Research map / Learning theory and algorithms / Prediction and decision losses
Joint Dimensionality Reduction and Metric Learning: A Geometric Take
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Learn the projection W jointly with the metric M (vs. PCA preprocessing then metric learning) | DRML · ASLAN | AUC: 0.630 vs 0.602 for best PCA baseline at p=25 | Helped |
| Fix W to the PCA subspace and learn only the metric (no joint learning) (ablation) | DRML · ASLAN HoG | CRR: roughly 1% drop, 57.4% CRR | Hurt |
| Use quotient geometry on W M W^T (full DRML) vs LL^T factorization with Euclidean geometry (ablation) | Metric factorization · ASLAN | AUC: 0.617 vs 0.601 at p=1000 | Helped |
| Kernelize the joint formulation (kDRML) with RBF kernel on ASLAN | DRML · ASLAN HoF | AUC: 0.64 vs 0.60 (DRML HoF 0.64 vs kDRML 0.64) | Helped |
| Kernelize formulation (kDRML) with Chi-square kernel on iLIDS | DRML · iLIDS | CMC rank-1: 39.2% vs 32.0% | Helped |
| Replace PCA preprocessing with joint learning across ASLAN features (DRML AUC vs PCA-based baselines) | Metric learning on ASLAN · ASLAN HnF | AUC: DRML 0.63 vs LDML 0.61 | Helped |
| Use projection kernel on Grassmann-manifold subspaces (kDRML) instead of PCA-based baselines | kDRML · YTF | Accuracy: 71.9% vs 67.5% for KISSME (closest) | Helped |
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- RMLR: Extending Multinomial Logistic Regression into General Geometries (NeurIPS 2024 · similarity 0.85)
- Follow the Energy, Find the Path: Riemannian Metrics from Energy-Based Models (NeurIPS 2025 · similarity 0.85)
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