\}=1\\\}contains only neighbors with observed image modalities\. Restricting message passing to observed neighbors prevents missing or corrupted representations from propagating through the graph while preserving the neighborhood consensus\.

The reliability of each reconstruction further depends on the quality of its supporting neighbors\. We therefore estimate a reconstruction confidenceci=exp⁡\(−β​vi\)⋅wiwi\+1c\_\{i\}=\\exp\(\-\\beta v\_\{i\}\)\\cdot\\frac\{w\_\{i\}\}\{w\_\{i\}\+1\}, whereβ\>0\\beta\>0is a decay coefficient,wi=∑j∈𝒩\+​\(i\)𝐀~i​jw\_\{i\}=\\sum\_\{j\\in\\mathcal\{N\}^\{\+\}\(i\)\}\\tilde\{\\mathbf\{A\}\}\_\{ij\}measures the available neighborhood evidence, andviv\_\{i\}is the mean per\-dimension variance of the donor embeddings\. Consequently, reconstruction confidence increases when more neighboring observations are available and their representations are mutually consistent, and decreases otherwise\. This confidence serves as an absolute reliability measure that complements the relative reliability and is subsequently incorporated into the topology\-aware clustering objective \(Sec\.[4\.3](https://arxiv.org/html/2608.00621#S4.SS3)\)\.

Finally, the reconstructed modality representations are fused according to the estimated modality reliability:

𝐳i=ρi,txt​𝐳i\(txt\)\+ρi,img​𝐳~i\(img\),\\mathbf\{z\}\_\{i\}=\\rho\_\{i,\\mathrm\{txt\}\}\\mathbf\{z\}^\{\(\\mathrm\{txt\}\)\}\_\{i\}\+\\rho\_\{i,\\mathrm\{img\}\}\\tilde\{\\mathbf\{z\}\}^\{\(\\mathrm\{img\}\)\}\_\{i\},\(5\)where𝐳~i\(img\)\\tilde\{\\mathbf\{z\}\}^\{\(\\mathrm\{img\}\)\}\_\{i\}is the image representation used for downstream fusion\. Specifically, when nodeiiis identified as unreliable or missing \(i∈ℛi\\in\\mathcal\{R\}\), its image feature is substituted by the reconstructed embedding𝐳^i\(img\)\\hat\{\\mathbf\{z\}\}^\{\(\\mathrm\{img\}\)\}\_\{i\}; otherwise, the original observed embedding𝐳i\(img\)\\mathbf\{z\}^\{\(\\mathrm\{img\}\)\}\_\{i\}is retained\.

### 4\.3Reliability\-Aware Clustering

At the core of RHEA is a reliability\-aware clustering mechanism that turns the estimated modality reliability into the actual cluster assignments\. It comprises two coupled components: a reliability\-aware optimal transport assignment that lets reliable modalities dominate the transport cost \(Eq\. \([7](https://arxiv.org/html/2608.00621#S4.E7)\)\), and a neighbor\-consensus assignment distillation objective that repairs assignments where neighborhood evidence is weak \(Eq\. \([9](https://arxiv.org/html/2608.00621#S4.E9)\)\)\. Together they constitute the primary learning signal of our model\.

#### Reliability\-aware Optimal Transport\.

The estimated reliability is incorporated into cluster assignment\. Since multimodal representations have already been reconstructed and fused according to their estimated reliability \(Sec\.[4\.2](https://arxiv.org/html/2608.00621#S4.SS2)\), we first smooth the fused node embeddings over the graph to integrate local topological context before clustering,𝐡i=norm​\(∑j𝐀~i​j​𝐳j\)\\mathbf\{h\}\_\{i\}=\\mathrm\{norm\}\(\\sum\\nolimits\_\{j\}\\tilde\{\\mathbf\{A\}\}\_\{ij\}\\mathbf\{z\}\_\{j\}\), wherenorm​\(⋅\)\\mathrm\{norm\}\(\\cdot\)isℓ2\\ell\_\{2\}normalization\. Cluster assignments are then obtained by solving an entropy\-regularized optimal transport problem between node embeddings andKKlearnable cluster prototypes\{𝝁k\}\\\{\\boldsymbol\{\\mu\}\_\{k\}\\\}\. The transport cost is defined as follows:

𝐂i​k=1−⟨𝐡i,𝝁k⟩,\\mathbf\{C\}\_\{ik\}=1\-\\langle\\mathbf\{h\}\_\{i\},\\boldsymbol\{\\mu\}\_\{k\}\\rangle,\(6\)where𝐡i\\mathbf\{h\}\_\{i\}already encodes the node\-specific modality reliability through Eq\. \([5](https://arxiv.org/html/2608.00621#S4.E5)\)\. Consequently, unreliable modalities contribute less to the transport cost and exert reduced influence on the resulting cluster assignment\. The optimal transport plan is then computed as:

𝐏⋆=arg​min𝐏∈Π​\(𝐫,𝐜\)⁡⟨𝐏,𝐂⟩−ϵ​H​\(𝐏\),\\mathbf\{P\}^\{\\star\}=\\operatorname\*\{arg\\,min\}\_\{\\mathbf\{P\}\\in\\Pi\(\\mathbf\{r\},\\mathbf\{c\}\)\}\\;\\langle\\mathbf\{P\},\\mathbf\{C\}\\rangle\-\\epsilon H\(\\mathbf\{P\}\),\(7\)whereH​\(⋅\)H\(\\cdot\)denotes the entropy regularizer,ϵ\\epsilonis the regularization strength, andΠ​\(𝐫,𝐜\)\\Pi\(\\mathbf\{r\},\\mathbf\{c\}\)denotes the transport polytope with row and column marginals\. Crucially, both marginals are made reliability\-aware\. To account for reconstruction uncertainty, the row marginal is weighted by the reconstruction confidence \(i\.e\.,ri∝cir\_\{i\}\\propto c\_\{i\}\) such that nodes reconstructed from limited or inconsistent neighborhood evidence contribute less transport mass; the column marginal𝐜\\mathbf\{c\}is estimated from the graph topology to reflect the empirical cluster\-size prior rather than assuming uniform cluster proportions\. The optimization problem in Eq\. \([7](https://arxiv.org/html/2608.00621#S4.E7)\) can be solved using entropic Sinkhorn iterations\(Cuturi[2013](https://arxiv.org/html/2608.00621#bib.bib32)\)\.

The clustering objective is then defined as follows:

ℒclu=⟨𝐏⋆,𝐂⟩,\\mathcal\{L\}\_\{\\mathrm\{clu\}\}=\\langle\\mathbf\{P\}^\{\\star\},\\mathbf\{C\}\\rangle,\(8\)where𝐏⋆\\mathbf\{P\}^\{\\star\}is treated as a fixed target via stop\-gradient, and the final cluster assignment is obtained asy^i=arg⁡maxk⁡Pi​k⋆\\hat\{y\}\_\{i\}=\\arg\\max\_\{k\}P^\{\\star\}\_\{ik\}\.

#### Neighbor\-consensus Assignment Distillation \(NCRC\)\.

Although reliability\-aware optimal transport substantially improves assignment robustness, reconstructed nodes may still receive inaccurate assignments when neighborhood evidence is insufficient\. We therefore introduce a neighbor\-consensus assignment distillation objective that further regularizes cluster assignments using neighborhood consensus\. Specifically, let𝐪i=softmax​\(⟨𝐡i,𝝁⟩/τa\)\\mathbf\{q\}\_\{i\}=\\mathrm\{softmax\}\\\!\\left\(\\langle\\mathbf\{h\}\_\{i\},\\boldsymbol\{\\mu\}\\rangle/\\tau\_\{a\}\\right\)denote the soft cluster assignment, with assignment temperatureτa\\tau\_\{a\}\. The assignments are propagated over the graph forLLhops,𝐪~=𝐀~L​𝐪\\tilde\{\\mathbf\{q\}\}=\\tilde\{\\mathbf\{A\}\}^\{L\}\\mathbf\{q\}, and sharpened to a neighbor\-consensus targetq~i​ksharp∝q~i​k1/Ts\\tilde\{q\}^\{\\mathrm\{sharp\}\}\_\{ik\}\\propto\\tilde\{q\}\_\{ik\}^\{1/T\_\{s\}\}\(Ts<1T\_\{s\}\{<\}1, renormalized per node\)\. Each node is then distilled toward this consensus via:

ℒncrc=−1N​∑i∑ksg​\[q~i​ksharp\]​log⁡qi​k,\\mathcal\{L\}\_\{\\mathrm\{ncrc\}\}=\-\\frac\{1\}\{N\}\\sum\_\{i\}\\sum\_\{k\}\\mathrm\{sg\}\\\!\\left\[\\tilde\{q\}^\{\\mathrm\{sharp\}\}\_\{ik\}\\right\]\\log q\_\{ik\},\(9\)wheresg​\[⋅\]\\mathrm\{sg\}\[\\cdot\]denotes the stop\-gradient operator\. This objective encourages locally consistent cluster assignments while preventing the propagated consensus target from being updated by the student predictions\.

### 4\.4Optimization Objectives

The clustering objectives introduced above provide the primary supervision signal\. Since reliability estimation depends on encoder representations, we further regularize the encoder with two lightweight auxiliary contrastive objectives defined on the fused embeddings𝐡\\mathbf\{h\}\. These objectives improve representation quality without directly affecting cluster assignment\.

