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Independent sets lifting (graph to simplicial) #2

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d1f6d55
Add independent sets lifting
FredericWantiez May 21, 2024
81e92dc
Fix imports
FredericWantiez May 28, 2024
d0a31dd
init notebook
FredericWantiez May 28, 2024
4f5ccb6
Add docstring
FredericWantiez May 28, 2024
0a6d513
Notebook
FredericWantiez Jun 8, 2024
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6 changes: 6 additions & 0 deletions configs/transforms/liftings/graph2simplicial/independent_set_lifting.yaml
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Original file line number Diff line number Diff line change
@@ -0,0 +1,6 @@
transform_type: 'lifting'
transform_name: "SimplicialIndependentSetLifting"
complex_dim: 3
preserve_edge_attr: False
signed: False
feature_lifting: ProjectionSum
4 changes: 4 additions & 0 deletions modules/transforms/data_transform.py
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Expand Up @@ -15,12 +15,16 @@
from modules.transforms.liftings.graph2simplicial.clique_lifting import (
SimplicialCliqueLifting,
)
from modules.transforms.liftings.graph2simplicial.independent_set_lifting import (
SimplicialIndependentSetsLifting,
)

TRANSFORMS = {
# Graph -> Hypergraph
"HypergraphKNNLifting": HypergraphKNNLifting,
# Graph -> Simplicial Complex
"SimplicialCliqueLifting": SimplicialCliqueLifting,
"SimplicialIndependentSetLifting": SimplicialIndependentSetsLifting,
# Graph -> Cell Complex
"CellCycleLifting": CellCycleLifting,
# Feature Liftings
Expand Down
31 changes: 25 additions & 6 deletions modules/transforms/liftings/graph2simplicial/clique_lifting.py
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Original file line number Diff line number Diff line change
Expand Up @@ -19,6 +19,30 @@ class SimplicialCliqueLifting(Graph2SimplicialLifting):
def __init__(self, **kwargs):
super().__init__(**kwargs)

@staticmethod
def generate_simplices(dim: int, graph: nx.Graph) -> list:
r"""Generates list of simplices from cliques of a given graph

Parameters
----------
dim: int
Maximum dimension of the complex
graph: nx.Graph
Input graph

Returns
-------
list[tuple]
List of simplices
"""
cliques = nx.find_cliques(graph)
simplices = [set() for _ in range(2, dim + 1)]
for clique in cliques:
for i in range(2, dim + 1):
for c in combinations(clique, i + 1):
simplices[i - 2].add(tuple(c))
return simplices

def lift_topology(self, data: torch_geometric.data.Data) -> dict:
r"""Lifts the topology of a graph to a simplicial complex by identifying the cliques as k-simplices.

Expand All @@ -34,13 +58,8 @@ def lift_topology(self, data: torch_geometric.data.Data) -> dict:
"""
graph = self._generate_graph_from_data(data)
simplicial_complex = SimplicialComplex(graph)
cliques = nx.find_cliques(graph)
simplices = [set() for _ in range(2, self.complex_dim + 1)]
for clique in cliques:
for i in range(2, self.complex_dim + 1):
for c in combinations(clique, i + 1):
simplices[i - 2].add(tuple(c))

simplices = self.generate_simplices(self.complex_dim, graph)
for set_k_simplices in simplices:
simplicial_complex.add_simplices_from(list(set_k_simplices))

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59 changes: 59 additions & 0 deletions modules/transforms/liftings/graph2simplicial/independent_set_lifting.py
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@@ -0,0 +1,59 @@
import networkx as nx
import torch_geometric
from toponetx.classes import SimplicialComplex

from modules.transforms.liftings.graph2simplicial.base import Graph2SimplicialLifting
from modules.transforms.liftings.graph2simplicial.clique_lifting import (
SimplicialCliqueLifting,
)


class SimplicialIndependentSetsLifting(Graph2SimplicialLifting):
r"""Lifts graphs to simplicial complex domain by identifying the independent sets as k-simplices

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 the independent sets as k-simplices

We use the fact that the independent sets of a graph G are the cliques of its complement graph Gc. The nodes and the edges
of the complement graph represent the 0-simplices and 1-simplices respectively.

Parameters
----------
data : torch_geometric.data.Data
The input data to be lifted.

Returns
-------
dict
The lifted topology.
"""
graph = self._generate_graph_from_data(data)
complement_graph = nx.complement(graph)

# Since we lose the original edges, not sure we can keep the edge features ? Should we warn ?
self.contains_edge_attr = False

# Propagate node features to complement
nodes_attributes = {
n: dict(features=data.x[n], dim=0) for n in range(data.x.shape[0])
}
nx.set_node_attributes(complement_graph, nodes_attributes)

simplicial_complex = SimplicialComplex(complement_graph)
simplices = SimplicialCliqueLifting.generate_simplices(
self.complex_dim, complement_graph
)

for set_k_simplices in simplices:
simplicial_complex.add_simplices_from(list(set_k_simplices))

return self._get_lifted_topology(simplicial_complex, graph)
202 changes: 202 additions & 0 deletions test/transforms/liftings/graph2simplicial/test_independent_set_lifting.py
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"""Test the message passing module."""
import torch

from modules.data.utils.utils import load_manual_graph
from modules.transforms.liftings.graph2simplicial.independent_set_lifting import (
SimplicialIndependentSetsLifting,
)


class TestSimplicialIndependentSetsLiftingClass:
"""Test the SimplicialIndependentSetsLifting class."""

def setup_method(self):
# Load the graph
self.data = load_manual_graph()

# Initialise the class
self.lifting_unsigned = SimplicialIndependentSetsLifting(
complex_dim=3, signed=False
)

def test_lift_topology(self):
"""Test the lift_topology method."""

# Test the lift_topology method
lifted_data_unsigned = self.lifting_unsigned.forward(self.data.clone())

expected_incidence_1 = torch.tensor(
[
[
1.0,
1.0,
1.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
],
[
0.0,
0.0,
0.0,
1.0,
1.0,
1.0,
1.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
],
[
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
1.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
],
[
1.0,
0.0,
0.0,
1.0,
0.0,
0.0,
0.0,
0.0,
1.0,
1.0,
1.0,
0.0,
0.0,
0.0,
0.0,
],
[
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
1.0,
0.0,
0.0,
1.0,
1.0,
1.0,
0.0,
],
[
0.0,
1.0,
0.0,
0.0,
1.0,
0.0,
0.0,
0.0,
0.0,
1.0,
0.0,
1.0,
0.0,
0.0,
0.0,
],
[
0.0,
0.0,
1.0,
0.0,
0.0,
1.0,
0.0,
1.0,
0.0,
0.0,
0.0,
0.0,
1.0,
0.0,
1.0,
],
[
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
1.0,
0.0,
0.0,
0.0,
1.0,
0.0,
0.0,
1.0,
1.0,
],
]
)

assert (
abs(expected_incidence_1) == lifted_data_unsigned.incidence_1.to_dense()
).all(), "Something is wrong with unsigned incidence_1 (nodes to edges)."

expected_incidence_2 = torch.tensor(
[
[1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0],
[1.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0],
[0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0],
[0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0],
]
)

assert (
abs(expected_incidence_2) == lifted_data_unsigned.incidence_2.to_dense()
).all(), "Something is wrong with unsigned incidence_2 (edges to triangles)."

expected_incidence_3 = torch.empty(7, 0)
assert (
abs(expected_incidence_3) == lifted_data_unsigned.incidence_3.to_dense()
).all(), (
"Something is wrong with unsigned incidence_3 (triangles to tetrahedrons)."
)
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