Research map / Learning theory and algorithms / Matrix and tensor methods
Random Tensor Theory for Tensor Decomposition
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace unfolding matrices with tetrahedral matrices in HOOI (ablation) | HOOI · Yale Face Database B with Gaussian noise | normalized Frobenius error: 0.696 ±0.008 -> 0.610 ±0.017; 0.845 ±0.006 -> 0.648 ±0.010; 0.993 ±0.008 -> 0.707 ±0.019; 1.125 ±0.007 -> 0.754 ±0.013 | Helped |
| Use the tetrahedral graph instead of the melon graph | Tensor PCA · Symmetric tensor PCA | correlation with the signal vector | Helped |
| Use the tetrahedral method instead of ALS or power iteration | CP decomposition · Synthetic CP decomposition | success rate | Helped |
| Use Tetra-HOOI instead of HOOI or HOSVD | Tucker decomposition · Synthetic symmetric Tucker decomposition | normalized Frobenius error | Helped |
| Use the melon graph for tensors with unequal axis dimensions | Tensor PCA · Asymmetric Tensor PCA | recovery threshold β | Mixed |
Closest papers by meaning
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- Fitting Low-Rank Tensors in Constant Time (NeurIPS 2017 · similarity 0.89)
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- Approximately Optimal Core Shapes for Tensor Decompositions (ICML 2023 · similarity 0.88)
- Tensor Wheel Decomposition and Its Tensor Completion Application (NeurIPS 2022 · similarity 0.88)
- Low-Rank Tucker Decomposition of Large Tensors Using TensorSketch (NeurIPS 2018 · similarity 0.88)
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