#### Auxiliary contrastive regularization\.

We first introduce a graph\-walk\-based contrastive lossℒnbr\\mathcal\{L\}\_\{\\mathrm\{nbr\}\}, which preserves topology\-aware invariance by enforcing agreement between random\-walk co\-occurrence pairs\. Given an anchor nodeii, its positive set𝒫i\\mathcal\{P\}\_\{i\}and negative set𝒬i\\mathcal\{Q\}\_\{i\}are constructed from random walks \(walk length 5, 10 walks per node, context window 3\)\. We then optimize an InfoNCE objective with temperatureτc\\tau\_\{c\}over the fused representation𝐡\\mathbf\{h\}:

ℒnbr=−1N​∑i1\|𝒫i\|​∑j∈𝒫ilog⁡e⟨𝐡i,𝐡j⟩/τc∑k∈𝒫i∪𝒬ie⟨𝐡i,𝐡k⟩/τc\.\\mathcal\{L\}\_\{\\mathrm\{nbr\}\}=\-\\frac\{1\}\{N\}\\sum\_\{i\}\\frac\{1\}\{\|\\mathcal\{P\}\_\{i\}\|\}\\sum\_\{j\\in\\mathcal\{P\}\_\{i\}\}\\log\\frac\{e^\{\\langle\\mathbf\{h\}\_\{i\},\\mathbf\{h\}\_\{j\}\\rangle/\\tau\_\{c\}\}\}\{\\sum\_\{k\\in\\mathcal\{P\}\_\{i\}\\cup\\mathcal\{Q\}\_\{i\}\}e^\{\\langle\\mathbf\{h\}\_\{i\},\\mathbf\{h\}\_\{k\}\\rangle/\\tau\_\{c\}\}\}\.\(10\)
We further introduce a cross\-modal alignment lossℒmod\\mathcal\{L\}\_\{\\mathrm\{mod\}\}, which aligns modality\-specific representations with the fused embedding after reliability\-aware fusion\. Let𝐳i\(txt\)\\mathbf\{z\}^\{\(\\mathrm\{txt\}\)\}\_\{i\}and𝐳~i\(img\)\\tilde\{\\mathbf\{z\}\}^\{\(\\mathrm\{img\}\)\}\_\{i\}denote the text and \(possibly reconstructed\) image representations, respectively\. The alignment objective is defined as follows:

ℒmod=1N​∑i\[2−⟨𝐡i,𝐳i\(txt\)⟩−⟨𝐡i,𝐳~i\(img\)⟩\]\+Ωcm,\\mathcal\{L\}\_\{\\mathrm\{mod\}\}=\\frac\{1\}\{N\}\\sum\_\{i\}\\big\[2\-\\langle\\mathbf\{h\}\_\{i\},\\mathbf\{z\}^\{\(\\mathrm\{txt\}\)\}\_\{i\}\\rangle\-\\langle\\mathbf\{h\}\_\{i\},\\tilde\{\\mathbf\{z\}\}^\{\(\\mathrm\{img\}\)\}\_\{i\}\\rangle\\big\]\+\\Omega\_\{\\mathrm\{cm\}\},\(11\)whereΩcm\\Omega\_\{\\mathrm\{cm\}\}is a small inter\-node repulsion term that discourages trivial collapse by enforcing margin separation across nodes \(Detailed in Appendix[E](https://arxiv.org/html/2608.00621#A5)\)\.

#### Joint objective\.

The model is trained end\-to\-end by minimizing the following optimization objective:

ℒ=ℒclu\+λncrc​ℒncrc\+λnbr​ℒnbr\+λmod​ℒmod\.\\mathcal\{L\}=\\mathcal\{L\}\_\{\\mathrm\{clu\}\}\+\\lambda\_\{\\mathrm\{ncrc\}\}\\mathcal\{L\}\_\{\\mathrm\{ncrc\}\}\+\\lambda\_\{\\mathrm\{nbr\}\}\\mathcal\{L\}\_\{\\mathrm\{nbr\}\}\+\\lambda\_\{\\mathrm\{mod\}\}\\mathcal\{L\}\_\{\\mathrm\{mod\}\}\.\(12\)The first two terms constitute the core clustering objective, combining reliability\-aware optimal transport assignment \(ℒclu\\mathcal\{L\}\_\{\\mathrm\{clu\}\}\) and neighbor\-consensus assignment distillation \(ℒncrc\\mathcal\{L\}\_\{\\mathrm\{ncrc\}\}\)\. The remaining terms act as auxiliary representation regularizers that improve encoder robustness, withλnbr\\lambda\_\{\\mathrm\{nbr\}\}andλmod\\lambda\_\{\\mathrm\{mod\}\}controlling their influence, whileλncrc\\lambda\_\{\\mathrm\{ncrc\}\}balances the two clustering losses\. Algorithm[1](https://arxiv.org/html/2608.00621#algorithm1)summarizes the procedure\.

Table 1:Performance under standard settings on 4 MAG datasets\. Thebest,second, andthirdresults are marked in bold, underline, and italics, respectively\.1

Input:Multimodal graph

G=\(𝒱,𝐀,\{𝐗\(m\)\}\)G=\(\\mathcal\{V\},\\mathbf\{A\},\\\{\\mathbf\{X\}^\{\(m\)\}\\\}\), cluster number

KK, reliability threshold

γ\\gamma, temperatures

τ\\tau,

τa\\tau\_\{a\}\.

2

3initialize modality encoders

\{fm\}\\\{f\_\{m\}\\\}and cluster prototypes

\{𝝁k\}\\\{\\boldsymbol\{\\mu\}\_\{k\}\\\};

4

5while*not converged*do

6

/\*Neighbor\-Consensus Reliability Estimation \*/

7

8compute modality embeddings

\{𝐙\(m\)\}\\\{\\mathbf\{Z\}^\{\(m\)\}\\\};

9

10compute neighbor agreement

ai,ma\_\{i,m\}and modality reliability

ρi,m\\rho\_\{i,m\}via Eq\. \([1](https://arxiv.org/html/2608.00621#S4.E1)\)–\([2](https://arxiv.org/html/2608.00621#S4.E2)\);

11

/\*Reliability\-Aware Representation Learning \*/

12

13identify unreliable or missing modalities via Eq\. \([3](https://arxiv.org/html/2608.00621#S4.E3)\);

14

15reconstruct unreliable representations and estimate reconstruction confidence via Eq\. \([4](https://arxiv.org/html/2608.00621#S4.E4)\);

16

17obtain reliability\-aware fused embeddings

𝐳\\mathbf\{z\}via Eq\. \([5](https://arxiv.org/html/2608.00621#S4.E5)\);

18

/\*Reliability\-Aware Clustering \*/

19

20compute topology\-aware embeddings

𝐡\\mathbf\{h\};

21

22solve reliability\-aware optimal transport via Eq\. \([7](https://arxiv.org/html/2608.00621#S4.E7)\);

23

24compute neighbor\-consensus assignments via Eq\. \([9](https://arxiv.org/html/2608.00621#S4.E9)\);

25

26optimize the joint objective in Eq\. \([12](https://arxiv.org/html/2608.00621#S4.E12)\) and update model parameters\.

27end while

28

Output:Cluster assignments

\{y^i\}i=1N\\\{\\hat\{y\}\_\{i\}\\\}\_\{i=1\}^\{N\}\.

29

Algorithm 1Overall Procedure ofRHEA

## 5Experiments

In this section, we conduct a comprehensive evaluation of RHEA\. We first describe the experimental settings \(Sec\.[5\.1](https://arxiv.org/html/2608.00621#S5.SS1)\), and then answer the following research questions:RQ1:Is RHEA competitive with state\-of\-the\-art baselines under clean and complete MAGs \(Sec\.[5\.2](https://arxiv.org/html/2608.00621#S5.SS2)\)?RQ2:Does RHEA consistently outperform existing methods when modalities are corrupted or partially missing \(Sec\.[5\.3](https://arxiv.org/html/2608.00621#S5.SS3)\)?RQ3:What are the individual contributions of each module in RHEA to the overall robustness gains \(Sec\.[5\.4](https://arxiv.org/html/2608.00621#S5.SS4)\)?RQ4:How stable are RHEA’s performance gains under different hyperparameter settings and perturbation intensities \(Sec\.[5\.5](https://arxiv.org/html/2608.00621#S5.SS5)\)?RQ5:Does the reliability field track real corruption, and what does it reveal about how RHEA works \(Sec\.[5\.6](https://arxiv.org/html/2608.00621#S5.SS6)\)? Computational cost and complexity are analyzed in Appendix[E](https://arxiv.org/html/2608.00621#A5)\.

### 5\.1Experimental Setup

#### Datasets\.

We evaluate RHEA on four public MAG datasets: the social network RedditS\(Desaiet al\.[2021](https://arxiv.org/html/2608.00621#bib.bib56)\), two e\-commerce networks \(Toys and Grocery\)\(Niet al\.[2019](https://arxiv.org/html/2608.00621#bib.bib57)\), and the co\-purchase graph Amazon\(Guoet al\.[2025](https://arxiv.org/html/2608.00621#bib.bib2)\)\. Detailed statistics and descriptions are in Appendix[G](https://arxiv.org/html/2608.00621#A7)\.

