Research map / Learning theory and algorithms / Kernels and regression theory
Persistence weighted Gaussian kernel for topological data analysis
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use PWGK instead of PSSK with linear RKHS kernel | SVM on persistence diagrams · Synthetic circles XOR classification (99 test sets) | classification rate (%): 49.5 -> 60.0 | Helped |
| use PWGK instead of PSSK with Gaussian RKHS kernel | SVM on persistence diagrams · Synthetic circles XOR classification (99 test sets) | classification rate (%): 54.5 -> 83.0 | Helped |
| use PWGK instead of unweighted Gauss embedding, Gaussian RKHS | SVM on persistence diagrams · Synthetic circles XOR classification (99 test sets) | classification rate (%): 69.7 -> 83.0 | Helped |
| use nonlinear Gaussian RKHS kernel instead of linear (ablation) | PWGK · Synthetic circles XOR classification (99 test sets) | classification rate (%): 60.0 -> 83.0 | Helped |
| use nonlinear Gaussian RKHS kernel instead of linear (ablation) | PSSK · Synthetic circles XOR classification (99 test sets) | classification rate (%): 49.5 -> 54.5 | Helped |
| PSSK versus plain Gaussian kernel (no weights) | SVM on persistence diagrams · Synthetic circles XOR classification (99 test sets) | classification rate (%), Gaussian RKHS: 69.7 -> 54.5 | Hurt |
| PWGK instead of MTF-SVM | SVM · Hemoglobin | CV classification rate (%): 84.50 -> 88.90 | Helped |
| PWGK instead of MTF-SVM (nbd) | SVM · Protein-Drug | CV classification rate (%): 93.91 -> 100 | Helped |
| PWGK instead of MTF-SVM (bd) | SVM · Protein-Drug | CV classification rate (%): 98.31 -> 100 | Helped |
| random Fourier features (PWGK) instead of Nystrom (PSSK) approximation, ~500 samples | change-point detection · SiO2 | computation time (sec): 1530 -> 40 | Helped |
| increase approximation sample size from 500 to 5000 | PWGK · SiO2 | computation time (sec): 40 -> 410 | Hurt |
| increase approximation columns from 100 to 500 | PSSK · SiO2 | computation time (sec): 130 -> 1530 | Hurt |
Closest papers by meaning
- A Class of Topological Pseudodistances for Fast Comparison of Persistence Diagrams (AAAI 2024 · similarity 0.86)
- Persistent Homology for High-dimensional Data Based on Spectral Methods (NeurIPS 2024 · similarity 0.85)
- Point-Level Topological Representation Learning on Point Clouds (ICML 2025 · similarity 0.85)
- Topological Periodicity Test (TopPT) via Confidence Bound of Time-Delay Embeddings (NeurIPS 2026 · similarity 0.85)
- ToMAToMP: Robust and Multi-Parameter Topological Clustering (NeurIPS 2026 · similarity 0.85)
- Wasserstein convergence of Cech persistence diagrams for samplings of submanifolds (NeurIPS 2024 · similarity 0.84)
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