Research map / Learning theory and algorithms / Prediction and decision losses
Nearly Isometric Embedding by Relaxation
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Run Riemannian Relaxation starting from the output of Isomap, Laplacian Eigenmaps, HLLE or MVU | Swiss hole and half sphere embeddings · Pairwise distance error dis vs noise level | dis | Helped |
| Run RR after Isomap initialization | Isomap · Swiss hole and half sphere | dis | No clear effect |
| Initialize RR at an hourglass shape and optimize Loss using only the Laplacian and weights from the sphere data | RR · Hourglass to sphere | recovery of sphere and noise | Helped |
| Apply PCS-RR to rescale a Laplacian Eigenmaps embedding along three principal curves | Laplacian Eigenmaps embedding of SDSS galaxies · SDSS main galaxy sample | ||H_k|| distortion | Helped |
| Subsample the loss to n'=2000 points chosen via principal curves instead of using all points | RR (PCS-RR) · SDSS galaxies | scalability | Helped |
| Compare RR convergence time against Isomap | RR · Swiss hole and half sphere | convergence speed | Helped |
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