Research map / Learning theory and algorithms / Matrix and tensor methods
Efficient, Sparse Representation of Manifold Distance Matrices for Classical Scaling
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use sparse biharmonic interpolation instead of FMDS | Geodesic distance matrix approximation · Dragon320k | memory at error of one part in 100,000: 200 MB vs. 4 GB; roughly 20x less memory | Helped |
| Use sparse biharmonic interpolation instead of FMDS | Geodesic distance matrix approximation · Brain | memory at the same approximation performance: 3-4x less memory | Helped |
| Use sparse BMDS with Lanczos rather than dense BMDS | MDS on large meshes · Dragon meshes | memory usage | Helped |
| Use sBMDS rather than FMDS | MDS · Brain | stress at the same landmark count | Mixed |
| Use sBMDS rather than LMDS | MDS · Brain | stress | Helped |
| Use sBMDS rather than normal MDS | MDS · Dragon meshes | scalability under memory constraints | Helped |
| Use sBHA with p_row=50 rather than denser interpolation (ablation) | BHA · Brain | relative approximation error | Hurt |
| Use sBHA with p_row below 50 (ablation) | BHA · Brain | relative approximation error | Hurt |
| Vary sBHA p_row from 10 to 100 (ablation) | BHA · Brain | relative approximation error | Mixed |
| Increase the number of landmarks (ablation) | BHA, sBHA, FMDS, SMDS, and Nyström · Brain | relative approximation error | Helped |
| Use the Nyström pseudoinverse approximation instead of biharmonic interpolation | Geodesic distance matrix approximation · Brain | relative approximation error | Hurt |
| Use FMDS rather than BHA | Geodesic distance matrix approximation · Brain | relative approximation error at the same landmark count | Helped |
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