Table 2 Simulation results. Average of the angles between the space spanned by the true and estimated canonical vectors; average true positive rate and true negative rate are reported for each method
Design | Method | No contamination | t-distribution | Contamination | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Â | Â | \(\bar {\theta }(\hat {\mathbf {A}},\mathbf {A})\) | TPR | TNR | \(\bar {\theta }(\hat {\mathbf {A}},\mathbf {A})\) | TPR | TNR | \(\bar {\theta }(\hat {\mathbf {A}},\mathbf {A})\) | TPR | TNR |
Uncorrelated | CCA | 0.11 | 1.00 | 0.00 | 0.22 | 1.00 | 0.00 | 0.38 | 1.00 | 0.00 |
Sparse | Robust CCA | 0.14 | 1.00 | 0.00 | 0.15 | 1.00 | 0.00 | 0.15 | 1.00 | 0.00 |
Low-dimensional | Sparse CCA | 0.04 | 0.98 | 0.97 | 0.19 | 0.94 | 0.63 | 0.34 | 1.00 | 0.04 |
| Â | Robust Sparse CCA | 0.04 | 1.00 | 0.82 | 0.11 | 1.00 | 0.52 | 0.05 | 1.00 | 0.76 |
Correlated | CCA | 0.06 | 1.00 | 0.00 | 0.13 | 1.00 | 0.00 | 0.43 | 1.00 | 0.00 |
Sparse | Robust CCA | 0.08 | 1.00 | 0.00 | 0.09 | 1.00 | 0.00 | 0.09 | 1.00 | 0.00 |
Low-dimensional | Sparse CCA | 0.13 | 1.00 | 1.00 | 0.19 | 0.96 | 0.76 | 0.57 | 0.52 | 0.02 |
| Â | Robust Sparse CCA | 0.07 | 1.00 | 0.57 | 0.09 | 1.00 | 0.34 | 0.07 | 1.00 | 0.53 |
NonSparse | CCA | 0.08 | 1.00 | NA | 0.32 | 1.00 | NA | 0.20 | 1.00 | NA |
Low-dimensional | Robust CCA | 0.11 | 1.00 | NA | 0.12 | 1.00 | NA | 0.12 | 1.00 | NA |
| Â | Sparse CCA | 0.41 | 0.93 | NA | 0.67 | 0.82 | NA | 0.23 | 1.00 | NA |
| Â | Robust Sparse CCA | 0.16 | 0.99 | NA | 0.22 | 0.99 | NA | 0.13 | 1.00 | NA |
Sparse | Sparse CCA | 0.65 | 0.62 | 0.99 | 0.70 | 0.71 | 0.87 | 0.36 | 1.00 | 0.80 |
High-Dimensional 1 | Robust Sparse CCA | 0.66 | 0.84 | 0.86 | 0.56 | 0.82 | 0.86 | 0.16 | 0.96 | 0.97 |
Sparse | Sparse CCA | 1.08 | 0.31 | 1.00 | 1.14 | 0.23 | 1.00 | 1.25 | 0.38 | 0.97 |
High-Dimensional 2 | Robust Sparse CCA | 0.59 | 0.87 | 0.87 | 0.60 | 0.94 | 0.89 | 0.84 | 0.97 | 0.82 |
Sparse Ultra | Sparse CCA | 1.18 | 0.17 | 1.00 | 1.22 | 0.15 | 1.00 | 1.25 | 0.40 | 1.00 |
High-dimensional | Robust Sparse CCA | 1.42 | 0.93 | 1.00 | 1.24 | 0.98 | 1.00 | 0.98 | 1.00 | 1.00 |