Table 2.
Summary of topological data analysis (TDA) methods for structures
| Method | Topological space | Node attribute | Edge attribute |
|---|---|---|---|
| Homology-based | |||
| Persistent homology [62, 63] | Simplicial complex | None | None |
| Element-specific PH (ESPH) [16] | Simplicial complex | Group labeled | Group labeled |
| Persistent cohomology [64] | Simplicial complex | Labeled | Labeled |
| Persistent path homology [65] | Path complex | Path | Directed |
| Persistent flag homology [66] | Flag complexes | None | Directed |
| Evolutionary homology [67] | Simplicial complex | Weighted | Weighted |
| Weighted persistent homology [68] | Simplicial complex | Weighted | Weighted |
| Laplacian-based | |||
| Persistent spectral graph [69, 70] | Simplicial complex | None | None |
| Persistent Hodge Laplacians [71] | Manifold | Continuum | Continuum |
| Persistent sheaf Laplacians [72] | Cellular complex | Labeled | Sheaf relation |
| Persistent path Laplacians [73] | Path complex | Path | Direction |
| Persistent hypergraph [74] | Hypergraph | Hypernode | Hyperedge |
| Persistent directed hypergraphs [75] | Hypergraph | Hypernode | Directed hyperedge |