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synthetic_data.py
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/
synthetic_data.py
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import numpy as np
import random
from random import choice
import networkx as nx
import os
os.chdir('C:/Kaige_Research/Graph Learning/graph_learning_code/')
import pandas as pd
from sklearn.metrics.pairwise import cosine_similarity, rbf_kernel
from sklearn.preprocessing import StandardScaler, Normalizer, MinMaxScaler
from scipy.sparse import csgraph
from sklearn.datasets import make_blobs
from utils import *
from knn_models import *
from sklearn.preprocessing import normalize
def RGG(node_num, dimension=2):
RS=np.random.RandomState(seed=100)
features=RS.uniform(low=0, high=1, size=(node_num, dimension))
adj_matrix=rbf_kernel(features, gamma=(1)/(2*(0.5)**2))
np.fill_diagonal(adj_matrix,0)
laplacian=csgraph.laplacian(adj_matrix, normed=False)
return adj_matrix, laplacian, features
def rbf_graph(node_num, dimension=2, threshold=0.5):
RS=np.random.RandomState(seed=100)
features=RS.uniform(low=0, high=1, size=(node_num, dimension))
adj_matrix=rbf_kernel(features, gamma=(1)/(2*(0.5)**2))
adj_matrix[adj_matrix<threshold]=0.0
np.fill_diagonal(adj_matrix,0)
laplacian=csgraph.laplacian(adj_matrix, normed=False)
return adj_matrix, laplacian, features
def knn_graph(node_num, dimension=2, k=5):
RS=np.random.RandomState(seed=100)
features=RS.uniform(low=0, high=1, size=(node_num, dimension))
adj_matrix=rbf_kernel(features, gamma=(1)/(2*(0.5)**2))
for i in range(node_num):
rbf_row=adj_matrix[i,:]
neighbors=np.argsort(rbf_row)[:node_num-k]
adj_matrix[i, neighbors]=0
adj_matrix[neighbors,i]=0
np.fill_diagonal(adj_matrix,0)
laplacian=csgraph.laplacian(adj_matrix, normed=False)
return adj_matrix, laplacian, features
def er_graph(node_num, prob=0.2, seed=2018):
graph=nx.erdos_renyi_graph(node_num, prob, seed=seed)
adj_matrix=nx.to_numpy_array(graph)
np.fill_diagonal(adj_matrix,0)
laplacian=nx.laplacian_matrix(graph).toarray()
return adj_matrix, laplacian
def ba_graph(node_num, seed=2018):
graph=nx.barabasi_albert_graph(node_num, m=1, seed=seed)
adj_matrix=nx.to_numpy_array(graph)
np.fill_diagonal(adj_matrix,0)
laplacian=nx.laplacian_matrix(graph).toarray()
return adj_matrix, laplacian
def generate_signal_gl_siprep(signal_num, node_num, laplacian, error_sigma):
mean=np.zeros(node_num)
normed_lap=normalized_trace(laplacian, node_num)
pinv_lap=np.linalg.pinv(normed_lap)
cov=pinv_lap+error_sigma*np.identity(node_num)
signals=np.random.multivariate_normal(mean, cov, size=signal_num)
return signals
def generate_signal(signal_num, node_num, node_pos):
# linear combination of item feature and node feature
RS=np.random.RandomState(seed=100)
item_f=RS.normal(size=(signal_num, node_pos.shape[1]))
signals=np.dot(node_pos, item_f.T).T
return signals
def f1(x,y):
return np.sin((2-x-y)**2)
def f2(x,y):
return np.cos((x+y)**2)
def f3(x,y):
return (x-0.5)**2+(y-0.5)**3+x-y
def f4(x,y):
return np.sin(3*(x-0.5)**2+(y-0.5)**2)
def f5(x,y):
return (x-0.5)+(y-0.5)
def Tikhonov_filter(x, alpha=10):
return 1/(1+alpha*x)
def Heat_diffusion_filter(x, t=10):
return np.exp(-t*x)
def Generative_model_filter(x):
if x>0:
y=1/np.sqrt(x)
else:
y=0
return y
def original_signal(signal_num, node_num):
signal=np.random.normal(loc=1.0, size=(signal_num, node_num))
return signal
def Tikhonov_signal(original_signal, adj_matrix):
laplacian=csgraph.laplacian(adj_matrix, normed=False)
laplacian=laplacian/np.linalg.norm(laplacian)
eigenvalues, eigenvectors=np.linalg.eig(laplacian)
filtered_signal=[]
for j in range(len(original_signal)):
a=0
for i in range(len(eigenvalues)):
