Research map / Learning theory and algorithms / Matrix and tensor methods
HoroPCA: Hyperbolic Dimensionality Reduction via Horospherical Projections
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Horospherical projection (HoroPCA) instead of geodesic projection for hyperbolic PCA | HoroPCA · 10-dim to 2-dim dimensionality reduction on 4 hierarchical datasets | average distortion: e.g. Phylo Tree 0.13 vs 0.32 for best baseline hAE | Helped |
| Base point perturbation (Gaussian noise) added to PGA (ablation) | PGA · Balanced Tree dimensionality reduction | distortion: 0.63 to 0.87 | Hurt |
| Base point perturbation (Gaussian noise) added to BSA (ablation) | BSA · Diseases dimensionality reduction | distortion: 0.52 to 0.80 | Hurt |
| Horospherical whitening (HoroPCA Busemann coordinates) before classifier | eSVM classification · Football whitening | accuracy: 25.0 vs 20.7 for eSVM without whitening | Helped |
| Geodesic-projection whitening (PGA log map) before classifier | eSVM classification · Polblogs whitening | accuracy: 82.3 vs 92.3 for eSVM | Hurt |
| Horospherical whitening vs tPCA whitening | HoroPCA+eSVM · Polbooks, Football, Polblogs whitening | accuracy: Polblogs gain only 92.8 vs 92.4 | Mixed |
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