Research map / Learning theory and algorithms / Matrix and tensor methods
Efficient Algorithms for Large-scale Generalized Eigenvector Computation and Canonical Correlation Analysis
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Reduce CCA to top-k generalized eigenvector problem and solve with inexact linear-solver-based power/orthogonal iteration with warm starts | CCA (CCALin) · theory: runtime vs S-AppGrad | runtime complexity | Helped |
| Use accelerated gradient descent instead of plain GD as the inner linear solver (ablation) | GenELinK linear solver · theory: CCA runtime | runtime complexity | Helped |
| Use variance-reduced SVRG/ASVRG inner solver instead of AGD (ablation) | GenELinK linear solver · theory: CCA runtime | runtime complexity | Mixed |
| Empirically, theta_B (B-norm principal angle) decreases monotonically and sin theta_B converges linearly on MNIST and PTB | CCALin · MNIST, Penn Tree Bank | sin theta_B convergence | Helped |
| Use CCALin (GenELinK with stochastic AGD and sparsity) instead of one-shot and S-AppGrad baselines | CCA on URL Reputation · URL Reputation | TCC vs computation | Helped |
| Add ridge regularization S_xx + lambda I to ill-conditioned covariance matrices | CCA on Penn Tree Bank · PTB | convergence | No clear effect |
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