a+=eigenvectors[i]*Generative_model_filter(eigenvalues[i])*np.dot(eigenvectors[i], original_signal[j])
filtered_signal.append(a)
return np.array(filtered_signal)
def Heat_diffusion_signal(original_signal, adj_matrix):
laplacian=csgraph.laplacian(adj_matrix, normed=False)
laplacian=laplacian/np.linalg.norm(laplacian)
eigenvalues, eigenvectors=np.linalg.eig(laplacian)
resulted_signal=[]
for j in range(len(original_signal)):
a=0
for i in range(len(eigenvalues)):
a+=eigenvectors[i]*Heat_diffusion_filter(eigenvalues[i])*np.dot(eigenvectors[i], original_signal[j])
resulted_signal.append(a)
return np.array(resulted_signal)
def Generative_model_signal(original_signal, adj_matrix):
laplacian=csgraph.laplacian(adj_matrix, normed=False)
laplacian=laplacian/np.linalg.norm(laplacian)
eigenvalues, eigenvectors=np.linalg.eig(laplacian)
filtered_signal=[]
for j in range(len(original_signal)):
a=0
for i in range(len(eigenvalues)):
a+=eigenvectors[i]*Generative_model_filter(eigenvalues[i])*np.dot(eigenvectors[i], original_signal[j])
filtered_signal.append(a)
return np.array(filtered_signal)
def find_corrlation_matrix(signals):
corr_matrix=np.corrcoef(signals.T)
return corr_matrix
def create_networkx_graph(node_num, adj_matrix):
G=nx.Graph()
G.add_nodes_from(list(range(node_num)))
for i in range(node_num):
for j in range(node_num):
if adj_matrix[i,j]!=0:
G.add_edge(i,j,weight=adj_matrix[i,j])
else:
pass
return G
def find_eigenvalues_matrix(eigen_values):
eigenvalues_matrix=np.diag(np.sort(eigen_values))
return eigenvalues_matrix
def normalized_trace(matrix, target_trace):
normed_matrix=target_trace*matrix/np.trace(matrix)
return normed_matrix
def learn_knn_graph(signals, node_num, k=5):
#print('Learning KNN Graph')
adj=rbf_kernel(signals.T)
np.fill_diagonal(adj,0)
knn_adj=filter_graph_to_knn(adj, node_num, k=k)
knn_lap=csgraph.laplacian(knn_adj, normed=False)
return knn_adj, knn_lap
def learn_knn_signal(adj, signals, signal_num, node_num):
#print('Learning KNN Signals')
new_signals=np.zeros((signal_num, node_num))
for i in range(signal_num):
for j in range(node_num):
rbf_row=adj[j,:]
neighbors=rbf_row>0
weights=rbf_row[rbf_row>0]
if len(weights)==0:
new_signals[i,j]=signals[i,j]
else:
new_signals[i,j]=np.average(signals[i][neighbors], weights=weights)
return new_signals
def signal_noise(signal_num, node_num, scale):
RS=np.random.RandomState(seed=100)
noise=RS.normal(scale=scale, size=(signal_num, node_num))
return noise
def blob_data(node_num, signal_num, dimension, cluster_num, cluster_std, noise_scale):
x, y=make_blobs(n_samples=node_num, n_features=dimension, centers=cluster_num, cluster_std=cluster_std, center_box=(0,1.0), shuffle=False)
x=MinMaxScaler().fit_transform(x)
item_f, item_y=make_blobs(n_samples=signal_num, n_features=dimension, centers=cluster_num, cluster_std=cluster_std, center_box=(0,1.0), shuffle=False)
item_f=MinMaxScaler().fit_transform(item_f)
signal=np.dot(item_f, x.T)
noise=np.random.normal(size=(signal_num, node_num), scale=noise_scale)
noisy_signal=signal+noise
return noisy_signal, signal, item_f, x, y
def generate_all_random_users(iterations, user_num):
random_users=np.random.choice(np.arange(user_num), size=iterations, replace=True)
return random_users
def generate_all_article_pool(iterations, pool_size, article_num):
all_article_pool=[]
for i in range(iterations):
pool=np.random.choice(np.arange(article_num), size=pool_size, replace=True)
all_article_pool.append(pool)
all_article_pool=np.array(all_article_pool)
return all_article_pool
# adj, f=RGG(10)
# laplacian=csgraph.laplacian(adj, normed=False)
# laplacian=laplacian/np.linalg.norm(laplacian)
# eigenvalues, eigenvectors=np.linalg.eig(laplacian)
# y=Tikhonov_signal(x, adj)
# y=Generative_model_signal(x, adj)
# y=Heat_diffusion_signal(x, adj)