#### Baselines\.

We compare RHEA against four categories of representative baselines\. \(1\)Classical clustering methods, which perform clustering solely based on node representations without exploiting graph topology, including KMeans\. \(2\)General attributed graph clustering methods, which leverage graph structure and node attributes but do not explicitly model multimodal reliability, including DFCN\(Tuet al\.[2021](https://arxiv.org/html/2608.00621#bib.bib10)\), DMoN\(Tsitsulinet al\.[2023](https://arxiv.org/html/2608.00621#bib.bib23)\), MVGRL\(Hassani and Khasahmadi[2020](https://arxiv.org/html/2608.00621#bib.bib17)\)and S3GC\(Devvritet al\.[2022](https://arxiv.org/html/2608.00621#bib.bib18)\)\. \(3\)Incomplete multi\-view clustering methods, which are specifically designed to handle missing\-view scenarios, including COMPLETER\(Linet al\.[2021](https://arxiv.org/html/2608.00621#bib.bib27)\)and APADC\(Xuet al\.[2023](https://arxiv.org/html/2608.00621#bib.bib28)\)\. \(4\)MAG clustering methods, which jointly exploit graph topology and multiple modalities for clustering\. These are our primary comparison methods, including DGF\(Zhenget al\.[2025](https://arxiv.org/html/2608.00621#bib.bib1)\)and DMGC\(Guoet al\.[2025](https://arxiv.org/html/2608.00621#bib.bib2)\)\. All baselines are implemented using their official codebases under an identical experimental protocol; per\-baseline descriptions are in Appendix[H](https://arxiv.org/html/2608.00621#A8)\. We report NMI, ACC, ARI, and F1 \(defined in Appendix[I](https://arxiv.org/html/2608.00621#A9)\) as the mean over five seeds under the protocol of Appendix[F\.1](https://arxiv.org/html/2608.00621#A6.SS1)\.

### 5\.2Performance under Standard Setting

To answerRQ1, we evaluate clustering quality on all four benchmarks in the standard setting, where every modality is complete and uncorrupted\. The results are summarized in Table[1](https://arxiv.org/html/2608.00621#S4.T1)\. We summarize our observations as follows\.

#### RHEA consistently achieves the best performance\.

RHEA attains the best result on all four datasets across every evaluation metric, demonstrating its effectiveness in the clean, full\-modality setting\. On RedditS it clearly outperforms the strongest baseline DGF \(NMI:0\.8680\.868vs\.0\.8360\.836; ARI:0\.8690\.869vs\.0\.8110\.811\), and on Grocery and Amazon it surpasses the second\-best method by0\.0340\.034and0\.0360\.036in NMI, respectively\. RHEA also maintains consistently low standard deviations, in contrast to methods such as DMoN and APADC, which show high variance and on the harder datasets cluster little better than chance\. This stability indicates that the neighbor\-consensus reliability estimation converges to a stable fusion solution \(Appendix[F\.3](https://arxiv.org/html/2608.00621#A6.SS3)\)\.

![Refer to caption](https://arxiv.org/html/2608.00621v1/x2.png)Figure 2:NMI vs\. perturbation severity on RedditS\. Each panel varies one perturbation regime\.
#### RHEA is particularly effective on complex MAGs\.

The advantage of multimodal fusion is most pronounced on benchmarks with many categories, such as Toys \(1818clusters\) and Grocery \(2020clusters\)\. On Grocery, RHEA reaches an NMI of0\.4900\.490, well above the deep attributed clusterer DFCN \(0\.4020\.402\) and the multimodal competitor DGF \(0\.4560\.456\), showing its capacity to synthesize complementary information across views\. Amazon is a special case: with only three clusters and highly discriminative attributes, even strong baselines such as KMeans \(0\.3580\.358\) and DFCN \(0\.3810\.381\) are competitive\. Even there, RHEA still ranks first \(0\.4170\.417NMI\), confirming that its reliability\-guided fusion remains beneficial when simpler baselines are already strong\.

### 5\.3Robustness to Modality Perturbation

To evaluateRQ2, we degrade one modality while keeping the other intact\. Table[2](https://arxiv.org/html/2608.00621#S5.T2)reports NMI across five settings, including clean data, image and text corruption withη=0\.4\\eta=0\.4, and image and text missingness withm=0\.5m=0\.5\. Results for other metrics are in Appendix[A](https://arxiv.org/html/2608.00621#A1)\(Tables[5](https://arxiv.org/html/2608.00621#A1.T5)–[7](https://arxiv.org/html/2608.00621#A1.T7)\)\. Fig\.[2](https://arxiv.org/html/2608.00621#S5.F2)illustrates performance trends as perturbation severity increases\.

#### Overall performance\.

RHEA achieves the highest NMI across all configurations \(4 datasets×\\times5 settings, 20 cases\), consistently outperforming all baselines under both corruption and missingness\. The average margin over DGF increases from\+0\.04\+0\.04in clean conditions to\+0\.07\+0\.07under image corruption,\+0\.08\+0\.08under image missingness, and∼\+0\.07\\sim\+0\.07under text perturbations, indicating stronger robustness under modality degradation\.

#### Robustness under increasing perturbation\.

All methods degrade as perturbation severity increases, while RHEA exhibits the slowest performance drop\. On RedditS, its NMI decreases from0\.8680\.868to0\.7290\.729whenm=0\.8m=0\.8, whereas DGF drops from0\.8360\.836to0\.6470\.647, increasing the performance gap from\+0\.03\+0\.03to\+0\.08\+0\.08\. Similar trends hold across datasets and perturbation types, as shown in Figure[2](https://arxiv.org/html/2608.00621#S5.F2)\. These results indicate that modeling node\-wise reliability improves stability under severe modality degradation\.

Table 2:Robustness \(NMI\) across standard, image\-, and text\-modality perturbation\. Image/text corruptionη=0\.4\\eta\{=\}0\.4, missingm=0\.5m\{=\}0\.5\.

### 5\.4Ablation Study

To answerRQ3, we remove each component of RHEA in turn and report mean NMI across the four datasets under the clean, corruption, and missing\-modality regimes \(Table[3](https://arxiv.org/html/2608.00621#S5.T3)\)\. Each component contributes most in the regime it is designed for\.

Table 3:Component ablation across regimes \(mean NMI±\\pmstd; four datasets, five seeds; image corruptionη=0\.4\\eta\{=\}0\.4, missingm=0\.5m\{=\}0\.5\)\. Each row removes one component from full RHEA; the last removes all \(only backbone\)\.Reconstruction dominates the missing regime and the reliability gate the corrupted one\.Removing the gated reconstruction lowers mean NMI by0\.0610\.061under missingness but by only0\.0040\.004when modalities are clean, the sharpest regime contrast of any component, and recovers most of RHEA’s advantage over the bare backbone there, which is why its lead over DGF is widest under missing modalities \(Sec\.[5\.3](https://arxiv.org/html/2608.00621#S5.SS3)\)\. The reliability gate makes that reconstruction selective: reconstructing every modality rather than only the ones the field flags as unreliable costs0\.0500\.050NMI under corruption, the largest gate\-sensitive drop, because overwriting an already\-reliable modality injects noise; under missingness the gate matters less \(0\.0150\.015\), since an absent modality is always flagged\. The field thus helps mainly by deciding which modality to repair, a role examined further in Sec\.[5\.6](https://arxiv.org/html/2608.00621#S5.SS6)\.

The clean base comes from assignment distillation over the shared backbone\.Neighbor\-consensus assignment distillation \(NCRC\) is the most useful clean\-regime component outside the repair pathway \(0\.0190\.019NMI when removed\); with every component off, NMI falls to the DGF\-level backbone \(0\.5180\.518/0\.4370\.437/0\.4420\.442for clean/corruption/missing\), so the clean\-setting accuracy rests on NCRC over that backbone while the repair mechanisms above add the missing\-modality robustness on top\. Reliability\-weighted fusion and the confidence\-shrunk optimal\-transport marginal only refine the result \(each at most0\.0160\.016\); the choice of reconstruction operator and the generality of the mechanism across text, joint, and asymmetric degradation are in Appendix[B](https://arxiv.org/html/2608.00621#A2)\.

### 5\.5Sensitivity Analysis

To answerRQ4, we check that the gains are stable across RHEA’s four main hyperparameters: the entropic\-OT strengthϵ\\epsilon, the number of Sinkhorn iterations, the reconstruction gate thresholdγ\\gamma, and the reliability temperatureτ\\tau\(Table[4](https://arxiv.org/html/2608.00621#S5.T4)\)\. We sweep each in the clean setting and under missing modalities \(m=0\.5m\{=\}0\.5\), the regime where RHEA’s advantage is largest and its components contribute most \(Sec\.[5\.3](https://arxiv.org/html/2608.00621#S5.SS3)and[5\.4](https://arxiv.org/html/2608.00621#S5.SS4)\); the corruption regime is intermediate, so these two settings bracket the operating range\. Across every sweep NMI stays within a narrow band around the default: a2020\-fold change inϵ\\epsilonshifts it by at most0\.0200\.020, Sinkhorn iterations andτ\\tauby at most0\.0060\.006\. The gateγ\\gamma\(swept over\[0\.30,0\.65\]\[0\.30,0\.65\]around its default0\.450\.45\) is the most regime\-sensitive knob—its band widens from0\.0080\.008\(clean\) to0\.0220\.022under missingness, where it decides which modality to repair—yet the default still sits near the top of the band rather than at a sharp optimum, so RHEA needs no per\-dataset tuning; homophily sensitivity is in Appendix[C](https://arxiv.org/html/2608.00621#A3)\.

