Eccentricity Lifting (Graph to Complex)

configs/transforms/liftings/graph2simplicial/eccentricity_lifting.yaml

@@ -0,0 +1,6 @@
+transform_type: 'lifting'
+transform_name: "SimplicialEccentricityLifting"
+complex_dim: 3
+preserve_edge_attr: False
+signed: True
+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.eccentricity_lifting import (
+    SimplicialEccentricityLifting,
+)
 
 TRANSFORMS = {
     # Graph -> Hypergraph
     "HypergraphKNNLifting": HypergraphKNNLifting,
     # Graph -> Simplicial Complex
     "SimplicialCliqueLifting": SimplicialCliqueLifting,
+    "SimplicialEccentricityLifting": SimplicialEccentricityLifting,
     # Graph -> Cell Complex
     "CellCycleLifting": CellCycleLifting,
     # Feature Liftings

modules/transforms/liftings/graph2simplicial/eccentricity_lifting.py

@@ -0,0 +1,54 @@
+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 SimplicialEccentricityLifting(Graph2SimplicialLifting):
+    r"""Lifts graphs to simplicial complex domain using eccentricity.
+
+    Parameters
+    ----------
+    **kwargs : optional
+        Additional arguments for the class.
+    """
+
+    def __init__(self, **kwargs):
+        super().__init__(**kwargs)
+
+    def lift_topology(self, data: torch_geometric.data.Data) -> dict:
+        r"""Lifts the topology of a graph to a simplicial complex by identifying connected subgraphs as simplices.
+
+        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()
+        eccentricities = nx.eccentricity(graph)
+        simplices = [set() for _ in range(2, self.complex_dim + 1)]
+
+        for node in graph.nodes:
+            simplicial_complex.add_node(node, features=data.x[node])
+
+        for node, ecc in eccentricities.items():
+            neighborhood = list(
+                nx.single_source_shortest_path_length(graph, node, cutoff=ecc).keys()
+            )
+            for k in range(1, self.complex_dim):
+                for combination in combinations(neighborhood, k + 1):
+                    simplices[k - 1].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_eccentricity_lifting.py

@@ -0,0 +1,131 @@
+"""Test the message passing module."""
+
+import torch
+
+from modules.data.utils.utils import load_manual_graph
+from modules.transforms.liftings.graph2simplicial.eccentricity_lifting import (
+    SimplicialEccentricityLifting,
+)
+
+
+class TestSimplicialEccentricityLifting:
+    """Test the SimplicialEccentricityLifting class."""
+
+    def setup_method(self):
+        # Load the graph
+        self.data = load_manual_graph()
+
+        # Initialise the SimplicialCliqueLifting class
+        self.lifting_signed = SimplicialEccentricityLifting(complex_dim=3, signed=True)
+        self.lifting_unsigned = SimplicialEccentricityLifting(
+            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(
+            [3.7417, 2.4495, 2.4495, 2.4495, 2.4495, 2.4495, 2.4495, 2.4495]
+        )
+
+        expected_incidence_1_singular_values_signed = torch.tensor(
+            [
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                6.8993e-08,
+            ]
+        )
+
+        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(
+            [
+                4.2426,
+                3.1623,
+                3.1623,
+                3.1623,
+                3.1623,
+                3.1623,
+                3.1623,
+                3.1623,
+                2.0000,
+                2.0000,
+                2.0000,
+                2.0000,
+                2.0000,
+                2.0000,
+                2.0000,
+                2.0000,
+                2.0000,
+                2.0000,
+                2.0000,
+                2.0000,
+                2.0000,
+                2.0000,
+                2.0000,
+                2.0000,
+                2.0000,
+                2.0000,
+                2.0000,
+                2.0000,
+            ]
+        )
+
+        expected_incidence_2_singular_values_signed = torch.tensor(
+            [
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                2.8284e00,
+                7.0866e-07,
+                4.0955e-07,
+                3.2154e-07,
+                2.9976e-07,
+                2.8069e-07,
+                2.3097e-07,
+                9.4821e-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)."