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MDTE: Minority-Aware Diffusion over Temporal Edge Events for Imbalanced Node Classification
Zhou Zelong, Zhang Tianming, Yang Zhengyi, Tang Yifu, Hou Chenyu, Cao Bin, Fan Jing
TL;DR
Class-imbalanced temporal node classification must preserve minority representations despite majority-dominated propagation and limited discriminative evidence. MDTE applies conditional diffusion to temporal edge events using selective propagation and multi-view discriminative fusion, and experiments on five real-world datasets report the best minority-oriented performance among the evaluated methods.
Problem
Minority representations can be assimilated toward majority patterns during temporal propagation, while sparse minority patterns and single-view information limit discriminative evidence.
Method
MDTE conditionally denoises temporal edge-event representations using LOF filtering, cluster-aware low-frequency propagation, feature reconstruction, and topology prediction.
Results
MDTE consistently achieves the best performance on minority-class-oriented metrics across five real-world datasets and outperforms thirteen baseline methods.
Takeaways & Limitations
MDTE provides temporally stable and class-discriminative minority representations for imbalanced temporal-graph node classification.
Takeaways & Limitations
Most existing comparison methods do not explicitly capture temporal interaction order or accumulated historical information, limiting the scope of static-graph baselines.
Abstract
from arXiv · showhide
Class-imbalanced node classification on temporal graphs is challenging because majority-dominated temporal propagation progressively assimilates minority representations, while conventional node and neighborhood information provides insufficient discriminative evidence for minority classes. To address these issues, we propose MDTE, a minority-aware diffusion framework that reconstructs stable and discriminative temporal edge-event representations through conditional diffusion denoising. Specifically, MDTE introduces Distribution-Aware Selective Propagation, which combines Local Outlier Factor (LOF)-based propagation filtering with cluster-aware low-frequency propagation. The module preserves informative neighborhood dependencies while mitigating harmful propagation and majority-class information assimilation. It further develops Multi-View Discriminative Fusion, which exploits feature reconstruction and topology prediction to characterize class-wise differences in distribution learning and extracts complementary discriminability signals to guide denoising. Experiments on five real-world datasets demonstrate that MDTE consistently achieves the best performance on minority-class-oriented metrics, improving minority-class recall by up to 23.53 percentage points, minority-class F1 by 8.68 percentage points, and AUPRC by 2.67 percentage points over the strongest baselines.
1 Introduction
Temporal graphs make minority-node classification difficult because repeated majority-dominated propagation destabilizes minority representations, while minority-specific evidence remains sparse. MDTE addresses these challenges with selective propagation and multi-view conditional diffusion denoising.
- Minority nodes are scarce but practically important in financial, blockchain, and social interaction networks represented as temporal graphs.
- Repeated temporal propagation can assimilate minority representations toward majority patterns and amplify harmful neighborhood influence over time.
- Effective learning must preserve minority-representation stability while enhancing class discriminability through complementary evidence.
- MDTE uses LOF-based filtering and cluster-aware low-frequency propagation to suppress harmful propagation while retaining useful neighborhood dependencies.
- MDTE combines feature reconstruction and topology prediction to extract complementary discriminability signals for conditional diffusion reconstruction.
- MDTE is evaluated extensively on five real-world datasets against thirteen baseline methods.
2 Related Work
Existing imbalanced graph-learning methods mainly target static graphs, while diffusion methods for dynamic graphs do not explicitly model class imbalance. These limitations leave temporal interaction order, accumulated propagation interference, and minority-specific discriminability insufficiently addressed.
- Class-imbalanced graph-learning methods include data-level interpolation, adversarial generation, pseudo-labeling, model refinement, loss design, and long-tailed representation enhancement.
- Most existing imbalanced-learning methods are designed for static graphs and do not explicitly capture interaction order or accumulated historical information.
- Static methods also inadequately address deviating-representation interference and repeated majority influence during temporal aggregation.
- Graph diffusion methods learn representations or graph distributions through forward perturbation and reverse denoising over features, structures, or latent representations.
- Recent continuous-time diffusion studies address dynamic graph augmentation or temporal link prediction through conditional diffusion and denoising.
- Existing dynamic diffusion methods do not explicitly address class imbalance, allowing majority patterns to dominate training while minority characteristics remain difficult to learn.
3 Preliminaries
The preliminaries define continuous-time temporal subgraphs, multi-scale temporal encodings, random-walk positional encodings, and imbalanced temporal node classification. Together, these represent node structure and historical interactions up to an observation time.
- A continuous-time temporal subgraph contains nodes, timestamped edge events, an interaction-derived adjacency matrix, and node representations.
- Temporal encoding represents each edge event’s position relative to the observation cutoff using multi-scale sine and cosine functions with learnable frequencies.
- Random-walk positional encoding concatenates return probabilities across walk lengths to characterize a node’s structural position across neighborhood ranges.
- Imbalanced temporal node classification predicts node labels from representations and historical interactions up to time T, emphasizing minority-node identification.
4 Methodology
MDTE models timestamped interactions as temporal edge events and applies conditional diffusion denoising with minority-aware conditions. Its conditions combine selective propagation, cluster-aware low-frequency propagation, and complementary feature-topology discriminability signals.
