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Enhancing Ensemble Clustering with Adaptive High-Order Topological Weights
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Proposes AWEC, an ensemble clustering method that compensates missing connections in the co-association matrix using adaptive-weighted high-order connectivity and then learns a topology graph via ADMM, evaluated on 14 datasets against 9 ensemble baselines.
Problem
Ensemble clustering relies on the co-association (CA) matrix, which assigns zero to same-class sample pairs that all base clusterings separate (missing connections), limiting consensus quality.
Approach
Mines neighborhood high-order connectivity of the CA matrix, learns an optimal connection matrix as an adaptively weighted combination of multi-order connectivity matrices, denoises it with a CA-enhancement assumption, and embeds it into topology learning with a rank constraint on the Laplacian, all in one unified ADMM framework.
Key results
- AWEC-H reaches ARI 0.4659 on Appendicitis versus 0.4533 for the best baseline TRCE, and ARI 0.2794 on Breast Tissue versus 0.1868 for SPCE.
- The ARI of AWEC on Vertebral3c is reported as improved by 38% over ECCMS.
- Maximum order of 2 is recommended; higher orders did not consistently improve NMI (Table 5).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add the topology module (ablation) | AWEC-H · Appendicitis | NMI: 0.1640 -> 0.2989 | Helped |
| Add high-order learning (ablation) | AWEC-H · Appendicitis | NMI: 0.1524 -> 0.2989 | Helped |
| Add the topology module (ablation) | AWEC-H · Coil20 | NMI: 0.8183 -> 0.8416 | Helped |
| Add high-order learning (ablation) | AWEC-H · Coil20 | NMI: 0.8146 -> 0.8416 | Helped |
| Add the topology module (ablation) | AWEC-H · MF | NMI: 0.6547 -> 0.6972 | Helped |
| Add high-order learning (ablation) | AWEC-H · MF | NMI: 0.6007 -> 0.6972 | Helped |
| Use maximum order 2 instead of 1 (ablation) | AWEC-H · Appendicitis | NMI: 0.2510 -> 0.2989 | Helped |
| Increase maximum order from 2 to 3 (ablation) | AWEC-H · Appendicitis | NMI: 0.2989 -> 0.1824 | Hurt |
| Use maximum order 2 instead of 1 (ablation) | AWEC-S · Vertebral3c | NMI: 0.4933 -> 0.5278 | Helped |
| Use AWEC-S rather than the strongest ARI baseline | Appendicitis · Appendicitis | ARI: 0.4533 -> 0.3723 | Hurt |
| Use AWEC-H rather than the strongest ARI baseline | Breast Cancer · Breast Cancer | ARI: 0.8888 -> 0.8894 | Helped |
| Use AWEC-S rather than the strongest ARI baseline | Led7digit · Led7digit | ARI: 0.4934 -> 0.4896 | Hurt |
Surprising findings
- Higher maximum connectivity order (3rd to 5th) does not increase performance, with the optimum usually at order 3 or lower.
Limitations
- Performance on some datasets is sensitive to the hyperparameters lambda and gamma.
- Iterative ADMM with O(n^3) per-iteration complexity is costly for large n.
- Not every dataset is best on every metric (e.g., NMI on Coil20 and Control, F1 on Vertebral2c).
Experimental setup
Datasets: Appendicitis Breast Cancer Binalpha Breast Tissue Coil20 Control Fertility IS Led7digit Ionosphere MF Vertebral3c
Benchmarks: Appendicitis Breast Cancer Binalpha Breast Tissue Coil20 Control Fertility IS Led7digit Ionosphere MF Vertebral3c
Metrics: NMI ARI F1-score
Baselines: KM KM-best CESHL ECCMS SPCE DREC TRCE LWEA ECPCS-HC RSEC-Z RSEC-H
Builds on: ECCMS co-association matrix topology learning (Huang et al. 2022) high-order connectivity (Zhou et al. 2020)
Closest papers by meaning
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- Learning Persistent Community Structures in Dynamic Networks via Topological Data Analysis (AAAI 2024 · similarity 0.84)
- ToMAToMP: Robust and Multi-Parameter Topological Clustering (NeurIPS 2026 · similarity 0.84)
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