Research map / Learning theory and algorithms / Matrix and tensor methods
Convergence of Alternating Gradient Descent for Matrix Factorization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the proposed initialization with column-span initialization and asymmetric scaling instead of standard random initialization | Gradient descent for matrix factorization · Synthetic rank-5 matrix, 100×100 | convergence rate | Helped |
| Add asymmetric scaling to the column-span initialization (ablation) | Gradient descent for matrix factorization · Synthetic rank-5 matrix, 100×100 | convergence rate | Helped |
| Initialize asymmetrically without placing X₀ in the column span of A (ablation) | Gradient descent for matrix factorization · Synthetic rank-5 matrix, 100×100 | convergence rate | Hurt |
| Increase factor width from d=6 to d=10 (ablation) | All tested initializations · Synthetic rank-5 matrix, 100×100 | convergence rate | Helped |
| Use the proposed initialization on an approximately rank-5 matrix with 10% noise | Gradient descent for matrix factorization · Noisy approximately rank-5 matrix, 100×100 (10% noise) | convergence rate | Helped |
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