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receptive_field.py
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receptive_field.py
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import os
import sys
import networkx as nx
from util import betweenness_centrality, compute_distance
from pynauty.graph import Graph, canon_label
labelling_procedures = {
'betweenness': betweenness_centrality
}
# Class that generates a receptive field for a graph
class ReceptiveField():
# graph: Input graph to generate receptive field on
# w: Number of neighbourhoods. Automatically calculated if None
# s: Stride of sequence selection
# k: Neighbourhood size
def __init__(self, graph, w, s=1, k=10, l='betweenness', default=None, attribute_name='node_attributes',
rank_name='node_rank', num_attr=None):
self.graph = graph
self.w = w
self.s = s
self.k = k
self.l = l
self.node_labels = {}
# Attribute names(Optional)
self.attribute_name = attribute_name
self.rank_name = rank_name
# Default attribute initialization
self.default_attributes = {}
if not default: # Automatically fixes zero values
# Handle empty graphs
if not list(self.graph.nodes()) and num_attr:
self.default_attributes[attribute_name] = 0.0 if num_attr == 1 else [0.0 for i in range(num_attr)]
else:
first_node = list(self.graph.nodes)[0]
attributes = self.graph.nodes(data=True)[first_node]
for k, v in attributes.items():
self.default_attributes[k] = 0.0 if type(v) != list else [0.0 for i in range(len(v))]
else:
self.default_attributes = default
# Computes the ordering for the nodes given the set labelling procedure
# Returns sorted ordered list of tuple of (node, score)
def compute_labelling(self, graph):
labelling_procedure = labelling_procedures[self.l]
labelled_nodes = labelling_procedure(graph)
labelled_nodes = sorted(labelled_nodes, key=lambda x: x[1], reverse=True)
return labelled_nodes
# Creates all receptive fields for the current graph
# with respect to w,s,k and l
def make_all_receptive_fields(self):
top_w = self.select_node_sequence()
ordered_nodes = [x[0] for x in top_w]
f = []
i, j = 0, 0
while j < self.w:
if i < len(ordered_nodes):
f.append(self.make_receptive_field(ordered_nodes[i], self.node_labels))
else:
f.append(self.make_zero_receptive_field()) # Stride s may be too large
i += self.s
j += 1
return f
# Selects the top w elements according the labelling l
def select_node_sequence(self):
node_labels = self.compute_labelling(self.graph)
self.node_labels = dict(node_labels) # Internal memory of node labelling
node_labels = node_labels[:self.w] # Top w elements
return node_labels
# Creates the receptive field for the input graph
# by calling neighbourhood assembly and graph normalization methods
def make_receptive_field(self, v, node_labels):
# Assembles the neighbourhood
local_neighbourhood = self.assemble_neighbourhoods(v)
# Normalizes the graph
normalized_neighbourhood = self.normalize_graph(local_neighbourhood, v, dict(node_labels))
# Reshaping and relabelling
nb_tensor = []
for i, attributes in list(normalized_neighbourhood.nodes(data=True)):
# Sort by computed ranking, and
nb_tensor.append((attributes[self.rank_name], attributes[self.attribute_name]))
nb_tensor = [x[1] for x in sorted(nb_tensor)]
return nb_tensor
# Creates receptive field with default values
def make_zero_receptive_field(self):
zero_padded_graph = nx.star_graph(self.k - 1)
# Initialize default values for all nodes
for k, v in self.default_attributes.items():
nx.set_node_attributes(zero_padded_graph, v, k)
default_rank = {i: {self.rank_name: i + 1} for i in range(self.k)}
nx.set_node_attributes(zero_padded_graph, default_rank)
# Reshaping and relabelling
zero_rf_tensor = []
for i, attributes in list(zero_padded_graph.nodes(data=True)):