- Temporal Edge-Event Construction: MDTE represents each timestamped interaction as a temporal edge event and uses conditional diffusion to learn stable edge-event representations.Each event incorporates endpoint representations, continuous-time encoding, historical-interaction encoding, and source/destination roles before downstream aggregation.
- Edge-to-Node Aggregation: The resulting denoised edge-event representations are combined with temporal, historical-interaction, and endpoint-role encodings before attention-based edge-to-node aggregation.This aggregation preserves edge-level information for downstream node classification after dimensional alignment.
- Minority-Aware Temporal Edge-Event Diffusion: The forward process adds controlled, distribution-informed directional noise, while conditional reverse denoising uses minority-oriented propagation and discriminability conditions.The cumulative retention coefficient controls the balance between original edge-event information and noise across diffusion steps.
- Distribution-Aware Selective Propagation: LOF-based propagation filtering suppresses transmission from representations that deviate from their neighborhood while self-loops preserve each node’s own information.LOF compares local reachability density with neighboring densities; rank-normalized deviation scores determine the propagation mask.
- Distribution-Aware Selective Propagation: Cluster-aware low-frequency propagation preserves within-cluster messages and downweights cross-cluster propagation to limit dissimilar majority-class information.K-means clustering with an elbow-selected cluster count supplies cluster labels for propagation weighting, and the weighted filtered graph feeds a GAT-based low-frequency encoder.
- Multi-View Discriminative Fusion: Multi-View Discriminative Fusion combines feature-based and topology-based discriminability signals extracted from original and low-frequency node representations.Feature reconstruction captures attribute-learning differences, while topology prediction captures connection-pattern information not represented by attributes alone.
5 Experiments
Experiments evaluate MDTE on five financial temporal-graph datasets against thirteen baselines using minority-oriented and overall classification metrics. MDTE consistently improves minority-class recognition, its components are necessary, and performance is generally robust to parameter variation.
- 5.1 Experimental Setup: Experiments use five financial transaction graph datasets, thirteen baselines across four categories, shared preprocessing and splits, and AUROC, AUPRC, minority Recall, minority F1, and Macro-F1.MDTE performs label-free self-supervised learning on the complete temporal graph, processing edge events chronologically.
- RQ1 (Classification Performance): MDTE achieves the best results on all non-AUROC metrics across five datasets against temporal graph methods.On Ethereum, minority-class Recall and F1 improve by 14.94 and 8.68 percentage points over the strongest temporal baselines, respectively.
- RQ1 (Classification Performance): MDTE ranks first across all metrics on four datasets against static graph autoencoder methods.On Ethereum, minority-class Recall and F1 increase by 19.64 and 9.94 percentage points, respectively, while AUROC remains comparable.
- RQ1 (Classification Performance): MDTE consistently achieves the best non-AUROC results against class-imbalanced graph methods.On Ethereum, minority-class Recall and F1 gains are 26.60 and 17.68 percentage points, respectively, with comparable AUROC.
- RQ1 (Classification Performance): MDTE achieves the best results across all metrics on four datasets against graph diffusion methods.On Ethereum, minority-class Recall and F1 improve by 29.78 and 23.43 percentage points, respectively; on Elliptic, it trails only slightly in AUROC.
- RQ2 (Ablation: Necessity of Components): Removing any core component degrades performance, including drops of 14.19 points from removing Temporal Edge-Event Construction and 5.47 points from removing Debiased Contrastive Learning.Removing Distribution-Aware Selective Propagation lowers DGraph-Fin minority Recall by 4.66 points, while removing Multi-View Discriminative Fusion lowers Elliptic minority Recall by 2.48 points.
- RQ3 (Parameter Sensitivity): The settings 𝜏= 0.85, 𝜏+ = 0.025, 𝑘= 30, and 𝜏𝑐= 0.05 yield favorable performance across datasets, with relative stability on four datasets.Ethereum is more sensitive because of its extremely high class imbalance and limited minority samples.
- RQ4 (Core Mechanism Analysis): Removing Distribution-Aware Selective Propagation moves illicit nodes toward dense licit regions, while removing Multi-View Discriminative Fusion makes class boundaries less distinct.These observations come from UMAP visualizations of 500 licit and 500 illicit Elliptic test nodes.
6 Conclusion
MDTE targets minority-node identification in imbalanced temporal graphs through two complementary mechanisms and is validated on five real-world datasets. The paper identifies improving minority-representation discriminability and robustness as future work.
- 6 Conclusion: MDTE combines Distribution-Aware Selective Propagation and Multi-View Discriminative Fusion to mitigate majority-class interference and enhance minority-class discriminability.The framework is evaluated through extensive experiments on five real-world datasets.
- 6 Conclusion: Future work will further improve the discriminability and robustness of minority-node representations.
7 Ethical Considerations
The work concerns consequential applications including fraud, phishing, and illicit-activity detection. Its outputs should support rather than replace human review, with deployment-specific calibration and subgroup evaluation.
- 7 Ethical Considerations: MDTE is studied for imbalanced temporal-graph node classification with potential applications to fraud, phishing, and illicit-activity detection.
- 7 Ethical Considerations: Because false positives can misclassify legitimate accounts, MDTE should support rather than replace human review in consequential decisions.Practical deployments should calibrate thresholds to application-specific costs and evaluate performance across relevant subgroups.