Research map / Learning theory and algorithms / Matrix and tensor methods
Input-Sparsity Low Rank Approximation in Schatten Norm
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the Schatten 1-norm algorithm instead of the Frobenius-norm solution | Low-rank approximation on synthetic data · Synthetic data, k=5, k=10, k=20 | relative Schatten 1-norm approximation error: 0.00412 -> 0.00372; 0.00485 -> 0.00377; 0.00637 -> 0.00486 | Helped |
| Use the Schatten 1-norm algorithm instead of the Frobenius-norm solution | Low-rank approximation on KOS · KOS, k=5, k=10, k=20 | relative Schatten 1-norm approximation error: 0.0183 -> 0.0149; 0.0216 -> 0.0145; 0.0259 -> 0.0132 | Helped |
| Use the Schatten 1-norm algorithm instead of the Frobenius-norm solution | Low-rank approximation on synthetic data · Synthetic data, k=5, k=10, k=20 | runtime: 0.044s -> 0.067s; 0.073s -> 0.196s; 0.191s -> 0.428s | Hurt |
| Use the Schatten 1-norm algorithm instead of the Frobenius-norm solution | Low-rank approximation on KOS · KOS, k=5, k=10, k=20 | runtime: 0.113s -> 0.155s; 0.154s -> 0.204s; 0.242s -> 0.323s | Hurt |
| Use the Schatten 1-norm algorithm instead of a full SVD | Low-rank approximation on synthetic data · Synthetic data, k=5, k=10, k=20 | runtime: 5.788s; 0.067s; 0.196s; 0.428s | Helped |
| Use the Schatten 1-norm algorithm instead of a full SVD | Low-rank approximation on KOS · KOS, k=5, k=10, k=20 | runtime: 4.999s; 0.155s; 0.204s; 0.323s | Helped |
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