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Max-Mahalanobis Anchors Guidance for Multi-View Clustering
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Proposes Max-Mahalanobis Anchors (MMA), a fixed geometric anchor design maximizing minimum inter-anchor Mahalanobis distance, and the MAGIC multi-view clustering method that aligns consensus representations to these anchors.
Problem
Anchor-based multi-view clustering suffers from unstable anchor initialization (fixed anchors) and over-restrictive orthogonal constraints (optimized anchors), and the desired properties of anchors are not formally specified.
Approach
Formalizes anchor desiderata (Diversity, Balance, Compactness) via angles between anchors and constructs closed-form Max-Mahalanobis Anchors that satisfy them with theoretical bounds; then guides cross-view consensus representations to align with these fixed anchors via coordinate descent.
Key results
- MAGIC improves ACC over the second-best method by 18.25% on BBC, 7.92% on Reuters, 6.00% on 100Leaves, 11.08% on Cora and 7.22% on Wiki fea.
- Plugging MMA into SMVSC raises BBC accuracy from 35.91 to 83.80 and 100Leaves from 38.19 to 78.13.
- The overall time complexity of MAGIC is stated as O(N), and it runs out-of-memory-free on the largest datasets where some baselines fail.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MAGIC with Max-Mahalanobis Anchors | multi-view clustering methods · BBC, Wikipedia, Reuters, 100Leaves, Cora, Wiki fea, ALOI-100, VGGFace, YouTubeFace, CIFAR100 | ACC | Helped |
| Replace orthogonal anchors with MMA (ablation) | SMVSC · BBC, 100Leaves, ALOI-100, YouTubeFace | accuracy: (+47.89), (+39.94), (+38.95), (+10.08) | Helped |
| Replace orthogonal anchors with MMA (ablation) | OMSC · BBC, 100Leaves, YouTubeFace | accuracy: (+3.50), (+0.62), (+4.98) | Helped |
| Replace orthogonal anchors with MMA (ablation) | OMSC · ALOI-100 | accuracy: (-0.22) | Hurt |
| Replace orthogonal anchors with MMA (ablation) | AIMC · BBC, 100Leaves, ALOI-100, YouTubeFace | accuracy: (+1.75), (+0.81), (+2.31), (+0.42) | Helped |
Surprising findings
- Orthogonal anchors in OMSC are replaced by MMA with a slight accuracy drop on ALOI-100 (-0.22%), showing MMA is not uniformly better.
Limitations
- Anchor count is set to K (number of clusters) in ablations, and the approach is evaluated only on anchor-based clustering with a single hyperparameter lambda.
- The compactness property is argued geometrically rather than empirically measured; the theoretical bound is stated for uniform norm anchors.
- Several baselines OOM on large datasets, and the reported comparisons rely on a fixed default constant C=1.
Experimental setup
Datasets: BBC Wikipedia Reuters 100Leaves Cora Wiki fea ALOI-100 VGGFace YouTubeFace CIFAR100
Benchmarks: BBC Wikipedia Reuters 100Leaves Cora Wiki fea ALOI-100 VGGFace YouTubeFace CIFAR100
Metrics: ACC NMI Purity Fscore
Baselines: BMVC LMVSC SFMC FPMVS OMSC AIMC AWMVC SMSC RCAGL
Builds on: anchor-based multi-view clustering Max-Mahalanobis center loss orthogonal anchor learning
Closest papers by meaning
- Learn from View Correlation: An Anchor Enhancement Strategy for Multi-view Clustering (CVPR 2024 · similarity 0.94)
- Anchor Learning with Potential Cluster Constraints for Multi-view Clustering (AAAI 2025 · similarity 0.94)
- Learning Cluster-Wise Anchors for Multi-View Clustering (AAAI 2024 · similarity 0.93)
- Towards Learnable Anchor for Deep Multi-View Clustering (AAAI 2025 · similarity 0.92)
- From Spectrum-free towards Baseline-view-free: Double-track Proximity Driven Multi-view Clustering (ICML 2025 · similarity 0.90)
- Alleviate Anchor-Shift: Explore Blind Spots with Cross-View Reconstruction for Incomplete Multi-View Clustering (NeurIPS 2024 · similarity 0.90)
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