模型介紹

TransE模型的基本思想是使head向量和relation向量的和盡可能靠近tail向量。這里我們用L1或L2范數來衡量它們的靠近程度。

損失函數是使用了負抽樣的max-margin函數。

L(y, y’) = max(0, margin - y + y’)

y是正樣本的得分，y'是負樣本的得分。然后使損失函數值最小化，當這兩個分數之間的差距大于margin的時候就可以了(我們會設置這個值，通常是1)。

由于我們使用距離來表示得分，所以我們在公式中加上一個減號，知識表示的損失函數為：

其中，d是：

這是L1或L2范數。至于如何得到負樣本，則是將head實體或tail實體替換為三元組中的隨機實體。

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代碼實現：

具體的代碼和數據集（YAGO、umls、FB15K、WN18）請見Github：
https://github.com/Colinasda/TransE.git

import codecs import numpy as np import copy import time import randomentities2id = {} relations2id = {}def dataloader(file1, file2, file3):print("load file...")entity = []relation = []with open(file2, 'r') as f1, open(file3, 'r') as f2:lines1 = f1.readlines()lines2 = f2.readlines()for line in lines1:line = line.strip().split('\t')if len(line) != 2:continueentities2id[line[0]] = line[1]entity.append(line[1])for line in lines2:line = line.strip().split('\t')if len(line) != 2:continuerelations2id[line[0]] = line[1]relation.append(line[1])triple_list = []with codecs.open(file1, 'r') as f:content = f.readlines()for line in content:triple = line.strip().split("\t")if len(triple) != 3:continueh_ = entities2id[triple[0]]r_ = relations2id[triple[1]]t_ = entities2id[triple[2]]triple_list.append([h_, r_, t_])print("Complete load. entity : %d , relation : %d , triple : %d" % (len(entity), len(relation), len(triple_list)))return entity, relation, triple_listdef norm_l1(h, r, t):return np.sum(np.fabs(h + r - t))def norm_l2(h, r, t):return np.sum(np.square(h + r - t))class TransE:def __init__(self, entity, relation, triple_list, embedding_dim=50, lr=0.01, margin=1.0, norm=1):self.entities = entityself.relations = relationself.triples = triple_listself.dimension = embedding_dimself.learning_rate = lrself.margin = marginself.norm = normself.loss = 0.0def data_initialise(self):entityVectorList = {}relationVectorList = {}for entity in self.entities:entity_vector = np.random.uniform(-6.0 / np.sqrt(self.dimension), 6.0 / np.sqrt(self.dimension),self.dimension)entityVectorList[entity] = entity_vectorfor relation in self.relations:relation_vector = np.random.uniform(-6.0 / np.sqrt(self.dimension), 6.0 / np.sqrt(self.dimension),self.dimension)relation_vector = self.normalization(relation_vector)relationVectorList[relation] = relation_vectorself.entities = entityVectorListself.relations = relationVectorListdef normalization(self, vector):return vector / np.linalg.norm(vector)def training_run(self, epochs=1, nbatches=100, out_file_title = ''):batch_size = int(len(self.triples) / nbatches)print("batch size: ", batch_size)for epoch in range(epochs):start = time.time()self.loss = 0.0# Normalise the embedding of the entities to 1for entity in self.entities.keys():self.entities[entity] = self.normalization(self.entities[entity]);for batch in range(nbatches):batch_samples = random.sample(self.triples, batch_size)Tbatch = []for sample in batch_samples:corrupted_sample = copy.deepcopy(sample)pr = np.random.random(1)[0]if pr > 0.5:# change the head entitycorrupted_sample[0] = random.sample(self.entities.keys(), 1)[0]while corrupted_sample[0] == sample[0]:corrupted_sample[0] = random.sample(self.entities.keys(), 1)[0]else:# change the tail entitycorrupted_sample[2] = random.sample(self.entities.keys(), 1)[0]while corrupted_sample[2] == sample[2]:corrupted_sample[2] = random.sample(self.entities.keys(), 1)[0]if (sample, corrupted_sample) not in Tbatch:Tbatch.append((sample, corrupted_sample))self.update_triple_embedding(Tbatch)end = time.time()print("epoch: ", epoch, "cost time: %s" % (round((end - start), 3)))print("running loss: ", self.loss)with codecs.open(out_file_title +"TransE_entity_" + str(self.dimension) + "dim_batch" + str(batch_size), "w") as f1:for e in self.entities.keys():# f1.write("\t")# f1.write(e + "\t")f1.write(str(list(self.entities[e])))f1.write("\n")with