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An Effective Augmented Lagrangian Method for Fine-Grained Multi-View Optimization
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Proposes ALMOND, a sample-level (fine-grained) graph fusion method for multi-view clustering, optimized with an augmented Lagrangian method so no auxiliary intermediate variable is needed.
Problem
Existing graph-based multi-view clustering assigns weights to views in a view-wise manner, ignoring that views contribute differently to each sample, and prior fusion methods introduce inexplicable intermediate variables that break self-consistency.
Approach
Replaces view-level graph weighting with per-sample view weights in a unified objective combining multi-view subspace learning and sample-wise consensus graph fusion, and optimizes it with an augmented Lagrangian method (ALM) using closed-form updates for Z(v), J(v), W, S and the multiplier Y(v).
Key results
- On Cora, ALMOND reaches 73.00 ACC and 53.93 NMI, improving over the second-best method by 13.79% ACC and 16.00% NMI.
- On Citeseer, ALMOND reaches 62.43 ACC versus 60.37 for CoMSC, the second-best.
- On Cornell, LMVSC slightly beats ALMOND on ACC (61.45 vs 56.62 reported for ALMOND), and CoMSC beats it on F-score; MVCTM has best F-score on Yale.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ALMOND instead of the strongest reported baseline | Multi-view clustering · Cora | ACC: 13.79% | Helped |
| Use ALMOND instead of the strongest reported baseline | Multi-view clustering · Cora | NMI: 16.00% | Helped |
| Use ALMOND instead of the strongest reported baseline | Multi-view clustering · Cora | Purity: 6.76% | Helped |
| Use ALMOND instead of the strongest reported baseline | Multi-view clustering · Cora | F-score: 20.93% | Helped |
| Use ALMOND instead of the strongest reported baseline | Multi-view clustering · Citeseer | ACC: 3.41% | Helped |
| Use ALMOND instead of the strongest reported baseline | Multi-view clustering · Citeseer | NMI: 6.09% | Helped |
| Use ALMOND instead of the strongest reported baseline | Multi-view clustering · Citeseer | Purity: 7.04% | Helped |
| Use ALMOND instead of the strongest reported baseline | Multi-view clustering · Citeseer | F-score: 5.63% | Helped |
| Use ALMOND instead of the strongest reported baseline | Multi-view clustering · BBC | ACC: 3.12% | Helped |
| Use ALMOND instead of the strongest reported baseline | Multi-view clustering · BBC | NMI: 8.17% | Helped |
| Vary α, β, and γ within the tested parameter ranges (ablation) | ALMOND · ORL | clustering performance | No clear effect |
Surprising findings
- The method is not best on every dataset: on Cornell, CoMSC has higher F-score and LMVSC higher ACC; on Yale MVCTM has the best F-score.
- The authors report that clustering performance is unstable over a wider hyperparameter range, which they attribute to the ALM penalty parameter rho growing by 1.2x per iteration.
Limitations
- Performance is unstable across a wider range of hyperparameters, attributed to the penalty parameter rho.
- Loss curve is not smooth in early iterations, reflecting a conflict between global subspace learning and local fine-grained weighting.
- Method is not uniformly best across all benchmarks.
Experimental setup
Datasets: Yale ORL BBC (bbcseg13of3) Cora Cornell Citeseer
Benchmarks: Yale Citeseer Cora BBC ORL Cornell
Metrics: ACC NMI Purity F-score
Baselines: AWP CDG mPAC Co-reg Co-train FPMVS LMVSC MCGC MLAN MVCTM MVGL SwMC
Builds on: multi-view subspace clustering auto-weighted multiple graph learning augmented Lagrangian method
Closest papers by meaning
- Medusa: A Multi-Scale High-order Contrastive Dual-Diffusion Approach for Multi-View Clustering (CVPR 2025 · similarity 0.87)
- EASEMVC:Efficient Dual Selection Mechanism for Deep Multi-View Clustering (CVPR 2025 · similarity 0.86)
- Multi-view Granular-ball Contrastive Clustering (AAAI 2025 · similarity 0.86)
- Learn from View Correlation: An Anchor Enhancement Strategy for Multi-view Clustering (CVPR 2024 · similarity 0.85)
- Bifurcate then Alienate: Incomplete Multi-view Clustering via Coupled Distribution Learning with Linear Overhead (ICML 2025 · similarity 0.85)
- Robust Multi-view Clustering against Imperfect Information (NeurIPS 2026 · similarity 0.85)
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