Table 4:Hyperparameter sensitivity on RedditS \(NMI\)\. Each row sweeps one hyperparameter over the listed range with all others fixed at their default \(in parentheses\); clean and missingm=0\.5m\{=\}0\.5regimes\.
### 5\.6Interpretability Investigation

To answerRQ5, we test what the reliability field learns and how it shapes the embedding through synthetic\-corruption recoverability: we inject corruption into a known subset of nodes and ask, without supervision, whether the field recovers it\. The detector\(1−ρi,img\)\(1\-\\rho\_\{i,\\mathrm\{img\}\}\)separates injected\-corrupt from clean nodes at AUROC0\.9580\.958–0\.9820\.982across all four benchmarks, rising with the corruption severityη\\eta\(Fig\.[3](https://arxiv.org/html/2608.00621#S5.F3)a\); restricting to the clean\-neighbor stratum, where a majority vote has nothing corrupt to imitate, it still scores0\.920\.92–0\.960\.96\(Fig\.[3](https://arxiv.org/html/2608.00621#S5.F3)b\), so it reads each node’s own corruption rather than echoing its neighborhood\. Accurate detection turns into a clustering gain only through repair: the improvement under corruption is smaller and more dataset\-dependent than under missingness \(Sec\.[5\.3](https://arxiv.org/html/2608.00621#S5.SS3)\), because repair acts only on gate\-flagged nodes: an absent modality is always flagged and replaced by the neighbor average \(Eq\.[4](https://arxiv.org/html/2608.00621#S4.E4)\), while sub\-threshold corruption is retained\. This is visible in the embedding \(Fig\.[4](https://arxiv.org/html/2608.00621#S5.F4)\): clusters are well separated in the standard setting, preserved under50%50\\%image missingness when reconstruction is on, and collapse together when it is off, corroborating the ablation \(Sec\.[5\.4](https://arxiv.org/html/2608.00621#S5.SS4)\) that graph\-neighbor reconstruction underlies the missing\-modality robustness\.

![Refer to caption](https://arxiv.org/html/2608.00621v1/x3.png)Figure 3:Synthetic\-corruption recoverability of the reliability field \(corruption regime\)\. \(a\) AUROC of\(1−ρi,img\)\(1\-\\rho\_\{i,\\mathrm\{img\}\}\)vs\. injected corruptionη\\eta, per dataset\. \(b\) AUROC stratified by clean\- vs\. corrupt\-neighbor nodes \(η=0\.4\\eta\{=\}0\.4\)\.![Refer to caption](https://arxiv.org/html/2608.00621v1/x4.png)Figure 4:t\-SNE of RHEA fused embeddings on RedditS\. \(a\) standard setting; \(b\) missingm=0\.5m\{=\}0\.5with reconstruction; \(c\) missingm=0\.5m\{=\}0\.5without reconstruction\.

## 6Conclusion

We presented RHEA, a multimodal graph clustering framework that estimates node\-level modality reliability from neighborhood consensus, enabling adaptive feature reconstruction, reliability\-aware reweighting of corrupted modalities, and topology\-aware cluster assignment\. Extensive experiments across diverse benchmarks and evaluation settings demonstrate that RHEA consistently outperforms competitive baselines, with particularly pronounced improvements under missing and corrupted modalities\. These findings highlight the importance of modeling node\-specific, graph\-induced reliability for robust multimodal representation learning and clustering, suggesting that local structural context provides an effective signal for identifying unreliable observations\. Future work will investigate extending the framework to low\-homophily and heterophilous graphs\.

