Research map / Learning theory and algorithms / Matrix and tensor methods
Recovery guarantee of weighted low-rank approximation via alternating minimization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add clipping step (zero out rows of X/Y with squared l2 norm above 2*mu*k/n) to vanilla alternating minimization | alternating minimization for weighted low-rank approximation · theoretical analysis (matrix completion special case) | recovery error bound ||M_hat - M*||_2 | Helped |
| Use random initialization (random sign matrix scaled by 1/sqrt(n)) instead of SVD initialization | alternating minimization with clipping · theoretical analysis | recovery error bound and required spectral gap gamma | No clear effect |
| Replace SVD-based initialization with random initialization | alternating minimization with clipping · theoretical analysis | spectral gap requirement on gamma: gamma order 1/(mu^{3/2} k^2) vs 1/(mu^2 k^{5/2}) | Hurt |
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