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graphon.py
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import copy
import pdb
import random
from typing import List, Tuple
import numpy as np
import torch
import torch.nn.functional as F
import torch_geometric.transforms as T
# from skimage.restoration import denoise_tv_chambolle
from torch_geometric.data import Data
from torch_geometric.utils import degree, dense_to_sparse, to_dense_adj
import time
def flip(x, dim):
"""
This function is used for inverse the tensor x.
"""
xsize = x.size()
dim = x.dim() + dim if dim < 0 else dim
x = x.view(-1, *xsize[dim:])
x = x.view(x.size(0), x.size(1), -1)[:, getattr(torch.arange(x.size(1)-1,
-1, -1), ('cpu','cuda')[x.is_cuda])().long(), :]
return x.view(xsize)
def align_graphs(graphs, padding: bool = False, N: int = None):
num_nodes = [graphs[i].shape[0] for i in range(len(graphs))]
max_num = max(num_nodes)
min_num = min(num_nodes)
aligned_graphs = []
normalized_node_degrees = []
for i in range(len(graphs)):
num_i = graphs[i].shape[0]
node_degree = 0.5 * torch.sum(graphs[i], dim=0) + 0.5 * torch.sum(graphs[i], dim=1)
node_degree = node_degree / torch.sum(node_degree)
idx = torch.argsort(node_degree) # ascending
idx = flip(idx, dim=0) # descending
sorted_node_degree = node_degree[idx]
sorted_node_degree = sorted_node_degree.reshape(-1, 1)
# sorted_graph = copy.deepcopy(graphs[i])
sorted_graph = graphs[i]
# TODO: check above line is correct or right!
sorted_graph = sorted_graph[idx, :]
sorted_graph = sorted_graph[:, idx]
max_num = max(max_num, N)
if padding:
# normalized_node_degree = np.ones((max_num, 1)) / max_num
normalized_node_degree = torch.zeros((max_num, 1))
normalized_node_degree[:num_i, :] = sorted_node_degree
aligned_graph = torch.zeros((max_num, max_num))
aligned_graph[:num_i, :num_i] = sorted_graph
normalized_node_degrees.append(normalized_node_degree)
aligned_graphs.append(aligned_graph.unsqueeze(dim=0))
else:
normalized_node_degrees.append(sorted_node_degree)
aligned_graphs.append(sorted_graph.unsqueeze(dim=0))
if N:
aligned_graphs = [aligned_graph[:, :N, :N] for aligned_graph in aligned_graphs]
normalized_node_degrees = [normalized_node_degree[:N, :] for normalized_node_degree in normalized_node_degrees]
aligned_graphs = torch.cat(aligned_graphs, dim=0)
return aligned_graphs, normalized_node_degrees, max_num, min_num
def gra2graphon(aligned_graphs, threshold: float = 2.02):
num_graphs = aligned_graphs.shape[0]
if num_graphs > 1:
sum_graph = torch.mean(aligned_graphs, dim=0)
else:
sum_graph = aligned_graphs[0, :, :] # (N, N)
return sum_graph
from sklearn.cluster import KMeans
def estimate_graphon(data, edge_att, N, h_graph_env, num_env):
batch_size = data.y.shape[0]
device = data.y.device
idx = torch.tensor(np.arange(batch_size)).to(device)
ys = torch.unique(data.y, sorted=True)
kmeans = KMeans(n_clusters=num_env, random_state=0)
envs = torch.tensor(list(np.arange(num_env))).to(device)
y_env_graphs = {}
graphons = {}
for y in ys:
for env in envs:
y_env_graphs['{}{}'.format(int(y), int(env))] = []
edge_index = data.edge_index
adj_cau = to_dense_adj(edge_index=edge_index, edge_attr=edge_att)[0]
for y in ys:
h_graph_env_y = h_graph_env[data.y.squeeze()==y]
idx_y = idx[data.y.squeeze()==y]
if h_graph_env_y.shape[0] < num_env:
return None, None, None
kmeans.fit(h_graph_env_y.to('cpu').detach().numpy())
for i in range(len(idx_y)):
y_env_graphs['{}{}'.format(int(data[idx_y[i]].y), int(kmeans.labels_[i]))].append(adj_cau[data.ptr[idx_y[i]]:data.ptr[idx_y[i]+1], data.ptr[idx_y[i]]:data.ptr[idx_y[i]+1]])
for y in ys:
for env in envs:
graphs = y_env_graphs['{}{}'.format(int(y), int(env))]
# print("y:{}, env:{}, num_graphs:{}".format(y, env, len(graphs)))
aligned_graphs, normalized_node_degrees, max_num, min_num = align_graphs(graphs, padding=True, N=N)
graphon = gra2graphon(aligned_graphs, threshold=0.2)
graphons['{}{}'.format(int(y),int(env))] = graphon
# for y, env, graphon in graphons:
# print("graphon info: class_label: {}, env_label: {}, mean: {}, shape, {}".format(y, env, graphon.mean(), graphon.shape))
return graphons, ys, envs
def stat_graph(dataset):
num_total_nodes = []
num_total_edges = []
for graph in dataset:
num_total_nodes.append(graph.num_nodes)
num_total_edges.append(graph.edge_index.shape[1] )
avg_num_nodes = sum( num_total_nodes ) / len(dataset)
avg_num_edges = sum( num_total_edges ) / len(dataset) / 2.0
avg_density = avg_num_edges / (avg_num_nodes * avg_num_nodes)
median_num_nodes = np.median( num_total_nodes )
median_num_edges = np.median(num_total_edges)
median_density = median_num_edges / (median_num_nodes * median_num_nodes)
return avg_num_nodes, avg_num_edges, avg_density, median_num_nodes, median_num_edges, median_density
def draw_graphon(data, edge_att, N, h_graph_env, num_env):
"""
Here we use the ground truth env label to draw graphons
"""
batch_size = data.y.shape[0]
device = data.y.device
idx = torch.tensor(np.arange(batch_size)).to(device)
ys = torch.unique(data.y, sorted=True)
envs = torch.unique(data.env_id, sorted=True)
y_env_graphs = {}
graphons = {}
for y in ys:
for env in envs:
y_env_graphs['{}{}'.format(y, env)] = []
edge_index = data.edge_index
adj_cau = to_dense_adj(edge_index=edge_index, edge_attr=edge_att)[0]
for y in ys:
idx_y = idx[data.y==y]
for i in range(len(idx_y)):
y_env_graphs['{}{}'.format(int(data[idx_y[i]].y), int(data[idx_y[i]].env_id))].append(adj_cau[data.ptr[idx_y[i]]:data.ptr[idx_y[i]+1], data.ptr[idx_y[i]]:data.ptr[idx_y[i]+1]])
for y in ys:
for env in envs:
graphs = y_env_graphs['{}{}'.format(y, env)]
# print("y:{}, env:{}, num_graphs:{}".format(y, env, len(graphs)))
aligned_graphs, normalized_node_degrees, max_num, min_num = align_graphs(graphs, padding=True, N=N)
graphon = gra2graphon(aligned_graphs, threshold=0.2)
graphons['{}{}'.format(y,env)] = graphon
# for y, env, graphon in graphons:
# print("graphon info: class_label: {}, env_label: {}, mean: {}, shape, {}".format(y, env, graphon.mean(), graphon.shape))
return graphons, ys, envs