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link_prediction.py
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link_prediction.py
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import pickle
import networkx as nx
import numpy as np
class TransE:
"""
TransE model for learning low-dimensional embeddings of entities and relationships
in a knowledge graph, and for predicting missing relationships.
Attributes:
n_entities (int): Number of unique entities in the graph.
n_relations (int): Number of unique relationships in the graph.
dim (int): Dimensionality of the embeddings.
lr (float): Learning rate for the stochastic gradient descent.
margin (float): Margin hyperparameter for the margin-based ranking loss.
entity_embeddings (np.ndarray): Embeddings for the entities.
relation_embeddings (np.ndarray): Embeddings for the relationships.
"""
def __init__(self, n_entities, n_relations, dim, lr, margin):
"""
Initialize the TransE model with random embeddings for entities and relationships.
Args:
n_entities (int): Number of unique entities in the graph.
n_relations (int): Number of unique relationships in the graph.
dim (int): Dimensionality of the embeddings.
lr (float): Learning rate for the stochastic gradient descent.
margin (float): Margin hyperparameter for the margin-based ranking loss.
"""
self.n_entities = n_entities
self.n_relations = n_relations
self.dim = dim
self.lr = lr
self.margin = margin
# Initialize entity and relation embeddings with small random values
self.entity_embeddings = np.random.uniform(
-6/np.sqrt(dim), 6/np.sqrt(dim), (n_entities, dim))
self.relation_embeddings = np.random.uniform(
-6/np.sqrt(dim), 6/np.sqrt(dim), (n_relations, dim))
# Normalize the entity embeddings to unit length
self.entity_embeddings = self.entity_embeddings / \
np.linalg.norm(self.entity_embeddings, axis=1, keepdims=True)
def train_step(self, h, t, r, h_neg, t_neg):
"""
Perform a single training step using a mini-batch of positive and negative samples.
Args:
h (np.ndarray): Indices of the head entities in the positive samples.
t (np.ndarray): Indices of the tail entities in the positive samples.
r (np.ndarray): Indices of the relationships in the positive samples.
h_neg (np.ndarray): Indices of the head entities in the negative samples.
t_neg (np.ndarray): Indices of the tail entities in the negative samples.
Returns:
float: The loss value for the training step.
"""
# Get embeddings for positive and negative samples
h_e = self.entity_embeddings[h]
t_e = self.entity_embeddings[t]
r_e = self.relation_embeddings[r]
h_neg_e = self.entity_embeddings[h_neg]
t_neg_e = self.entity_embeddings[t_neg]
# Compute distances for positive and negative samples
pos_dist = np.linalg.norm(h_e + r_e - t_e, axis=1)
neg_dist = np.linalg.norm(h_neg_e + r_e - t_neg_e, axis=1)
# Calculate the margin-based loss
loss = np.maximum(0, self.margin + pos_dist - neg_dist).sum()
# Compute gradients for the embeddings
grad_pos = 2 * (h_e + r_e - t_e)
grad_neg = 2 * (h_neg_e + r_e - t_neg_e)
# Update embeddings based on the gradients
for i in range(len(h)):
if pos_dist[i] + self.margin > neg_dist[i]:
self.entity_embeddings[h[i]] -= self.lr * grad_pos[i]
self.entity_embeddings[t[i]] += self.lr * grad_pos[i]
self.relation_embeddings[r[i]] -= self.lr * grad_pos[i]
self.entity_embeddings[h_neg[i]] += self.lr * grad_neg[i]
self.entity_embeddings[t_neg[i]] -= self.lr * grad_neg[i]
# Re-normalize the entity embeddings to unit length after update
self.entity_embeddings = self.entity_embeddings / \
np.linalg.norm(self.entity_embeddings, axis=1, keepdims=True)
return loss
def train(self, train_data, n_epochs):
"""
Train the TransE model using the provided training data.
Args:
train_data (list of tuples): List of training samples, each represented as a tuple (h, t, r).
n_epochs (int): Number of epochs to train the model.
"""
# Train the model for a specified number of epochs
for epoch in range(n_epochs):
# Shuffle the training data
np.random.shuffle(train_data)
for i in range(0, len(train_data), 128):
# Process mini-batches of the training data
batch = train_data[i:i+128]
h, t, r = zip(*batch)
h = np.array(h)
t = np.array(t)
r = np.array(r)
# Generate negative samples by randomly corrupting head or tail entities
h_neg = np.random.randint(0, self.n_entities, len(h))
t_neg = np.random.randint(0, self.n_entities, len(t))
# Perform a training step
self.train_step(h, t, r, h_neg, t_neg)
def predict(self, h, t):
"""
Predict the relationship labels for given head and tail entities.
Args:
h (np.ndarray): Indices of the head entities.
t (np.ndarray): Indices of the tail entities.
Returns:
np.ndarray: Predicted relationship labels.
"""
# Get embeddings for head and tail entities
h_e = self.entity_embeddings[h]
t_e = self.entity_embeddings[t]
# Compute scores for all possible relations
scores = np.linalg.norm(
h_e[:, np.newaxis, :] + self.relation_embeddings - t_e[:, np.newaxis, :], axis=2)
# Return the relation with the minimum score (closest in embedding space)
return np.argmin(scores, axis=1)
if __name__ == "__main__":
# Load the graph data
with open("datasets/LINK/data.pkl", "rb") as f:
data = pickle.load(f)
G = nx.MultiDiGraph(data)
# Separate the edges into training and test sets
train_edges = []
test_edges = []
# Iterate over all edges in the graph
for u, v, data in G.edges(data=True):
if data['edge_label'] is None:
test_edges.append((u, v, data['id']))
else:
train_edges.append((u, v, data['edge_label']))
# Extract unique nodes and relationships
nodes = list(G.nodes())
relations = list(set(edge[2] for edge in train_edges))
# Create dictionaries to map nodes and relationships to unique indices
node2idx = {node: idx for idx, node in enumerate(nodes)}
rel2idx = {rel: idx for idx, rel in enumerate(relations)}
idx2rel = {idx: rel for rel, idx in rel2idx.items()}
# Convert edges to indices for easier processing in the TransE model
train_edges = [(node2idx[u], node2idx[v], rel2idx[rel])
for u, v, rel in train_edges]
test_edges = [(node2idx[u], node2idx[v], edge_id)
for u, v, edge_id in test_edges]
# Define parameters for the TransE model
dim = 50
lr = 0.01
margin = 1.0
n_epochs = 100
# Initialize and train the TransE model
model = TransE(len(nodes), len(relations), dim, lr, margin)
model.train(train_edges, n_epochs)
# Predict missing labels for test edges
test_h, test_t, edge_ids = zip(*test_edges)
predicted_labels = model.predict(np.array(test_h), np.array(test_t))
# Pair edge IDs with their corresponding predictions
id_prediction_pairs = list(zip(edge_ids, predicted_labels))
# Sort predictions by edge IDs
id_prediction_pairs.sort(key=lambda x: x[0])
# Extract sorted predictions
sorted_predictions = [pred for _, pred in id_prediction_pairs]
# Ensure the predictions are in the required format
pred = [int(pred) for pred in sorted_predictions]
# Save predictions to file
with open("LINK-Predictions.pkl", "wb") as f:
pickle.dump(pred, f)