## References

- D\. Bo, X\. Wang, C\. Shi, M\. Zhu, E\. Lu, and P\. Cui \(2020\)Structural deep clustering network\.InProceedings of The Web Conference \(WWW\),Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.
- J\. Chen, L\. Shi, and B\. Chen \(2025\)RSEA\-MVGNN: multi\-view graph neural network with reliable structural enhancement and aggregation\.Information Fusion121,pp\. 103143\.External Links:[Document](https://dx.doi.org/10.1016/j.inffus.2025.103143)Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px2.p1.1)\.
- G\. Cui, J\. Zhou, C\. Yang, and Z\. Liu \(2020\)Adaptive graph encoder for attributed graph embedding\.InProceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining \(KDD\),Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.
- M\. Cuturi \(2013\)Sinkhorn distances: lightspeed computation of optimal transport\.InAdvances in Neural Information Processing Systems \(NeurIPS\),Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px2.p1.1),[§4\.3](https://arxiv.org/html/2608.00621#S4.SS3.SSS0.Px1.p1.11)\.
- K\. Desai, G\. Kaul, Z\. T\. Aysola, and J\. Johnson \(2021\)RedCaps: web\-curated image\-text data created by the people, for the people\.InAdvances in Neural Information Processing Systems, NeurIPS, Datasets and Benchmarks Track, NeurIPS DB Track,Cited by:[Appendix G](https://arxiv.org/html/2608.00621#A7.SS0.SSS0.Px1.p1.2),[§5\.1](https://arxiv.org/html/2608.00621#S5.SS1.SSS0.Px1.p1.1)\.
- F\. Devvrit, A\. Sinha, I\. S\. Dhillon, and P\. Jain \(2022\)S3GC: scalable self\-supervised graph clustering\.InAdvances in Neural Information Processing Systems \(NeurIPS\),Cited by:[Appendix H](https://arxiv.org/html/2608.00621#A8.SS0.SSS0.Px5.p1.1),[§5\.1](https://arxiv.org/html/2608.00621#S5.SS1.SSS0.Px2.p1.1)\.
- Z\. Guo, Z\. Shen, X\. Xie, L\. Wen, and Z\. Kang \(2025\)Disentangling homophily and heterophily in multimodal graph clustering\.InProceedings of the 33rd ACM International Conference on Multimedia \(ACM MM\),Cited by:[Appendix G](https://arxiv.org/html/2608.00621#A7.SS0.SSS0.Px4.p1.3),[Appendix H](https://arxiv.org/html/2608.00621#A8.SS0.SSS0.Px9.p1.1),[§1](https://arxiv.org/html/2608.00621#S1.p1.1),[§1](https://arxiv.org/html/2608.00621#S1.p2.1),[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1),[§5\.1](https://arxiv.org/html/2608.00621#S5.SS1.SSS0.Px1.p1.1),[§5\.1](https://arxiv.org/html/2608.00621#S5.SS1.SSS0.Px2.p1.1)\.
- Z\. Han, C\. Zhang, H\. Fu, and J\. T\. Zhou \(2023\)Trusted multi\-view classification with dynamic evidential fusion\.IEEE Transactions on Pattern Analysis and Machine Intelligence\.Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px2.p1.1)\.
- K\. Hassani and A\. H\. Khasahmadi \(2020\)Contrastive multi\-view representation learning on graphs\.InProceedings of the 37th International Conference on Machine Learning \(ICML\),Cited by:[Appendix H](https://arxiv.org/html/2608.00621#A8.SS0.SSS0.Px4.p1.1),[§5\.1](https://arxiv.org/html/2608.00621#S5.SS1.SSS0.Px2.p1.1)\.
- L\. Hubert and P\. Arabie \(1985\)Comparing partitions\.Journal of Classification2\(1\),pp\. 193–218\.Cited by:[Appendix I](https://arxiv.org/html/2608.00621#A9.SS0.SSS0.Px3.p1.4)\.
- Y\. Jiang, L\. Xia, W\. Wei, D\. Luo, K\. Lin, and C\. Huang \(2024\)DiffMM: multi\-modal diffusion model for recommendation\.InProceedings of the 32nd ACM International Conference on Multimedia \(MM\),External Links:[Document](https://dx.doi.org/10.1145/3664647.3681498)Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px2.p1.1)\.
- G\. Ke, G\. Chao, X\. Wang, C\. Xu, and Y\. Yu \(2023\)A clustering\-guided contrastive fusion for multi\-view representation learning\.IEEE Transactions on Circuits and Systems for Video Technology\.Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.
- T\. N\. Kipf and M\. Welling \(2017\)Semi\-supervised classification with graph convolutional networks\.InInternational Conference on Learning Representations \(ICLR\),Cited by:[§4\.1](https://arxiv.org/html/2608.00621#S4.SS1.p2.7)\.
- H\. W\. Kuhn \(1955\)The hungarian method for the assignment problem\.Naval Research Logistics Quarterly2\(1\-2\),pp\. 83–97\.Cited by:[Appendix I](https://arxiv.org/html/2608.00621#A9.p1.3)\.
- B\. Li, Y\. Wang, B\. Zhao, H\. Gao, and B\. Yan \(2025a\)Attributed graph clustering with multi\-scale weight\-based pairwise coarsening and contrastive learning\.Neurocomputing\.Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.
- B\. Li, X\. Xiang, X\. Li, B\. Zhao, H\. Gao, and Q\. Yang \(2025b\)Tri\-learn graph fusion network for attributed graph clustering\.Pattern Analysis and Applications\.Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.
- X\. Li, Z\. Wu, Z\. Chen, H\. Sun, D\. Su, G\. Zeng, H\. Qin, R\. Li, and G\. Wang \(2026\)LION: a clifford neural paradigm for multimodal\-attributed graph learning\.arXiv preprint arXiv:2601\.21453\.Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.
- J\. Lin, M\. Chen, X\. Zhu, C\. Wang, and H\. Zhang \(2024\)Dual information enhanced multi\-view attributed graph clustering\.IEEE Transactions on Neural Networks and Learning Systems\.Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.
- R\. Lin and H\. Hu \(2022\)Multimodal contrastive learning via uni\-modal coding and cross\-modal prediction for multimodal sentiment analysis\.Findings of the Association for Computational Linguistics: EMNLP\.Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.
- Y\. Lin, Y\. Gou, Z\. Liu, B\. Li, J\. Lv, and X\. Peng \(2021\)COMPLETER: incomplete multi\-view clustering via contrastive prediction\.InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition \(CVPR\),Cited by:[Appendix H](https://arxiv.org/html/2608.00621#A8.SS0.SSS0.Px6.p1.1),[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px2.p1.1),[§5\.1](https://arxiv.org/html/2608.00621#S5.SS1.SSS0.Px2.p1.1)\.
- Y\. Liu, Y\. Zheng, D\. Zhang, H\. Chen, H\. Peng, and S\. Pan \(2022a\)Towards unsupervised deep graph structure learning\.InProceedings of the ACM Web Conference \(WWW\),Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.
- Y\. Liu, K\. Liang, J\. Xia, S\. Zhou, X\. Yang, X\. Liu, and S\. Z\. Li \(2023a\)Dink\-net: neural clustering on large graphs\.InProceedings of the 40th International Conference on Machine Learning \(ICML\),Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.
- Y\. Liu, W\. Tu, S\. Zhou, X\. Liu, L\. Song, X\. Yang, and E\. Zhu \(2022b\)Deep graph clustering via dual correlation reduction\.InProceedings of the AAAI Conference on Artificial Intelligence,Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.
- Y\. Liu, X\. Yang, S\. Zhou, X\. Liu, Z\. Wang, K\. Liang, W\. Tu, L\. Li, J\. Duan, and C\. Chen \(2023b\)Hard sample aware network for contrastive deep graph clustering\.InProceedings of the AAAI Conference on Artificial Intelligence,Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.
- Y\. Liu, J\. Li, Y\. Chen, R\. Wu, B\. Wang, J\. Zhou, S\. Tian, S\. Shen, X\. Fu, C\. Meng, W\. Wang, and L\. Chen \(2024a\)Revisiting modularity maximization for graph clustering: a contrastive learning perspective\.InProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining \(KDD\),Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.
- Y\. Liu, X\. Gao, T\. He, T\. Zheng, J\. Zhao, and H\. Yin \(2024b\)Reliable node similarity matrix guided contrastive graph clustering\.IEEE Transactions on Knowledge and Data Engineering\.Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.
- D\. Malitesta, E\. Rossi, C\. Pomo, T\. Di Noia, and F\. D\. Malliaros \(2026\)Training\-free graph\-based imputation of missing modalities in multimodal recommendation\.arXiv preprint arXiv:2602\.17354\.Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px2.p1.1)\.
- M\. McPherson, L\. Smith\-Lovin, and J\. M\. Cook \(2001\)Birds of a feather: homophily in social networks\.Annual Review of Sociology27,pp\. 415–444\.Cited by:[§1](https://arxiv.org/html/2608.00621#S1.p3.1)\.
- M\. E\. J\. Newman \(2006\)Modularity and community structure in networks\.Proceedings of the National Academy of Sciences103\(23\),pp\. 8577–8582\.Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.
- J\. Ni, J\. Li, and J\. J\. McAuley \(2019\)Justifying recommendations using distantly\-labeled reviews and fine\-grained aspects\.InEMNLP/IJCNLP \(1\),pp\. 188–197\.Cited by:[Appendix G](https://arxiv.org/html/2608.00621#A7.SS0.SSS0.Px2.p1.3),[Appendix G](https://arxiv.org/html/2608.00621#A7.SS0.SSS0.Px3.p1.3),[§5\.1](https://arxiv.org/html/2608.00621#S5.SS1.SSS0.Px1.p1.1)\.
- E\. Pan and Z\. Kang \(2021\)Multi\-view contrastive graph clustering\.InAdvances in Neural Information Processing Systems \(NeurIPS\),Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.
- Z\. Peng, H\. Liu, Y\. Jia, and J\. Hou \(2021\)Attention\-driven graph clustering network\.InProceedings of the 29th ACM International Conference on Multimedia \(ACM MM\),Cited by:[§1](https://arxiv.org/html/2608.00621#S1.p1.1),[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.
- G\. Peyré and M\. Cuturi \(2019\)Computational optimal transport\.Foundations and Trends in Machine Learning11\(5\-6\),pp\. 355–607\.Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px2.p1.1)\.
- A\. Radford, J\. W\. Kim, C\. Hallacy, A\. Ramesh, G\. Goh, S\. Agarwal, G\. Sastry, A\. Askell, P\. Mishkin, J\. Clark, G\. Krueger, and I\. Sutskever \(2021\)Learning transferable visual models from natural language supervision\.InProceedings of the 38th International Conference on Machine Learning \(ICML\),Cited by:[§3](https://arxiv.org/html/2608.00621#S3.SS0.SSS0.Px1.p1.13)\.
- Y\. Roh, J\. Kim, J\. Park, and W\. Shin \(2025\)Training\-free adjustable polynomial graph filtering for ultra\-fast multimodal recommendation\.Engineering Applications of Artificial Intelligence\.Note:arXiv:2503\.04406Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px2.p1.1)\.
- M\. S\. Shim, P\. Li, C\. Bao, and J\. Lai \(2019\)Robust deep multi\-modal sensor fusion using fusion weight regularization and target learning\.arXiv preprint arXiv:1901\.10610\.Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px2.p1.1)\.
- A\. Strehl and J\. Ghosh \(2002\)Cluster ensembles – a knowledge reuse framework for combining multiple partitions\.Journal of Machine Learning Research3,pp\. 583–617\.Cited by:[Appendix I](https://arxiv.org/html/2608.00621#A9.SS0.SSS0.Px1.p1.5)\.
- A\. Tsitsulin, J\. Palowitch, B\. Perozzi, and E\. Müller \(2023\)Graph clustering with graph neural networks\.Journal of Machine Learning Research24\(127\),pp\. 1–21\.Cited by:[Appendix H](https://arxiv.org/html/2608.00621#A8.SS0.SSS0.Px3.p1.1),[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1),[§5\.1](https://arxiv.org/html/2608.00621#S5.SS1.SSS0.Px2.p1.1)\.
- W\. Tu, S\. Zhou, X\. Liu, X\. Guo, Z\. Cai, E\. Zhu, and J\. Cheng \(2021\)Deep fusion clustering network\.InProceedings of the AAAI Conference on Artificial Intelligence,Cited by:[Appendix H](https://arxiv.org/html/2608.00621#A8.SS0.SSS0.Px2.p1.1),[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1),[§5\.1](https://arxiv.org/html/2608.00621#S5.SS1.SSS0.Px2.p1.1)\.
- A\. Vaswani, N\. Shazeer, N\. Parmar, J\. Uszkoreit, L\. Jones, A\. N\. Gomez, L\. Kaiser, and I\. Polosukhin \(2017\)Attention is all you need\.InAdvances in Neural Information Processing Systems \(NeurIPS\),Cited by:[§3](https://arxiv.org/html/2608.00621#S3.SS0.SSS0.Px1.p1.13)\.
- P\. Veličković, G\. Cucurull, A\. Casanova, A\. Romero, P\. Liò, and Y\. Bengio \(2018\)Graph attention networks\.InInternational Conference on Learning Representations \(ICLR\),Cited by:[§4\.1](https://arxiv.org/html/2608.00621#S4.SS1.p2.7)\.
- C\. Wan, X\. Li, Y\. Zuo, H\. Deng, S\. Li, B\. Fan, H\. Qin, R\. Li, and G\. Wang \(2026\)OpenMAG: a comprehensive benchmark for multimodal\-attributed graph\.arXiv preprint arXiv:2602\.05576\.Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px2.p1.1)\.
- C\. Wang, S\. Pan, R\. Hu, G\. Long, J\. Jiang, and C\. Zhang \(2019\)Attributed graph clustering: a deep attentional embedding approach\.InProceedings of the 28th International Joint Conference on Artificial Intelligence \(IJCAI\),Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.
- N\. Wanget al\.\(2025\)Modality\-uncertainty\-aware knowledge distillation framework for multimodal sentiment analysis\.Complex & Intelligent Systems\.External Links:[Document](https://dx.doi.org/10.1007/s40747-025-02135-w)Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px2.p1.1)\.
- R\. Wu, H\. Wang, H\. Chen, and G\. Carneiro \(2024\)Deep multimodal learning with missing modality: a survey\.Transactions on Machine Learning Research \(TMLR\)\.Note:arXiv:2409\.07825Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px2.p1.1)\.
- J\. Xia, L\. Wu, G\. Wang, J\. Chen, and S\. Z\. Li \(2022\)ProGCL: rethinking hard negative mining in graph contrastive learning\.InProceedings of the 39th International Conference on Machine Learning \(ICML\),Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.
- R\. Xia, H\. Liu, A\. Li, X\. Liu, Y\. Zhang, C\. Zhang, and B\. Yang \(2025\)Incomplete graph learning: a comprehensive survey\.Neural Networks190,pp\. 107682\.External Links:[Document](https://dx.doi.org/10.1016/j.neunet.2025.107682)Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px2.p1.1)\.
- J\. Xu, C\. Li, L\. Peng, Y\. Ren, X\. Shi, H\. T\. Shen, and X\. Zhu \(2023\)Adaptive feature projection with distribution alignment for deep incomplete multi\-view clustering\.IEEE Transactions on Image Processing\.Cited by:[Appendix H](https://arxiv.org/html/2608.00621#A8.SS0.SSS0.Px7.p1.1),[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px2.p1.1),[§5\.1](https://arxiv.org/html/2608.00621#S5.SS1.SSS0.Px2.p1.1)\.
- X\. Xue, Y\. Lei, Q\. Cai, H\. Shan, and J\. Zhang \(2025\)PROTOCOL: partial optimal transport\-enhanced contrastive learning for imbalanced multi\-view clustering\.InProceedings of the 42nd International Conference on Machine Learning \(ICML\),Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px2.p1.1)\.
- H\. Yan, C\. Li, J\. Yin, Z\. Yu, W\. Han, M\. Li, Z\. Zeng, H\. Sun, and S\. Wang \(2024a\)When graph meets multimodal: benchmarking and meditating on multimodal attributed graphs learning\.arXiv preprint arXiv:2410\.09132\.Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px2.p1.1)\.
- X\. Yan, Z\. Jin, F\. Han, and Y\. Ye \(2024b\)Differentiable information bottleneck for deterministic multi\-view clustering\.InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition \(CVPR\),Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px2.p1.1)\.
- X\. Yang, Y\. Liu, S\. Zhou, S\. Wang, W\. Tu, Q\. Zheng, X\. Liu, L\. Fang, and E\. Zhu \(2023\)Cluster\-guided contrastive graph clustering network\.InProceedings of the AAAI Conference on Artificial Intelligence,Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.
- Y\. You, T\. Chen, Y\. Sui, T\. Chen, Z\. Wang, and Y\. Shen \(2020\)Graph contrastive learning with augmentations\.InAdvances in Neural Information Processing Systems \(NeurIPS\),Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.
- H\. Zheng, R\. Yang, H\. Wang, and J\. Xu \(2025\)Cross\-contrastive clustering for multimodal attributed graphs with dual graph filtering\.arXiv preprint arXiv:2511\.20030\.Cited by:[Appendix H](https://arxiv.org/html/2608.00621#A8.SS0.SSS0.Px8.p1.1),[§1](https://arxiv.org/html/2608.00621#S1.p1.1),[§1](https://arxiv.org/html/2608.00621#S1.p2.1),[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1),[§5\.1](https://arxiv.org/html/2608.00621#S5.SS1.SSS0.Px2.p1.1)\.
- X\. Zhou and Z\. Shen \(2023\)A tale of two graphs: freezing and denoising graph structures for multimodal recommendation\.InProceedings of the 31st ACM International Conference on Multimedia \(MM\),External Links:[Document](https://dx.doi.org/10.1145/3581783.3611943)Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px2.p1.1)\.
- J\. Zhu, X\. Zou, J\. Sun, C\. Luo, L\. Liu, and L\. Zeng \(2026\)MoEGCL: mixture of ego\-graphs contrastive representation learning for multi\-view clustering\.InProceedings of the AAAI Conference on Artificial Intelligence,Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.
- Y\. Zhu, Y\. Xu, F\. Yu, Q\. Liu, S\. Wu, and L\. Wang \(2021\)Graph contrastive learning with adaptive augmentation\.InProceedings of the Web Conference \(WWW\),Cited by:[§2](https://arxiv.org/html/2608.00621#S2.SS0.SSS0.Px1.p1.1)\.