# Sort by computed ranking, and
zero_rf_tensor.append((attributes[self.rank_name], attributes[self.attribute_name]))
zero_rf_tensor = [x[1] for x in sorted(zero_rf_tensor)]
return zero_rf_tensor
# Assemble neighbourhood around vertex v
def assemble_neighbourhoods(self, v):
N = set() # Current set of vertices in neighourhood
L = set() # Neighbours of N
N.add(v)
L.add(v)
while len(N) < self.k and len(L) > 0:
for v in L:
L = L.union(set(self.graph.neighbors(v)))
L = L - N # Get only new neighbours
N = N.union(L)
return self.graph.subgraph(N)
# Impose order using graph normalization subject to labelling
def normalize_graph(self, neighbourhood, v, node_labels):
# Compute ranking:
# d(u, v) < d(w, v) -> r(u) < r(v)
ranking = self.compute_ranking(neighbourhood, v, node_labels, canonical=True)
# |U| > k
if len(ranking) > self.k:
top_k = [x for x, _ in ranking[:self.k]]
subgraph = nx.Graph(neighbourhood.subgraph(top_k))
# Recompute sugraph ranking
subgraph_labels = dict(self.compute_labelling(subgraph))
subgraph_ranking = self.compute_ranking(subgraph, v, subgraph_labels, canonical=True)
# |U| < k
elif len(ranking) < self.k:
subgraph = nx.Graph(neighbourhood)
subgraph, subgraph_ranking = self.pad_graph(subgraph, ranking, self.k)
# |U| = k
else:
subgraph = nx.Graph(neighbourhood)
subgraph_ranking = ranking
nx.set_node_attributes(subgraph, dict(subgraph_ranking), self.rank_name)
# return self.canonicalize(subgraph)
return subgraph
# Computes the ranking of the graph with respect to vertex v
# Node labels should be dictionary form
def compute_ranking(self, graph, v, node_labels, canonical=False):
distance = compute_distance(graph, v)
# Compute ranking wrt to distance then node_labels
distinct_distances = set([y for x, y in distance])
partitioned_list = []
for d in distinct_distances:
current_nodes = [x for x, y in distance if y == d]
# Sort by labelling first, then break ties with canonical labelling
if canonical:
canonical_labels = self.canonicalize(graph)
current_nodes = sorted(current_nodes, key=lambda x: (-node_labels[x], -canonical_labels[x]))
else:
current_nodes = sorted(current_nodes, key=lambda x: -node_labels[x])
partitioned_list.append(current_nodes)
ranking = [x for sub in partitioned_list for x in sub]
ranking = [(x, i + 1) for i, x in enumerate(ranking)]
return ranking
# Pads the graph with additional dummy nodes
# Until total number of nodes is N
def pad_graph(self, graph, ranking, N):
padded_graph = nx.Graph(graph)
node_next = max([x for x, _ in ranking])
rank_next = max([y for _, y in ranking])
step = 1
while len(padded_graph.nodes()) < N:
padded_graph.add_node(node_next + step, **self.default_attributes)
ranking.append((node_next + step, rank_next + step))
step += 1
return padded_graph, ranking
# Canonicalize the graph to find isomorphism
# Returns the canonical labelling to the graph
def canonicalize(self, graph):
# Relabel nodes for canonicalization
original_labels = list(graph.nodes())
original_to_relabeled = {x: i for i, x in enumerate(original_labels)}
relabeled_to_original = {i: x for i, x in enumerate(original_labels)}
relabeled_graph = nx.relabel_nodes(graph, original_to_relabeled)
nauty_graph = Graph(len(relabeled_graph), directed=False)
# Adjacency dictionary for relabeled graph
adjacency_dict = {n: list(nbrs) for n, nbrs in relabeled_graph.adjacency()}
nauty_graph.set_adjacency_dict(adjacency_dict)
canonical_labels = canon_label(nauty_graph)
# Break ties with nauty
canonical_labels = {k: canonical_labels[k] for k in range(len(relabeled_graph))}
# Switch back to original labels
canonical_labels = {relabeled_to_original[i]: canonical_labels[i] for i in range(len(relabeled_graph))}
return canonical_labels