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Upper Bounding Barlow Twins: A Novel Filter for Multi-Relational Clustering
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Proposes BTGF, a Barlow Twins-guided graph filter for multi-relational clustering that learns a feature-dependent filter so the encoder input inner product is positive semi-definite, giving a Barlow Twins upper bound, paired with a linear autoencoder and DEC-style clustering loss.
Problem
Multi-relational (multi-layer graph with attributes) clustering struggles to fuse diverse relations; existing graph filters are fixed low-pass filters that ignore cross-view correlation, and Barlow Twins-based multi-view clustering suffers insufficient optimization.
Approach
Theoretically show that a negative semi-definite cross-view inner product of filtered inputs gives a lower bound on Barlow Twins loss, while a positive semi-definite one gives an upper bound; learn a feature-based graph filter (closed-form via a regularized least-squares objective with Woodbury identity) that makes the inner product positive semi-definite, so the filter is correlated across views
Key results
- BTGF reaches ACC 0.9322 on ACM, 0.8309 on DBLP, 0.6603 on Amazon and 0.7308 on AMiner, outperforming all compared methods on all four metrics.
- Relative to MGCCN, the paper reports average improvements of 11% ACC, 16% F1, 45% NMI and 34% ARI.
- Ablation: removing the feature decorrelation loss drops ACC on Amazon from 0.6603 to 0.5885; filter variants (low-pass, mix-pass, no filter) all underperform the proposed filter.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add feature decorrelation loss L_FD (ablation) | BTGF · ACM, DBLP, Amazon, AMiner | ACC: 0.9121 -> 0.9322; 0.8212 -> 0.8309; 0.5885 -> 0.6603; 0.6817 -> 0.7308 | Helped |
| add feature reconstruction loss L_MSCE (ablation) | BTGF · ACM, DBLP, Amazon, AMiner | ACC: 0.9296 -> 0.9322; 0.8041 -> 0.8309; 0.5149 -> 0.6603; 0.5506 -> 0.7308 | Helped |
| replace BTGF filter with a low-pass filter (ablation) | BTGF · ACM, DBLP, Amazon, AMiner | ACC: 0.9088 -> 0.9322; 0.8195 -> 0.8309; 0.6184 -> 0.6603; 0.7116 -> 0.7308 | Hurt |
| replace BTGF filter with a mix-pass filter (ablation) | BTGF · ACM, DBLP, Amazon, AMiner | ACC: 0.9250 -> 0.9322; 0.8148 -> 0.8309; 0.6462 -> 0.6603; 0.5716 -> 0.7308 | Hurt |
| remove graph filter preprocessing (ablation) | BTGF · ACM, DBLP, Amazon, AMiner | ACC: 0.8707 -> 0.9322; 0.7166 -> 0.8309; 0.6004 -> 0.6603; 0.3326 -> 0.7308 | Hurt |
Surprising findings
- On Amazon the paper observes that the Barlow Twins upper bound is even smaller than the lower bound of the negative semi-definite case, suggesting better solutions than that bound allows.
- Low-pass filtering alone can underperform even when a mix-pass filter is used, e.g., AMiner ACC is 0.7116 for low-pass versus 0.5716 for mix-pass, showing filter choice is dataset dependent.
Limitations
- Encoder and decoder are a single linear layer each, so the architecture is very simple and not tuned for deep models.
- Hyperparameters k and gamma are tuned over grids, with sensitivity to gamma (too small or too large degrades performance).
Experimental setup
Datasets: ACM DBLP Amazon AMiner
Benchmarks: ACM DBLP Amazon AMiner
Metrics: ACC F1 NMI ARI
Baselines: HAN HDMI O2MAC MvAGC MCGC MGCCN MGDCR
Builds on: Barlow Twins MCGC MvAGC DCRN SCE
Closest papers by meaning
- Attribute-Missing Multi-view Graph Clustering (CVPR 2025 · similarity 0.87)
- Homophily-Related: Adaptive Hybrid Graph Filter for Multi-View Graph Clustering (AAAI 2024 · similarity 0.86)
- THESAURUS: Contrastive Graph Clustering by Swapping Fused Gromov-Wasserstein Couplings (AAAI 2025 · similarity 0.86)
- ClusterFuG: Clustering Fully connected Graphs by Multicut (ICML 2023 · similarity 0.86)
- DGCLUSTER: A Neural Framework for Attributed Graph Clustering via Modularity Maximization (AAAI 2024 · similarity 0.86)
- Scalable Attribute-Missing Graph Clustering via Neighborhood Differentiation (ICML 2025 · similarity 0.86)
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