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Sharper Error Bounds in Late Fusion Multi-view Clustering with Eigenvalue Proportion Optimization
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Gives a local-Rademacher generalization bound for multiple kernel k-means with principal eigenvalue proportion (O(1/n) rate) and proposes GMLKM, a graph-filter-enhanced multiple linear k-means for late-fusion multi-view clustering.
Problem
Late fusion multi-view clustering suffers from noisy and redundant base partitions and fails to capture high-order correlations; existing LFMVC generalization bounds only reach O(sqrt(k/n)).
Approach
Derives a sharper O(1/n) generalization bound for multiple kernel k-means using local Rademacher complexity and principal eigenvalue proportion, then learns an optimal low-pass graph filter over base partitions (learnable combination of view-specific graph filters) within a multiple linear k-means framework to raise the eigenvalue proportion and denoise partitions.
Key results
- GMLKM achieves the best ACC on all ten datasets in the reported table, e.g., 87.2% on Lung and 97.3% on JAFFE versus OPLF's 86.7% and 97.3%.
- The theory claims a generalization error convergence rate of O(1/n) versus the prior O(sqrt(k/n)) for LFMVC methods, under a polynomial eigenspectrum decay assumption and a sufficiently large t.
- On CBMC, GMLKM reaches 68.5% ACC versus 66.0% for OPLF and 62.1% for avgH.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use graph-filter-enhanced multiple linear K-means (GMLKM) instead of OPLF | Late-fusion multi-view clustering · Lung | ACC (%): 86.7 ± 0.0 -> 87.2 ± 0.0 | Helped |
| Use graph-filter-enhanced multiple linear K-means (GMLKM) instead of OPLF | Late-fusion multi-view clustering · CSTR | ACC (%): 90.3 ± 0.0 -> 91.8 ± 0.0 | Helped |
| Use graph-filter-enhanced multiple linear K-means (GMLKM) instead of the strongest listed baseline | Late-fusion multi-view clustering · ISOLET | ACC (%): 57.1 ± 2.6 -> 60.4 ± 0.6 | Helped |
| Use graph-filter-enhanced multiple linear K-means (GMLKM) instead of the strongest listed baseline | Late-fusion multi-view clustering · WAP | ACC (%): 42.9 ± 3.4 -> 47.7 ± 0.5 | Helped |
| Use graph-filter-enhanced multiple linear K-means (GMLKM) instead of OPLF | Late-fusion multi-view clustering · Mfeat | ACC (%): 94.9 ± 2.8 -> 94.7 ± 2.7 | No clear effect |
| Use graph-filter-enhanced multiple linear K-means (GMLKM) instead of OPLF | Late-fusion multi-view clustering · K1b | ACC (%): 92.0 ± 0.3 -> 93.0 ± 0.0 | Helped |
| Use graph-filter-enhanced multiple linear K-means (GMLKM) instead of OPLF | Late-fusion multi-view clustering · MouseBladder | ACC (%): 61.6 ± 0.5 -> 62.3 ± 0.5 | Helped |
| Use graph-filter-enhanced multiple linear K-means (GMLKM) instead of OPLF | Late-fusion multi-view clustering · PBMC | ACC (%): 64.1 ± 0.7 -> 66.6 ± 0.6 | Helped |
| Use graph-filter-enhanced multiple linear K-means (GMLKM) instead of OPLF | Late-fusion multi-view clustering · CBMC | ACC (%): 66.0 ± 0.2 -> 68.5 ± 0.3 | Helped |
| Use graph-filter-enhanced multiple linear K-means (GMLKM) instead of OPLF | Late-fusion multi-view clustering · JAFFE | ACC (%): 97.3 ± 2.7 -> 97.3 ± 2.7 | No clear effect |
| Use GMLKM instead of OPLF | Late-fusion multi-view clustering · WAP | NMI (%): 52.0 ± 0.2 -> 47.9 ± 0.8 | Hurt |
| Use GMLKM instead of OPLF | Late-fusion multi-view clustering · Lung | NMI (%): 66.6 ± 0.0 -> 66.7 ± 0.0 | Helped |
Surprising findings
- Reported results show GMLKM tying OPLF on JAFFE ACC (97.3%) and ISOLET-level ties in some metrics, with several gains being small relative to standard deviations.
Limitations
- Theoretical O(1/n) rate depends on assumed polynomial spectral decay and a sufficiently large t, not verified empirically.
- Several reported improvements are within large standard deviations, and the neighborhood size is fixed at 5 without tuning.
- Theory is extended to kernel learning only as a future direction; the graph filter enhancement is not directly proven to raise PEP.
Experimental setup
Datasets: Lung JAFFE CSTR ISOLET WAP Mfeat K1b MouseBladder PBMC CBMC
Benchmarks: Lung JAFFE CSTR ISOLET WAP Mfeat K1b MouseBladder PBMC CBMC
Metrics: ACC NMI ARI
Baselines: AvgH AWP LFMVC OPLF LFLKA ALMVC M3LF sLGm RIWLF
Builds on: MKKM / SimpleMKKM One Pass Late Fusion (OPLF) Principal eigenvalue proportion (Liu et al. 2017) local Rademacher complexity (Bartlett et al. 2005)
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