Research map / Learning theory and algorithms / Prediction and decision losses
SpaceMAP: Visualizing High-Dimensional Data by Space Expansion
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Hierarchical manifold approximation (dlocal != dglobal) vs. single ID (dlocal = dglobal) (ablation) | SpaceMAP · MNIST and Fashion-MNIST (Table 2) | MKL and local normalized stress (lower is better): MNIST MKL 0.9961->0.9915; M'sigma 0.6714->0.6576; FMNIST MKL 1.2915->1.2594; M'sigma 0.9403->0.9218 | Helped |
| Replace UMAP similarity with SpaceMAP EED-based similarity (hierarchical) | SpaceMAP vs UMAP · MNIST local structure (Table 2) | MKL / local normalized stress (lower is better): MKL 1.0014->0.9915; M'sigma 0.9413->0.6576 | Helped |
| Use SpaceMAP instead of baselines (trustworthiness/continuity) | SpaceMAP · MNIST, FMNIST, COIL-20, RNA-Seq (Table 1) | trustworthiness and continuity: SpaceMAP ties or slightly beats t-SNE/UMAP on local metrics; t-SNE 1.00 on RNA-Seq Mt equals SpaceMAP | Mixed |
| Use SpaceMAP instead of UMAP/t-SNE (Shepard goodness) | SpaceMAP · RNA-Seq and FMNIST (Table 1) | Shepard goodness Ms: RNA-Seq 0.63 vs t-SNE 0.61, UMAP 0.22; FMNIST 0.67 vs t-SNE 0.64 | Helped |
| Use SpaceMAP instead of PCA/t-SNE (Shepard goodness) | SpaceMAP · MNIST and COIL-20 (Table 1) | Shepard goodness Ms: MNIST tied with t-SNE 0.35 and above UMAP 0.32; COIL-20 0.61 below PCA 0.89 and t-SNE 0.80 | Mixed |
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