Research map / Learning theory and algorithms / Matrix and tensor methods
Diffusion Approximations for Online Principal Component Estimation and Global Convergence
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the derived global three-phase convergence analysis to set the stepsize as \bar\beta(T) | Oja's iteration · Online PCA | expected sin² angle error: \frac{\log T }{(\lambda_1 - \lambda_2) T} | Helped |
| Use the proposed eigenvalue-dependent rate bound instead of earlier Oja bounds | Oja's iteration · Online PCA (convergence rate) | sin² angle error: C\cdot \dfrac{\lambda_1}{\lambda_1-\lambda_2}\displaystyle\sum_{k=2}^d \dfrac{\lambda_k}{\lambda_1-\lambda_k} \cdot \dfr | Helped |
| Use the proposed rate bound when λ₂=⋯=λ_d | Oja's iteration · Online PCA (convergence rate) | sin² angle error: C\cdot \dfrac{\lambda_1\lambda_2\cdot d}{(\lambda_1-\lambda_2)^2} \cdot \dfrac{1}{n} | Helped |
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