Mantra Betti Numbers
Description
Mantra Betti Numbers
Dataset Overview
Lifting Methods
Structural-based Liftings
- Cellular: Cycle-based lifting
- Simplicial: Clique complex lifting
- Hypergraph: k-hop lifting
Feature Lifting
- Projected sum
Model Performance
| Model | GCN | GAT | GIN | SCN | SCCNN | SaNN | GCCN | HOPSE-M | HOPSE-G |
|---|---|---|---|---|---|---|---|---|---|
| Betti 1 (Accuracy ± Std) | 46.86 ± 4.50 | 7.45 ± 0.05 | 88.13 ± 0.00 | 76.45 ± 3.06 | 90.20 ± 0.20 | 88.46 ± 0.09 | 84.20 ± 4.80 | 90.26 ± 0.55 | 88.28 ± 0.08 |
| Betti 2 (Accuracy ± Std) | 0.00 ± 0.00 | 0.00 ± 0.00 | 0.93 ± 1.21 | 5.45 ± 2.31 | 65.82 ± 2.70 | 39.22 ± 2.80 | 41.82 ± 20.19 | 71.69 ± 1.50 | 35.37 ± 2.25 |
Key Insights
- HOPSE-M achieves the best performance for both Betti numbers: 90.26% (±0.55) for Betti 1 and 71.69% (±1.50) for Betti 2.
- SCCNN is the second-best for both Betti numbers, with 90.20% (±0.20) for Betti 1 and 65.82% (±2.70) for Betti 2.
- GIN, SaNN, and HOPSE-G also perform strongly on Betti 1, but most models struggle on Betti 2.
- GAT and GCN perform poorly on Betti 2, with near-zero accuracy.
- GCCN shows high variability on Betti 2 (±20.19).
Reproducibility
to be released