## Appendix ARobustness to Modality Perturbation \(ACC, ARI, F1\)

The NMI robustness results are reported in Table[2](https://arxiv.org/html/2608.00621#S5.T2)\(Sec\.[5\.3](https://arxiv.org/html/2608.00621#S5.SS3)\)\. Tables[5](https://arxiv.org/html/2608.00621#A1.T5)–[7](https://arxiv.org/html/2608.00621#A1.T7)further present the corresponding ACC, ARI, and F1 scores under the same evaluation protocol, including identical perturbation settings \(η=0\.4\\eta=0\.4,m=0\.5m=0\.5\) and ranking marks\. TheStandardcolumn reproduces the clean\-performance results from the main comparison in Table[1](https://arxiv.org/html/2608.00621#S4.T1)\. As observed, across all metrics and all settings, RHEA consistently achieves the best performance in every case, in agreement with the NMI results\. This consistency suggests that the observed robustness gains are not metric\-specific, but instead reflect a general and stable improvement under perturbations\.

Table 5:Robustness \(ACC\) across standard, image\-, and text\-modality perturbation\. Image/text corruptionη=0\.4\\eta\{=\}0\.4, missingm=0\.5m\{=\}0\.5\.Table 6:Robustness \(ARI\) across standard, image\-, and text\-modality perturbation\. Image/text corruptionη=0\.4\\eta\{=\}0\.4, missingm=0\.5m\{=\}0\.5\.Table 7:Robustness \(F1\) across standard, image\-, and text\-modality perturbation\. Image/text corruptionη=0\.4\\eta\{=\}0\.4, missingm=0\.5m\{=\}0\.5\.
## Appendix BMore Ablation Study

Beyond the component ablation study in Sec\.[5\.4](https://arxiv.org/html/2608.00621#S5.SS4)\(Table[3](https://arxiv.org/html/2608.00621#S5.T3)\), we further conduct three analyses: the choice of reconstruction operator, the generality of the reliability mechanism across modality corruption settings, and a comparison against training\-free graph imputation baselines\.

#### Reconstruction operator\.

The reconstruction module in Sec\.[4\.2](https://arxiv.org/html/2608.00621#S4.SS2)aggregates one\-hop neighbors of each node from the reliable modality\. We evaluate alternative topology\-aware denoising operators, including personalized PageRank \(PPR, teleportα=0\.15\\alpha=0\.15\), heat kernel diffusion \(Heat\), a similarity\-gated one\-hop operator that down\-weights anti\-correlated edges \(Simgate\), and their compositions\.

As shown in Fig\.[5](https://arxiv.org/html/2608.00621#A2.F5), evaluated on RedditS and Grocery under missing \(m=0\.5m=0\.5\) and corruption \(η=0\.4\\eta=0\.4\) settings \(averaged over five seeds\), multi\-hop diffusion methods \(PPR/Heat\) yield only marginal improvements over the one\-hop mean aggregator \(\+0\.002\+0\.002NMI on average\)\. The similarity\-gated variant does not provide consistent gains \(−0\.004\-0\.004NMI on average\)\. This is likely because similarity gating effectively filters low\-confidence neighbors, while RHEA already leverages per\-node reliability viacic\_\{i\}to identify informative donors\. Since all alternatives lie within one standard deviation of the mean and do not affect overall conclusions, we retain the one\-hop mean as the default reconstruction operator\.

![Refer to caption](https://arxiv.org/html/2608.00621v1/x5.png)Figure 5:Reconstruction operator ablation\. NMI under missing \(m=0\.5m=0\.5\) and corruption \(η=0\.4\\eta=0\.4\) settings for different reconstruction operators\.
#### Generality across modality regimes\.

Since both the gating and reconstruction operate on the modality identified as unreliable, the mechanism is not restricted to a specific modality\. Table[8](https://arxiv.org/html/2608.00621#A2.T8)evaluates RHEA against the backbone without reliability modeling \(Sinkhorn\) under different corruption regimes, including text\-only corruption, joint corruption, and asymmetric modality degradation\.

RHEA consistently improves over the baseline across all settings, with the largest gains under asymmetric corruption \(\+0\.21\+0\.21NMI on RedditS and\+0\.06\+0\.06on Amazon\) and joint corruption \(\+0\.10\+0\.10and\+0\.06\+0\.06\)\. Even under single\-modality text perturbation, RHEA remains competitive \(\+0\.01\+0\.01on both datasets\)\. These results indicate that reliability\-aware reconstruction is most beneficial when modality quality is uneven across nodes, consistent with the design assumption\.

Table 8:Generality across modality degradation regimes\.
#### Learned reconstruction vs\. training\-free graph imputation\.

Table[9](https://arxiv.org/html/2608.00621#A2.T9)compares RHEA with training\-free graph imputation strategies applied as preprocessing, including one\-hop mean, personalized PageRank, and heat kernel diffusion, while keeping the downstream backbone fixed\.

RHEA consistently outperforms the best static imputation baseline \(one\-hop mean\) by\+0\.08\+0\.08–\+0\.09\+0\.09NMI\. In contrast, multi\-hop diffusion methods do not improve over simple neighborhood averaging when used as fixed preprocessing, highlighting the benefit of learning reconstruction jointly with reliability estimation\.

Table 9:Comparison with training\-free graph imputation under image\-missing settings\.

## Appendix CMore Sensitivity Analysis

Beyond the hyperparameter studies in Sec\.[5\.5](https://arxiv.org/html/2608.00621#S5.SS5)\(Table[4](https://arxiv.org/html/2608.00621#S5.T4)\), we examine the effect of graph structural properties on performance gains\.

#### Sensitivity to graph homophily\.

RHEA relies on neighbor agreement to estimate reliability, and thus its effectiveness depends on attribute homophily\. Across benchmarks, edge homophily ranges from0\.680\.68\(Grocery\) to0\.960\.96\(RedditS\)\. As shown in Table[2](https://arxiv.org/html/2608.00621#S5.T2), RHEA consistently improves over DGF under missing data settings across this range\.

Performance gains decrease smoothly as homophily decreases, rather than exhibiting abrupt degradation, indicating that the method remains stable but gradually approaches the behavior of non\-reliability\-aware baselines in heterophilous regimes \(see Appendix[J](https://arxiv.org/html/2608.00621#A10)\)\.

