Research map / Graph learning / Graph algorithms and clustering
The Persistent Laplacian for Data Science: Evaluating Higher-Order Persistent Spectral Representations of Data
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Persistent Laplacian embedding instead of persistent homology embedding | MNIST classification · MNIST | accuracy: 0.821 vs 0.625 | Helped |
| Persistent Laplacian embedding instead of persistent homology embedding | QM7-3D atomization energy · QM7-3D | MAE: 68.86 vs 92.43 (lower is better) | Helped |
| Persistent Laplacian embedding instead of persistent homology embedding | QM7 Coulomb matrix filtration 2 · QM7-CM Filtration 2 | MAE: 21.94 vs 45.47 (lower is better) | Helped |
| Persistent Laplacian embedding instead of persistent homology embedding | QM7b-CM-0 filtration 1 · QM7b-CM-0 Filtration 1 | MAE: 12.35 vs 73.12 (lower is better) | Helped |
| Persistent Laplacian embedding instead of persistent homology embedding | QM7b-CM-0 filtration 2 · QM7b-CM-0 Filtration 2 | MAE: 26.14 vs 84.53 for PH is an improvement, but PL is worse than GL 22.59 and CL 22.85 | Hurt |
| Persistent Laplacian vs graph Laplacian on Coulomb matrix filtration 1 | QM7 Coulomb matrix filtration 1 · QM7-CM Filtration 1 | MAE: 12.38 vs 12.42 | No clear effect |
| Persistent Laplacian vs graph Laplacian on Coulomb matrix filtration 2 | QM7 Coulomb matrix filtration 2 · QM7-CM Filtration 2 | MAE: 21.94 vs 23.19 on QM7; 26.14 vs 22.59 on QM7b task 0 | Mixed |
| Persistent Laplacian vs combinatorial Laplacian on MNIST | MNIST classification · MNIST | accuracy: 0.821 vs 0.798 | Helped |
| Truncating eigenvalues to the smallest n instead of the largest n (ablation) | Persistent Laplacian feature vector · MNIST | accuracy | Helped |
| Increasing filtration resolution R (ablation) | Persistent Laplacian feature vector · MNIST | accuracy | Helped |
Closest papers by meaning
- Persistent Homology for High-dimensional Data Based on Spectral Methods (NeurIPS 2024 · similarity 0.91)
- Graphcode: Learning from multiparameter persistent homology using graph neural networks (NeurIPS 2024 · similarity 0.89)
- Differentiability and Optimization of Multiparameter Persistent Homology (ICML 2024 · similarity 0.89)
- Wasserstein convergence of Cech persistence diagrams for samplings of submanifolds (NeurIPS 2024 · similarity 0.88)
- The Flood Complex: Large-Scale Persistent Homology on Millions of Points (NeurIPS 2025 · similarity 0.88)
- On topological descriptors for graph products (NeurIPS 2025 · similarity 0.88)
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