Research map / Learning theory and algorithms / Kernels and regression theory
Learning in Reproducing Kernel Kreı̆n Spaces
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Regularize via decomposition components H+/H- (KREIN) instead of stabilization (OMCS-KREIN) (ablation) | Kreĭn regularized risk minimization · Table 1 synthetic experiments | average RMSE | Helped |
| Spectrum clipping instead of Kreĭn regularization | kernel matrix spectrum · Table 1 synthetic GAUSS (n=100) | average RMSE: 23.14 vs 8.99 | Hurt |
| Spectrum squaring of kernel matrix instead of Kreĭn regularization | kernel matrix spectrum · Table 1 synthetic SIGMOID (n=500, starred) | average RMSE: 38.04 vs 14.59 (KREIN) | Hurt |
| Kreĭn SVM / LRR-SF baselines replaced by the proposed KREIN regularized risk minimization | indefinite dissimilarity kernels · Table 2 (12 datasets, misclassification) | misclassification %: e.g., chicken10 5.62 vs 11.91 (LRR-SF), 30.95 (K-SVM) | Helped |
| Indefinite RL-SIGMOID and DELTA-GAUSS kernels instead of positive definite kernels | vectorial regression datasets · Table 3 YACHT and AIRFOIL | RMSE: YACHT 1.63 (RL-SIGMOID) vs 5.09 (GAUSS); AIRFOIL 6.12 (DELTA-GAUSS) vs 8.54 (GAUSS) | Helped |
| Indefinite kernels instead of positive definite kernels on classification datasets | vectorial classification datasets (Table 3) · HABERMAN, IONOSPHERE, BREASTCANCER, AUSTRALIAN, DIABETES | misclassification % | Mixed |
| Spectrum-based OMCS-KREIN stabilization instead of KREIN regularization (ablation) | synthetic indefinite kernels · Table 1 synthetic SIGMOID (n=1000) | average RMSE: 16.58 vs 6.63 | Hurt |
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