Research map / Learning theory and algorithms / Kernels and regression theory
A Nonlinear Regression Technique for Manifold Valued Data With Applications to Medical Image Analysis
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use nonlinear kernel-based manifold regression rather than CCA | Synthetic SPD(3) data · Synthetic SPD(3) data | reported association score (R² for regression; CC for CCA): 0.771 CC; 0.895 R² | Mixed |
| Use nonlinear kernel-based manifold regression rather than CCA | Synthetic S⁹ data · Synthetic S⁹ data | reported association score (R² for regression; CC for CCA): 0.996 CC; 0.998 R² | Mixed |
| Regress SDT to age rather than CPⁿ to age | OASIS corpus callosum shape-to-age regression · OASIS: shape to age | R²: 0.474–0.737 -> 0.888–0.988 | Helped |
| Use CPⁿ as the input and SDT as the output rather than the reverse | OASIS corpus callosum representation regression · OASIS: CPⁿ and SDT | R²: 0.348, 0.626, 0.631 -> 0.479, 0.752, 0.754 | Helped |
| Increase the number of control points from 9 to 12 | Nonlinear manifold regression · OASIS: CPⁿ to SDT | R²: 0.479 -> 0.752 | Helped |
| Increase the number of control points from 12 to 18 | Nonlinear manifold regression · OASIS: CPⁿ to SDT | R²: 0.752 -> 0.754 | No clear effect |
| Replace the weighted Fréchet mean with the weighted Fréchet median (ablation) | SPD(3) to S² regression · Synthetic data with 0% outliers | R²: 0.349 -> 0.280 | Hurt |
| Replace the weighted Fréchet mean with the weighted Fréchet median (ablation) | SPD(3) to S² regression · Synthetic data with outliers | R²: 0.222 -> 0.265; 0.092 -> 0.251; −0.043 -> 0.262; −0.170 -> 0.350; −0.527 -> 0.377; −7.151 -> 0.354 | Helped |
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