Swiss roll
Benchmarks
| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| Manifold Learning | Swiss roll uniform sampling | Spearman Corr (row)99.3 | 24 | |
| Distance-level row-wise correlation | Swiss roll Non-uniform sampling (Beta(1, 4)) analytic geodesic ground truth | Spearman Correlation1 | 21 | |
| Distance-level row-wise correlation | Swiss roll Uniform sampling analytic geodesic ground truth | Spearman Correlation0.993 | 21 | |
| Manifold Learning Embedding | Swiss roll (non-uniform (Beta(1, 4)) sampling) | Trustworthiness0.995 | 12 | |
| Manifold Learning | Swiss Roll non-uniform sampling | Spearman Correlation1 | 12 | |
| Regression | Swiss Roll d = 1000 (cross-validation) | Median SSE458.2 | 9 | |
| Classification | Swiss Roll (test) | Accuracy96.7 | 9 | |
| Disentangled Representation Learning | Noisy Swiss Roll ρ = 0.3 | Mutual Information I(z; w)0.502 | 7 | |
| Distance matrix comparison | Swiss roll (test) | Spearman Correlation (row)0.991 | 7 | |
| Regression | Swiss Roll 100 points (test) | R2 Score97 | 6 | |
| Regression | Swiss Roll 100 points (train) | R2 Score0.99 | 6 | |
| Manifold Learning | Swiss roll non-unif., analytic | Trustworthiness98.1 | 5 | |
| Downstream Linear Separability | Swiss Roll 3 -> 2 | 5-Fold CV Accuracy96.3 | 5 | |
| Manifold embedding | Swiss Roll (mean) | Correlation0.8575 | 5 | |
| Manifold embedding | Swiss Roll (view 2) | Correlation0.9289 | 5 | |
| Manifold embedding | Swiss Roll (view 1) | Correlation0.8235 | 5 | |
| Clustering | Swiss roll | Homogeneity82 | 5 | |
| Manifold Sampling | Swiss Roll 2d | Sinkhorn Distance (W2^2)0.08 | 4 | |
| Sampling on manifolds | Swiss Roll 2d synthetic (test) | W2 Distance0.08 | 3 | |
| Manifold Learning | Swiss Roll | Correlation (View 1)0.9771 | 3 | |
| Intrinsic Dimension Estimation | Swiss roll | Estimated Intrinsic Dimension2.19 | 2 |
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