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Multi-View Randomized Kernel Classification via Nonconvex Optimization
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Proposes RMKL, a multiple kernel learning method that builds a pool of randomized Gaussian kernels and selects a subset maximizing pairwise diversity and minimizing error via a nonconvex quadratic integer program solved by an SDP-based branch-and-bound.
Problem
Multiple kernel learning for multi-view classification typically ignores the tradeoff between diversity and accuracy of the combined base kernels, limiting classification performance.
Approach
Generate a pool of randomized kernels (per-feature random widths), then select a kernel subset by minimizing a quadratic objective combining pairwise double-fault diversity and cross-validated error; the nonconvex binary QP is reformulated as convex and solved exactly via SDP relaxation inside branch-and-bound.
Key results
- RMKL achieves the highest average ACC of 89.44% across eight datasets, versus 88.51% for the next best (PMKL/RPMKL family) and 83.68% for NMKL.
- RMKL is best on all 8 datasets by ACC, e.g., 96.11% on Armstrong-like D5 vs 95.42% for RPMKL and 98.58% on Caltech101-7 vs 98.13% for GMKL.
- RMKL works across SVM, SVMWB, LSSVM and LSKELM classifiers, with LSSVM performing much worse on most datasets.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use RMKL instead of EAMKL | SVM kernel classification · 3Sources | ACC: 89.28 -> 89.49 | Helped |
| Use RMKL instead of TSMKL | SVM kernel classification · MSRC-v1 | ACC: 98.11 -> 98.18 | Helped |
| Use RMKL instead of EAMKL | SVM kernel classification · Caltech101-7 | ACC: 98.13 -> 98.58 | Helped |
| Use RMKL instead of EAMKL | SVM kernel classification · NUS-WIDE | ACC: 41.93 -> 42.08 | Helped |
| Use RMKL instead of RPMKL | SVM kernel classification · Armstrong | ACC: 95.42 -> 96.11 | Helped |
| Use RMKL instead of LMKL | SVM kernel classification · Chen | ACC: 93.20 -> 94.10 | Helped |
| Use RMKL instead of EAMKL | SVM kernel classification · Chowdary | ACC: 97.45 -> 97.65 | Helped |
| Use RMKL instead of TSMKL | SVM kernel classification · Emanuel | ACC: 99.32 -> 99.32 | No clear effect |
Surprising findings
- LSSVM performs much worse than other kernel classifiers on most datasets, while RMKL still works across the tested classifiers.
Limitations
- Diversity is measured with a double-fault measure with no formal definition; quality is based on cross-validation error on the validation set.
- Chosen M and m hyperparameters are heuristic (M 2-3x m), with defaults M=10, m=5 for one-view datasets.
- Experiments are on relatively small datasets; generalization to broader tasks is untested.
Experimental setup
Datasets: 3Sources MSRC-v1 Caltech101-7 NUS-WIDE Armstrong Chen Chowdary Emanuel
Benchmarks: 3Sources MSRC-v1 Caltech101-7 NUS-WIDE Armstrong Chen Chowdary Emanuel
Metrics: classification accuracy (ACC) standard deviation Rank1 count win/tie/loss via Wilcoxon test
Baselines: GMKL ALMKL TSMKL RPMKL EAMKL ELMKL DMKL PMKL NMKL LMKL
Builds on: randomized kernel (Ding et al. 2021) double-fault diversity measure (Giacinto and Roli 2001) SDP relaxation of quadratic binary programs spectral bundle method
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