主要讲和TransE代码的区别，TransE文章的链接
Java版本TransE代码的学习
关于范数的概念
什么是0范数、1范数、2范数？区别又是什么
初始化向量
初始化关系平面的向量Wr，初始化向量relation_vec,初始化节点向量entity_vec
Wr_vec = new double[relation_num][vector_dimension];
for (int i = 0; i < relation_num; i++) {
for (int j = 0; j < vector_dimension; j++) {
Wr_vec[i][j] = uniform(-1, 1);
}
norm2one(Wr_vec[i]);
}
relation_vec = new double[relation_num][vector_dimension];
for (int i = 0; i < relation_num; i++) {
for (int j = 0; j < vector_dimension; j++) {
relation_vec[i][j] = uniform(-1, 1);
}
}
entity_vec = new double[entity_num][vector_dimension];
for (int i = 0; i < entity_num; i++) {
for (int j = 0; j < vector_dimension; j++) {
entity_vec[i][j] = uniform(-1, 1);
}
}
负采样方法
对于 1-N 的关系，赋予更高的概率替换头实体，而对于 N-1 的关系，赋予更高的概率替换尾实体。具体地，对每个关系计算其 tph （每个头实体平均对应几个尾实体）和 hpt （每个尾实体平均对应几个头实体）。对于 tph/tph+hpt 越大的，说明是一对多的关系，在负采样时替换头实体，更容易获得 true negative。
tph：每个头实体平均对应几个尾实体
hpt：每个尾实体平均对应几个头实体
left_num.put(i, sum / count); // tph
right_num.put(i, sum / count);
double pr = 1000 * right_num.get(relation_id) / (right_num.get(relation_id) + left_num.get(relation_id));
if (method == 0) {
pr = 500;
}
if (rand() % 1000 < pr) {//替换头实体}
else{//替换尾实体}
计算向量的分数
转换
通过转换，得到
第一个for循环，计算
和
第二个for循环，计算L2范数的平方，开方以后平方，因为这个向量只有一个值，也就相当于是取绝对值
static double calc_sum(int head, int tail, int relation) {
double Wrh = 0;
double Wrt = 0;
for (int i = 0; i < vector_dimension; i++) {
Wrh += Wr_vec[relation][i] * entity_vec[head][i];
Wrt += Wr_vec[relation][i] * entity_vec[tail][i];
}
double sum = 0, tmp;
for (int i = 0; i < vector_dimension; i++) {
tmp = (entity_vec[tail][i] - Wrt * Wr_vec[relation][i])
- relation_vec[relation][i]
- (entity_vec[head][i] - Wrh * Wr_vec[relation][i]);
sum += abs(tmp);
}
return sum;
}
梯度下降
if (sum1 + margin > sum2) {
res = margin + sum1 - sum2;
gradient(head_a, tail_a, relation_a, -1);
gradient(head_b, tail_b, relation_b, 1);
}
private static void gradient(int head, int tail, int relation, double beta) {
double Wrh = 0;
double Wrt = 0;
for (int i = 0; i < vector_dimension; i++) {
Wrh += Wr_vec[relation][i] * entity_vec[head][i];
Wrt += Wr_vec[relation][i] * entity_vec[tail][i];
}
double sum = 0;
for (int i = 0; i < vector_dimension; i++) {
double delta = (entity_vec[tail][i] - Wrt * Wr_vec[relation][i])
- relation_vec[relation][i]
- (entity_vec[head][i] - Wrh * Wr_vec[relation][i]);
double x = (delta > 0) ? 1 : -1;
sum += x * Wr_vec[relation][i];
relation_vec[relation][i] -= beta * learning_rate * x;
entity_vec[head][i] -= beta * learning_rate * x;
entity_vec[tail][i] += beta * learning_rate * x;
Wr_vec[relation][i] += beta * x * learning_rate * (Wrh - Wrt);
}
for (int i = 0; i < vector_dimension; i++) {
Wr_vec[relation][i] += beta * learning_rate * sum * (entity_vec[head][i] - entity_vec[tail][i]);
}
norm(relation_vec[relation]);
norm(entity_vec[head]);
norm(entity_vec[tail]);
norm2one(Wr_vec[relation]);
norm(relation_vec[relation], Wr_vec[relation]);
}
使用L2范数归一化，先求平方和，再开方
norm(relation_vec[relation]);
static double vec_len(double[] a) {
// calculate the length of the vector
double res = 0;
for (int i = 0; i < vector_dimension; i++) {
res += sqr(a[i]);
}
return sqrt(res);
}
static void norm(double[] a) {
// limit the element a under 1
double x = vec_len(a);
if (x > 1) {
for (int i = 0; i < vector_dimension; i++) {
a[i] /= x;
}
}
}
dr与Wr的关系限制，dr就是relation，Wr是relation的映射平面
norm(relation_vec[relation], Wr_vec[relation]);
static void norm(double[] a, double[] Wr) {
double sum = 0;
while (true) {
for (int i = 0; i < vector_dimension; i++) {
sum += sqr(Wr[i]);
}
sum = sqrt(sum);
for (int i = 0; i < vector_dimension; i++) {
Wr[i] /= sum;
}
double x = 0;
for (int i = 0; i < vector_dimension; i++) {
x += Wr[i] * a[i];
}
if (x > 0.1) {
for (int i = 0; i < vector_dimension; i++) {
double tmp = a[i];
a[i] -= learning_rate * Wr[i];
Wr[i] -= learning_rate * tmp;
}
} else {
break;
}
}
norm2one(Wr);
}
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