Research map / Learning theory and algorithms / Matrix and tensor methods
Scalable Algorithms for Tractable Schatten Quasi-Norm Minimization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use tractable Schatten-2/3 (F/N) factored regularizer instead of LMaFit | matrix completion · MovieLens1M 70% SR | test RMSE: 0.9019 -> 0.8562 | Helped |
| use tractable Schatten-2/3 (F/N) factored regularizer instead of LMaFit | matrix completion · MovieLens10M 70% SR | test RMSE: 0.8496 -> 0.8021 | Helped |
| use tractable Schatten-2/3 (F/N) factored regularizer instead of LMaFit | matrix completion · Netflix 70% SR | test RMSE: 0.8923 -> 0.8459 | Helped |
| use Schatten quasi-norm (F/N) instead of nuclear-norm solver APGL | matrix completion · MovieLens1M 70% SR | test RMSE: 1.1431 -> 0.8562 | Helped |
| use F/N instead of IRucLq | matrix completion · MovieLens1M 70% SR | test RMSE: 0.8918 -> 0.8562 | Helped |
| use F/N instead of IRucLq | image recovery Boat · PSNR | PSNR: 26.36 -> 27.62 | Helped |
| use F/N instead of IRucLq (factor-matrix updates, no SVD) | image recovery Boat · running time | time (s): 805.81 -> 10.80 | Helped |
| use F/N instead of LMaFit | image recovery Boat · running time | time (s): 6.95 -> 10.80 | Hurt |
| use BiN (Schatten-1/2) instead of F/N (Schatten-2/3) | matrix completion · MovieLens1M 50% SR | test RMSE: 0.8764 -> 0.8741 | Mixed |
| vary Schatten p from 0.1 to 0.7 vs p=1 in IRucLq/IRNN-Lp | synthetic noisy matrix completion · RSE | RSE | Hurt |
| use Schatten quasi-norm methods instead of APGL at 20% SR | synthetic noisy matrix completion · RSE | RSE | Helped |
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