codecs.open(out_file_title +"TransE_relation_" + str(self.dimension) + "dim_batch" + str(batch_size), "w") as f2:for r in self.relations.keys():# f2.write("\t")# f2.write(r + "\t")f2.write(str(list(self.relations[r])))f2.write("\n")def update_triple_embedding(self, Tbatch):# deepcopy 可以保證，即使list嵌套list也能讓各層的地址不同， 即這里copy_entity 和# entitles中所有的elements都不同copy_entity = copy.deepcopy(self.entities)copy_relation = copy.deepcopy(self.relations)for correct_sample, corrupted_sample in Tbatch:correct_copy_head = copy_entity[correct_sample[0]]correct_copy_tail = copy_entity[correct_sample[2]]relation_copy = copy_relation[correct_sample[1]]corrupted_copy_head = copy_entity[corrupted_sample[0]]corrupted_copy_tail = copy_entity[corrupted_sample[2]]correct_head = self.entities[correct_sample[0]]correct_tail = self.entities[correct_sample[2]]relation = self.relations[correct_sample[1]]corrupted_head = self.entities[corrupted_sample[0]]corrupted_tail = self.entities[corrupted_sample[2]]# calculate the distance of the triplesif self.norm == 1:correct_distance = norm_l1(correct_head, relation, correct_tail)corrupted_distance = norm_l1(corrupted_head, relation, corrupted_tail)else:correct_distance = norm_l2(correct_head, relation, correct_tail)corrupted_distance = norm_l2(corrupted_head, relation, corrupted_tail)loss = self.margin + correct_distance - corrupted_distanceif loss > 0:self.loss += lossprint(loss)correct_gradient = 2 * (correct_head + relation - correct_tail)corrupted_gradient = 2 * (corrupted_head + relation - corrupted_tail)if self.norm == 1:for i in range(len(correct_gradient)):if correct_gradient[i] > 0:correct_gradient[i] = 1else:correct_gradient[i] = -1if corrupted_gradient[i] > 0:corrupted_gradient[i] = 1else:corrupted_gradient[i] = -1correct_copy_head -= self.learning_rate * correct_gradientrelation_copy -= self.learning_rate * correct_gradientcorrect_copy_tail -= -1 * self.learning_rate * correct_gradientrelation_copy -= -1 * self.learning_rate * corrupted_gradientif correct_sample[0] == corrupted_sample[0]:# if corrupted_triples replaces the tail entity, the head entity's embedding need to be updated twicecorrect_copy_head -= -1 * self.learning_rate * corrupted_gradientcorrupted_copy_tail -= self.learning_rate * corrupted_gradientelif correct_sample[2] == corrupted_sample[2]:# if corrupted_triples replaces the head entity, the tail entity's embedding need to be updated twicecorrupted_copy_head -= -1 * self.learning_rate * corrupted_gradientcorrect_copy_tail -= self.learning_rate * corrupted_gradient# normalising these new embedding vector, instead of normalising all the embedding togethercopy_entity[correct_sample[0]] = self.normalization(correct_copy_head)copy_entity[correct_sample[2]] = self.normalization(correct_copy_tail)if correct_sample[0] == corrupted_sample[0]:# if corrupted_triples replace the tail entity, update the tail entity's embeddingcopy_entity[corrupted_sample[2]] = self.normalization(corrupted_copy_tail)elif correct_sample[2] == corrupted_sample[2]:# if corrupted_triples replace the head entity, update the head entity's embeddingcopy_entity[corrupted_sample[0]] = self.normalization(corrupted_copy_head)# the paper mention that the relation's embedding don't need to be normalisedcopy_relation[correct_sample[1]] = relation_copy# copy_relation[correct_sample[1]] = self.normalization(relation_copy)self.entities = copy_entityself.relations = copy_relationif __name__ == '__main__':file1 = "/umls/train.txt"file2 = "/umls/entity2id.txt"file3 = "/umls/relation2id.txt"entity_set, relation_set, triple_list = dataloader(file1, file2, file3)# modify by yourselftransE = TransE(entity_set, relation_set, triple_list, embedding_dim=30, lr=0.01, margin=1.0, norm=2)transE.data_initialise()transE.training_run(out_file_title="umls_")

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