Research map / Learning theory and algorithms / Prediction and decision losses
On the Distribution of Minima in Intrinsic-Metric Rotation Averaging
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| increase graph connectivity (Watts-Strogatz rewiring) from row 1 to 3 | Rotation averaging landscape · Synthetic 40-node graphs | ease of finding dominant minimum: lambda2 4.6 -> 8.2 | Helped |
| increase connectivity further from row 3 to row 4 | Rotation averaging landscape · Watts-Strogatz graphs | difficulty: lambda2 8.2 -> 9.5 | No clear effect |
| increase noise level sigma_n | Rotation averaging landscape · Synthetic graphs | number of distinct local minima | Hurt |
| use more edges in Gnm graph (200 -> 400 edges) | Rotation averaging landscape · Gnm n=40 | landscape messiness: lambda2 4.2 -> 12.0 | Helped |
| fewer edges (m=200) vs m=240 | Rotation averaging landscape · Gnm n=40 | landscape messiness: lambda2 9.5 -> 4.2 | Hurt |
| use random initialization at low noise | Levenberg-Marquardt · Watts-Strogatz row 3 column 1 | success rate: 97.5% | Helped |
| rely on alpha_max certificate to predict difficulty | Eriksson et al. bound · Gnm graphs | agreement with observed difficulty: alpha_max 20.2 -> 12.0 as connectivity rises | Hurt |
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