## Appendix DMore Interpretability Investigation

We further analyze the behavior of the learned reliability signal\. As presented in Fig\.[6](https://arxiv.org/html/2608.00621#A4.F6), the node\-wise confidence scorecic\_\{i\}reflects agreement among donor neighbors and thus responds to input corruption even when all modalities are present\. On RedditS, the average confidence decreases monotonically from0\.9860\.986atη=0\\eta=0to0\.8510\.851atη=0\.4\\eta=0\.4, while image\-trustρimg\\rho\_\{\\mathrm\{img\}\}exhibits a consistent trend\.

![Refer to caption](https://arxiv.org/html/2608.00621v1/x6.png)Figure 6:Reconstruction confidence vs\. corruption \(RedditS\)\. Mean confidencecic\_\{i\}and image trustρimg\\rho\_\{\\mathrm\{img\}\}versus corruption levelη\\eta\.
## Appendix EEfficiency and Complexity Analysis

#### Time complexity\.

Modality\-specific encoding and graph propagation rely on sparse message passing over𝒢=\(𝒱,ℰ\)\\mathcal\{G\}=\(\\mathcal\{V\},\\mathcal\{E\}\), yielding𝒪​\(\|ℰ\|​d\)\\mathcal\{O\}\(\|\\mathcal\{E\}\|d\)per iteration, whereddis the embedding dimension\. Reliability\-aware reconstruction and fusion introduce only local neighborhood aggregation and remain bounded by the same sparsity pattern\.

The entropic optimal transport solver requiresTTSinkhorn iterations over anN×KN\\times Kcost matrix, resulting in𝒪​\(N​K​T\)\\mathcal\{O\}\(NKT\)complexity, and the inter\-node repulsion termΩcm\\Omega\_\{\\mathrm\{cm\}\}\(Eq\. \([13](https://arxiv.org/html/2608.00621#A5.E13)\) below\) contributes an additional dense𝒪​\(N2​d\)\\mathcal\{O\}\(N^\{2\}d\)computation\. Therefore, the overall per\-iteration time complexity is

𝒪​\(\|ℰ\|​d\+N​K​T\+N2​d\),\\mathcal\{O\}\(\|\\mathcal\{E\}\|d\+NKT\+N^\{2\}d\),whose quadratic cross\-modal term is shared with prior cross\-modal graph clustering frameworks such as DGF, while all graph and transport components remain sparse or linear inNN\.

#### Memory complexity and theO​\(N2\)O\(N^\{2\}\)term\.

The graph\-based components scale linearly with the number of edges and feature dimension\. The only super\-linear term arises from the inter\-node margin repulsionΩcm\\Omega\_\{\\mathrm\{cm\}\}inℒmod\\mathcal\{L\}\_\{\\mathrm\{mod\}\}\(Eq\. \([11](https://arxiv.org/html/2608.00621#S4.E11)\)\), which is defined as:

Ωcm=1N2​∑i∑j≠i\[m0\+⟨𝐡i,𝐳j\(txt\)⟩−⟨𝐡i,𝐳i\(txt\)⟩\]\+,\\Omega\_\{\\mathrm\{cm\}\}\\;=\\;\\frac\{1\}\{N^\{2\}\}\\sum\_\{i\}\\sum\_\{j\\neq i\}\\big\[\\,m\_\{0\}\+\\langle\\mathbf\{h\}\_\{i\},\\mathbf\{z\}^\{\(\\mathrm\{txt\}\)\}\_\{j\}\\rangle\-\\langle\\mathbf\{h\}\_\{i\},\\mathbf\{z\}^\{\(\\mathrm\{txt\}\)\}\_\{i\}\\rangle\\,\\big\]\_\{\+\},\(13\)wherem0m\_\{0\}is the repulsion margin and\[⋅\]\+=max⁡\(0,⋅\)\[\\cdot\]\_\{\+\}=\\max\(0,\\cdot\)\.

This term induces a denseN×NN\\times Nsimilarity computation𝐡​𝐳\(txt\)⊤\\mathbf\{h\}\\,\\mathbf\{z\}^\{\(\\mathrm\{txt\}\)\\top\}, leading to an𝒪​\(N2\)\\mathcal\{O\}\(N^\{2\}\)memory requirement\. All other operations—including reliability modeling, reconstruction, message passing, and Sinkhorn updates—remain sparse and scale at most linearly with graph size\. Therefore, the overall memory complexity is dominated by this quadratic term, consistent with prior cross\-modal graph clustering frameworks\.

## Appendix FAdditional Experimental Details

### F\.1Training Protocol

Unless otherwise specified, all reported results are presented as mean±\\pmstandard deviation over five random seeds\. For each seed, all methods share the same data split and, for robustness experiments, the same realization of missing\-modality or corruption patterns\. Perturbations are applied consistently to either image or text modalities under identical settings\. All models are trained for 120 epochs following the same protocol\. Baseline implementations use the official released code with the recommended hyperparameter settings, while ablated variants inherit the same configuration with only the corresponding component removed\.

#### Perturbation model\.

Both perturbations are injected into the raw features of the target modality before encoding, and both ratios are node fractions rather than noise amplitudes\. Corruption with ratioη\\etaselects⌊η​N⌋\\lfloor\\eta N\\rfloornodes uniformly at random and replaces each selected node’s feature vector with a random Gaussian vector rescaled to theℓ2\\ell\_\{2\}norm of the original feature, so the content of the modality is destroyed while its scale is preserved\. Missingness with ratiommselects⌊m​N⌋\\lfloor mN\\rfloornodes uniformly at random and sets the target modality’s feature vector to zero\. Node subsets are sampled with independent random streams per regime and per modality, and for a given seed every method receives the identical node mask and noise realization\.

### F\.2Model Configuration

Each node is associated with text and image features extracted from frozen pretrained encoders\. We use RoBERTa for text and CLIP\-ViT\-L/14 for images, producing 768\-dimensional representations for all MAGB datasets\. The DMGC Amazon dataset uses its provided 1433\-dimensional node attributes\. Unless otherwise stated, each modality is encoded by a linear projection followed by simplified graph propagation\.

The default hyperparameters are shared across all datasets\. Specifically, the reconstruction threshold isγ=0\.45\\gamma=0\.45, the reliability temperature isτ=1\\tau=1, the contrastive temperature isτc=0\.5\\tau\_\{c\}=0\.5, and the entropic regularization strength in optimal transport isϵ=0\.05\\epsilon=0\.05with 20 Sinkhorn iterations\. The remaining hyperparameters are likewise shared: the loss weights areλncrc=1\\lambda\_\{\\mathrm\{ncrc\}\}=1,λnbr=0\.5\\lambda\_\{\\mathrm\{nbr\}\}=0\.5, andλmod=0\.1\\lambda\_\{\\mathrm\{mod\}\}=0\.1; the assignment temperature isτa=1\\tau\_\{a\}=1; the consensus propagation depth isL=2L=2; the sharpening temperature isTs=0\.5T\_\{s\}=0\.5; the confidence decay coefficient isβ=3\\beta=3; and the repulsion margin ism0=0\.1m\_\{0\}=0\.1\. A sensitivity analysis of the main hyperparameters is reported in Sec\.[5\.5](https://arxiv.org/html/2608.00621#S5.SS5)\.

#### Optimization\.

All models are optimized using Adam with learning rate10−310^\{\-3\}and weight decay10−510^\{\-5\}for 120 epochs under full\-batch training\. The embedding dimension is fixed to6464, and graph propagation uses 10 layers throughout all experiments\.

#### Reconstruction confidence\.

The reconstruction confidence combines neighborhood consistency and neighborhood support\. Specifically, it increases when neighboring donor embeddings exhibit high agreement and sufficient coverage, and decreases when neighbor agreement is weak or only a few reliable donors are available\. Nodes without reliable neighbors fall back to their original modality representation, ensuring stable behavior across different graph structures\.

#### Initialization and normalization\.

All modality\-specific and fused embeddings areℓ2\\ell\_\{2\}\-normalized before reliability estimation, reconstruction, and optimal transport\. Cluster centers are initialized bykk\-means on the fused embeddings from the first epoch and optimized jointly during training\.

### F\.3Stabilizing the Reliability Field

The reliability field is updated using an exponential moving average \(EMA\) with momentum 0\.99 to improve training stability\. As illustrated in Fig\.[7](https://arxiv.org/html/2608.00621#A6.F7), EMA substantially reduces fluctuations of the reliability estimates across training while preserving clustering performance\. We therefore adopt EMA as the default setting in all experiments\.

![Refer to caption](https://arxiv.org/html/2608.00621v1/x7.png)Figure 7:Stability of the reliability field\. Per\-step variation of the reliability estimateρ\\rhowith and without EMA on RedditS under missing\-modality ratiom=0\.5m=0\.5\.
### F\.4Experimental Environment

All experiments are conducted on a single NVIDIA RTX PRO 6000 \(Blackwell Server Edition, 96 GB\) GPU using PyTorch 2\.10 with CUDA 12\.8\.

## Appendix GDataset Details

We evaluate on four public multimodal attributed graphs; every node carries two modalities \(text and image\), encoded by frozen pretrained models\. Table[10](https://arxiv.org/html/2608.00621#A7.T10)lists their statistics, with textual descriptions below\.

Table 10:Statistics of the four evaluation datasets\. All datasets are two\-modality \(text\+\{\+\}image\); the feature dimensions are those of the frozen pretrained encoders\.#### RedditS\.

