Vietoris-Rips Lifting (Graph to Complex)

configs/transforms/liftings/graph2simplicial/vietoris_rips_lifting.yaml

@@ -0,0 +1,7 @@
+transform_type: 'lifting'
+transform_name: "SimplicialVietorisRipsLifting"
+complex_dim: 3
+preserve_edge_attr: False
+signed: True
+distance_threshold: 2.0
+feature_lifting: ProjectionSum

modules/transforms/data_transform.py

@@ -15,12 +15,16 @@
 from modules.transforms.liftings.graph2simplicial.clique_lifting import (
     SimplicialCliqueLifting,
 )
+from modules.transforms.liftings.graph2simplicial.vietoris_rips_lifting import (
+    SimplicialVietorisRipsLifting,
+)
 
 TRANSFORMS = {
     # Graph -> Hypergraph
     "HypergraphKNNLifting": HypergraphKNNLifting,
     # Graph -> Simplicial Complex
     "SimplicialCliqueLifting": SimplicialCliqueLifting,
+    "SimplicialVietorisRipsLifting": SimplicialVietorisRipsLifting,
     # Graph -> Cell Complex
     "CellCycleLifting": CellCycleLifting,
     # Feature Liftings

modules/transforms/liftings/graph2simplicial/vietoris_rips_lifting.py

@@ -0,0 +1,57 @@
+from itertools import combinations
+
+import networkx as nx
+import torch_geometric
+from toponetx.classes import SimplicialComplex
+
+from modules.transforms.liftings.graph2simplicial.base import Graph2SimplicialLifting
+
+
+class SimplicialVietorisRipsLifting(Graph2SimplicialLifting):
+    r"""Lifts graphs to simplicial complex domain using the Vietoris-Rips complex based on pairwise distances.
+
+    Parameters
+    ----------
+    distance_threshold : float
+        The maximum distance between vertices to form a simplex.
+    **kwargs : optional
+        Additional arguments for the class.
+    """
+
+    def __init__(self, distance_threshold=1.0, **kwargs):
+        super().__init__(**kwargs)
+        self.distance_threshold = distance_threshold
+
+    def lift_topology(self, data: torch_geometric.data.Data) -> dict:
+        r"""Lifts the topology of a graph to a simplicial complex using the Vietoris-Rips complex.
+
+        Parameters
+        ----------
+        data : torch_geometric.data.Data
+            The input data to be lifted.
+
+        Returns
+        -------
+        dict
+            The lifted topology.
+        """
+        graph = self._generate_graph_from_data(data)
+        simplicial_complex = SimplicialComplex(graph)
+        all_nodes = list(graph.nodes)
+        simplices = [set() for _ in range(2, self.complex_dim + 1)]
+
+        # Calculate pairwise shortest path distances
+        path_lengths = dict(nx.all_pairs_shortest_path_length(graph))
+
+        for k in range(2, self.complex_dim + 1):
+            for combination in combinations(all_nodes, k + 1):
+                if all(
+                    path_lengths[u][v] <= self.distance_threshold
+                    for u, v in combinations(combination, 2)
+                ):
+                    simplices[k - 2].add(tuple(sorted(combination)))
+
+        for set_k_simplices in simplices:
+            simplicial_complex.add_simplices_from(list(set_k_simplices))
+
+        return self._get_lifted_topology(simplicial_complex, graph)

test/transforms/liftings/graph2simplicial/test_vietoris_rips_lifting.py

@@ -0,0 +1,87 @@
+"""Test the message passing module."""
+
+import torch
+
+from modules.data.utils.utils import load_manual_graph
+from modules.transforms.liftings.graph2simplicial.vietoris_rips_lifting import (
+    SimplicialVietorisRipsLifting,
+)
+
+
+class TestSimplicialVietorisRipsLifting:
+    """Test the SimplicialVietorisRipsLifting class."""
+
+    def setup_method(self):
+        # Load the graph
+        self.data = load_manual_graph()
+
+        # Initialise the SimplicialCliqueLifting class
+        self.lifting_signed = SimplicialVietorisRipsLifting(complex_dim=3, signed=True)
+        self.lifting_unsigned = SimplicialVietorisRipsLifting(
+            complex_dim=3, signed=False
+        )
+
+    def test_lift_topology(self):
+        """Test the lift_topology method."""
+
+        # Test the lift_topology method
+        lifted_data_signed = self.lifting_signed.forward(self.data.clone())
+        lifted_data_unsigned = self.lifting_unsigned.forward(self.data.clone())
+
+        expected_incidence_1_singular_values_unsigned = torch.tensor(
+            [2.8412, 2.1378, 1.9299, 1.7321, 1.5809, 1.4142, 1.2617, 0.7358]
+        )
+
+        expected_incidence_1_singular_values_signed = torch.tensor(
+            [
+                2.6622e00,
+                2.2830e00,
+                2.0000e00,
+                2.0000e00,
+                1.6697e00,
+                1.4142e00,
+                9.5538e-01,
+                1.7728e-07,
+            ]
+        )
+
+        U, S_unsigned, V = torch.svd(lifted_data_unsigned.incidence_1.to_dense())
+        U, S_signed, V = torch.svd(lifted_data_signed.incidence_1.to_dense())
+        assert torch.allclose(
+            expected_incidence_1_singular_values_unsigned, S_unsigned, atol=1.0e-04
+        ), "Something is wrong with unsigned incidence_1 (nodes to edges)."
+        assert torch.allclose(
+            expected_incidence_1_singular_values_signed, S_signed, atol=1.0e-04
+        ), "Something is wrong with signed incidence_1 (nodes to edges)."
+
+        expected_incidence_2_singular_values_unsigned = torch.tensor(
+            [2.5207, 2.0000, 1.5886, 1.4142, 1.4142, 1.0595]
+        )
+
+        expected_incidence_2_singular_values_signed = torch.tensor(
+            [2.2738e00, 2.0000e00, 2.0000e00, 1.8196e00, 1.2324e00, 3.2893e-08]
+        )
+
+        U, S_unsigned, V = torch.svd(lifted_data_unsigned.incidence_2.to_dense())
+        U, S_signed, V = torch.svd(lifted_data_signed.incidence_2.to_dense())
+
+        assert torch.allclose(
+            expected_incidence_2_singular_values_unsigned, S_unsigned, atol=1.0e-04
+        ), "Something is wrong with unsigned incidence_2 (edges to triangles)."
+        assert torch.allclose(
+            expected_incidence_2_singular_values_signed, S_signed, atol=1.0e-04
+        ), "Something is wrong with signed incidence_2 (edges to triangles)."
+
+        expected_incidence_3_singular_values_unsigned = torch.tensor([2.0000])
+
+        expected_incidence_3_singular_values_signed = torch.tensor([2.0000])
+
+        U, S_unsigned, V = torch.svd(lifted_data_unsigned.incidence_3.to_dense())
+        U, S_signed, V = torch.svd(lifted_data_signed.incidence_3.to_dense())
+
+        assert torch.allclose(
+            expected_incidence_3_singular_values_unsigned, S_unsigned, atol=1.0e-04
+        ), "Something is wrong with unsigned incidence_3 (triangles to tetrahedrons)."
+        assert torch.allclose(
+            expected_incidence_3_singular_values_signed, S_signed, atol=1.0e-04
+        ), "Something is wrong with signed incidence_3 (triangles to tetrahedrons)."