Research map / Learning theory and algorithms / Clustering
Ratio Trace Formulation of Wasserstein Discriminant Analysis
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace trace ratio WDA (gradient descent) with ratio trace WDA-eig (SCF), lambda=0.1 | WDA · Simulated 3-class data | probability of convergence: 25% -> 100% | Helped |
| Replace WDA with WDA-eig, lambda=0.1 | WDA · Simulated 3-class data | average accuracy: 0.712 -> 0.968 | Helped |
| Replace WDA with WDA-eig, lambda=0.1 | WDA · Simulated 3-class data | CPU time (s): 72 -> 0.677 | Helped |
| Replace WDA with WDA-eig, lambda=1.0 | WDA · Simulated 3-class data | CPU time (s): 6.37 -> 1.17 | Helped |
| Replace WDA with WDA-eig, lambda=5.0 | WDA · Simulated 3-class data | probability of convergence: 73% -> 100% | Helped |
| Ratio trace instead of trace ratio, converged trials only | WDA · Simulated 3-class data | converged-trial accuracy: 0.977 -> 0.968 | No clear effect |
| Ratio trace instead of trace ratio, converged trials, lambda=5.0 | WDA · Simulated 3-class data | converged-trial accuracy: 0.985 -> 0.985 | No clear effect |
| Subspace dimension p equal to true discriminative dimension 2 (ablation) | WDA-eig SCF · Simulated 3-class data | convergence rate | Helped |
| Larger Wasserstein regularizer lambda (ablation) | WDA-eig SCF · Simulated 3-class data | convergence rate: lambda 0.001 to 2 slower | Hurt |
| Vary initialization distance from true subspace (ablation) | WDA-eig SCF · Simulated data | convergence rate | No clear effect |
| Use WDA-eig+KNN instead of PCA/FDA | WDA-eig · MNIST (1000 train, 10000 test) | KNN prediction error | Helped |
| Replace FDAKm with WDAKm | K-means clustering · MNIST | ARI: 0.360 ± 0.006 -> 0.398 ± 0.008 | Helped |
Closest papers by meaning
- Trace Ratio Optimization With Feature Correlation Mining for Multiclass Discriminant Analysis (AAAI 2018 · similarity 0.88)
- Complex Moment-Based Supervised Eigenmap for Dimensionality Reduction (AAAI 2019 · similarity 0.85)
- Mixed-Features Vectors and Subspace Splitting (ICLR 2021 · similarity 0.85)
- Heterogeneous Sufficient Dimension Reduction and Subspace Clustering (ICML 2025 · similarity 0.84)
- An Optimal Transport View for Subspace Clustering and Spectral Clustering (AAAI 2024 · similarity 0.83)
- Fast unsupervised ground metric learning with tree-Wasserstein distance (ICLR 2025 · similarity 0.82)
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