\(Desaiet al\.[2021](https://arxiv.org/html/2608.00621#bib.bib56)\)A social\-network graph from the MAGB benchmark, sourced from RedCaps\. Each node is a post carrying its text \(title and body\) and its accompanying image; edges link related posts, and the2020clusters correspond to their communities\. Text and image features are the768768\-dimensional RoBERTa and CLIP\-ViT\-L/14 embeddings, respectively\.

#### Toys\.

\(Niet al\.[2019](https://arxiv.org/html/2608.00621#bib.bib57)\)As a core component of MAGB, the Toys dataset comprises roughly4242k products \(of which20,69520\{,\}695form the graph\)\. Age suitability, safety information, materials, and functional descriptions are encoded alongside visual features, and relations among products, including series membership and accessory compatibility, form the graph edges\. It spans1818product categories\.

#### Grocery\.

\(Niet al\.[2019](https://arxiv.org/html/2608.00621#bib.bib57)\)An Amazon\-derived grocery co\-purchase graph from MAGB with17,07417\{,\}074nodes and2020categories\. Each product carries a textual description and a product image, and edges connect co\-purchased or related items\. Text and image features follow the same768768\-dimensional RoBERTa / CLIP encoding as the other MAGB graphs\.

#### Amazon\.

\(Guoet al\.[2025](https://arxiv.org/html/2608.00621#bib.bib2)\)The multimodal co\-purchase graph used by DMGC, with6,1586\{,\}158nodes and only33clusters\. Nodes carry1,4331\{,\}433\-dimensional text and image attributes, and the graph combines item–item and item–user relations\. Its small cluster count and highly discriminative attributes make even simple attribute\-only baselines competitive, which is why it is a useful stress test for reliability\-guided fusion\.

## Appendix HBaseline Details

We compare against nine baselines spanning four families\. All are run from their official code under the identical protocol of Appendix[F\.1](https://arxiv.org/html/2608.00621#A6.SS1)\.

#### KMeans

clusters nodes by Lloyd’s algorithm on their concatenated text and image features, using no graph structure\. It is the classical attribute\-only reference point\.

#### DFCN

\(Tuet al\.[2021](https://arxiv.org/html/2608.00621#bib.bib10)\)is a deep fusion clustering network that couples an autoencoder with a graph autoencoder through a structure\-and\-attribute fusion module, and refines the fused representation with a triplet self\-supervision objective\.

#### DMoN

\(Tsitsulinet al\.[2023](https://arxiv.org/html/2608.00621#bib.bib23)\)trains a graph neural network with a differentiable spectral\-modularity objective and a collapse regularizer, producing soft cluster assignments that directly optimize graph community structure\.

#### MVGRL

\(Hassani and Khasahmadi[2020](https://arxiv.org/html/2608.00621#bib.bib17)\)is a contrastive multi\-view method that maximizes the mutual information between node\-level and graph\-level representations across two structural views, the adjacency and a graph\-diffusion view\.

#### S3GC

\(Devvritet al\.[2022](https://arxiv.org/html/2608.00621#bib.bib18)\)performs scalable self\-supervised graph clustering: a graph encoder is trained contrastively with random\-walk\-based positive pairs, so it scales to large graphs while remaining label\-free\.

#### COMPLETER

\(Linet al\.[2021](https://arxiv.org/html/2608.00621#bib.bib27)\)targets incomplete multi\-view data through information\-theoretic dual prediction, maximizing cross\-view mutual information while minimizing conditional entropy so that a missing view can be recovered from the observed one\.

#### APADC

\(Xuet al\.[2023](https://arxiv.org/html/2608.00621#bib.bib28)\)is a deep incomplete multi\-view clustering method that is imputation\-free: it aligns the view distributions with a maximum\-mean\-discrepancy term and adaptively projects and fuses whichever views are available for each sample\.

#### DGF

\(Zhenget al\.[2025](https://arxiv.org/html/2608.00621#bib.bib1)\)jointly exploits graph topology and multiple modalities with a dual\-graph filtering backbone and a community\-aware cross\-modality contrastive objective\. It is the strongest prior method and our primary point of comparison\.

#### DMGC

\(Guoet al\.[2025](https://arxiv.org/html/2608.00621#bib.bib2)\)disentangles homophilous and heterophilous signals with a dual\-frequency \(low\- and high\-pass\) graph filter, combines intra\- and cross\-modal contrastive objectives, and refines the assignment with a DEC clustering head\.

## Appendix IMetric Details

We report four standard clustering metrics; all are higher\-is\-better\. LetY=\{yi\}i=1NY=\\\{y\_\{i\}\\\}\_\{i=1\}^\{N\}be the ground\-truth labels andC=\{ci\}i=1NC=\\\{c\_\{i\}\\\}\_\{i=1\}^\{N\}the predicted clusters overNNnodes\. Because clustering is permutation\-invariant, ACC and F1 are computed after a best cluster\-to\-label matching obtained with the Hungarian algorithm\(Kuhn[1955](https://arxiv.org/html/2608.00621#bib.bib38)\)\.

#### Normalized Mutual Information \(NMI\)

\(Strehl and Ghosh[2002](https://arxiv.org/html/2608.00621#bib.bib39)\)measures the shared information between the predicted and ground\-truth partitions, normalized by their entropies,

NMI​\(Y,C\)=2​I​\(Y;C\)H​\(Y\)\+H​\(C\),\\mathrm\{NMI\}\(Y,C\)\\;=\\;\\frac\{2\\,I\(Y;C\)\}\{H\(Y\)\+H\(C\)\},\(14\)whereI​\(⋅;⋅\)I\(\\cdot;\\cdot\)is mutual information andH​\(⋅\)H\(\\cdot\)is entropy\. It lies in\[0,1\]\[0,1\], with11for a perfect match\.

#### Clustering Accuracy \(ACC\)

is the fraction of correctly assigned nodes under the best label permutationπ\\pi,

ACC=maxπ⁡1N​∑i=1N𝟙​\(yi=π​\(ci\)\),\\mathrm\{ACC\}\\;=\\;\\max\_\{\\pi\}\\;\\frac\{1\}\{N\}\\sum\_\{i=1\}^\{N\}\\mathbb\{1\}\\\!\\left\(y\_\{i\}=\\pi\(c\_\{i\}\)\\right\),\(15\)whereπ\\piranges over cluster\-to\-label mappings and𝟙​\(⋅\)\\mathbb\{1\}\(\\cdot\)is the indicator function\.

#### Adjusted Rand Index \(ARI\)

\(Hubert and Arabie[1985](https://arxiv.org/html/2608.00621#bib.bib40)\)counts agreeing node pairs, corrected for chance\. Withni​jn\_\{ij\}the number of nodes in ground\-truth clusteriiand predicted clusterjj, andai,bja\_\{i\},b\_\{j\}the corresponding row/column sums,

ARI=∑i​j\(ni​j2\)−\[∑i\(ai2\)​∑j\(bj2\)\]/\(N2\)12​\[∑i\(ai2\)\+∑j\(bj2\)\]−\[∑i\(ai2\)​∑j\(bj2\)\]/\(N2\)\.\\displaystyle\\mathrm\{ARI\}\\;=\\;\\frac\{\\sum\_\{ij\}\\binom\{n\_\{ij\}\}\{2\}\-\\big\[\\sum\_\{i\}\\binom\{a\_\{i\}\}\{2\}\\sum\_\{j\}\\binom\{b\_\{j\}\}\{2\}\\big\]\\big/\\binom\{N\}\{2\}\}\{\\tfrac\{1\}\{2\}\\big\[\\sum\_\{i\}\\binom\{a\_\{i\}\}\{2\}\+\\sum\_\{j\}\\binom\{b\_\{j\}\}\{2\}\\big\]\-\\big\[\\sum\_\{i\}\\binom\{a\_\{i\}\}\{2\}\\sum\_\{j\}\\binom\{b\_\{j\}\}\{2\}\\big\]\\big/\\binom\{N\}\{2\}\}\\,\.

\(16\)

#### F1

is the macro\-averaged harmonic mean of precision \(P\) and recall \(R\) over the matched clusters,F1=2​P​R/\(P\+R\)\\mathrm\{F1\}=2\\,\\mathrm\{P\}\\,\\mathrm\{R\}/\(\\mathrm\{P\}\+\\mathrm\{R\}\), which is robust to class imbalance\.

## Appendix JLimitations and Broader Impact

#### Limitations\.

RHEA assumes that local neighborhood information provides useful cues for estimating modality reliability and is therefore best suited to graphs with informative local structure\. As neighborhood agreement becomes less informative, the benefit of reliability\-aware reconstruction may diminish accordingly\. In addition, RHEA inherits the dense cross\-modal contrastive objective from DGF, whoseO​\(N2\)O\(N^\{2\}\)memory complexity \(Appendix[E](https://arxiv.org/html/2608.00621#A5)\) may limit scalability to very large graphs\. Exploring reliability estimation under more challenging graph structures and improving scalability are promising directions for future work\.

#### Broader Impacts\.

Multimodal attributed graphs are widely used in applications such as recommendation systems, social networks, and citation analysis, where data quality is often heterogeneous across modalities\. RHEA provides a label\-free mechanism to estimate modality reliability and improve robustness under imperfect data conditions, which may help reduce sensitivity to noise in downstream analysis\. As with other unsupervised representation learning methods, care should be taken when applying the resulting embeddings or clusters in high\-stakes decision scenarios\.