Research map / Learning theory and algorithms / Matrix and tensor methods
No Spurious Local Minima in Nonconvex Low Rank Problems: A Unified Geometric Analysis
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a norm-preserving Hessian and a shared direction of improvement | Matrix sensing, matrix completion, and robust PCA · Low-rank matrix optimization | spurious local minima | Helped |
| Add the balancing regularizer between factor Gram matrices | Asymmetric low-rank matrix problems · Asymmetric matrix sensing | Hessian norm preservation | Helped |
| Add a row-norm penalty to enforce incoherence | Matrix completion · Matrix completion | spurious local minima | Helped |
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