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阅读知识图谱随感

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阅读知识图谱随感

TransE

在这里插入图片描述

知识图谱的主要构成是三个东西。 h \bm{h} h表示头部,也叫做head。 r \bm{r} r表示关系,也叫做relation。 t \bm{t} t表示尾部,也叫做tail。一般而言,我们约定
G = { h , r , t } G= \{\bm{h},\bm{r},\bm{t}\} G={h,r,t}
这就表示一种关系。例如 h : = I t a l y \bm{h}:=Italy h:=Italy, r : = C a p i t o l \bm{r}:=Capitol r:=Capitol, t : = R o m e \bm{t}:=Rome t:=Rome,也就是意大利的首都是罗马。

说到知识图谱,必须介绍的就是TransE这个模型了。其得到得分函数(score function)的方法是
s = ∣ ∣ h + r − t ∣ ∣ 2 2 s= ||\bm{h} + \bm{r} - \bm{t}||_2^2 s=∣∣h+r−t∣∣22​
一般而言,可以采用Pairewise的训练策略。也就是找一个正样本对和一个负样本对
L = [ m + s ( h , r , t + ) − s ( h , r , t − ) ] + L= [m + s(h,r,t_+) - s(h,r,t_-)]_+ L=[m+s(h,r,t+​)−s(h,r,t−​)]+​
写出代码试试看

def TransE(self, head, relation, tail, mode):
	score = (head + relation) - tail
	score = self.gamma.item() - torch.norm(score, p=1, dim=2)
	return score

RotatE

如果有一天,知识之间的关系可以用旋转来表示,那么世界会变成什么样子呢?这时候我们利用欧拉公式,一个复数 c c c乘上 e i θ e^{i\theta} eiθ之后相当于把这个复数旋转了 θ \theta θ角度。然后把相关参数用复数来表示之
h = x h + i y h t = x t + i y t r = x r + i y r \bm{h} = \bm{x}_h + i \bm{y}_h\\ \bm{t} = \bm{x}_t + i \bm{y}_t\\ \bm{r} = \bm{x}_r + i \bm{y}_r h=xh​+iyh​t=xt​+iyt​r=xr​+iyr​
值得注意的是, ∣ ∣ r ∣ ∣ 2 2 = 1 ||\bm{r}||_2^2 = 1 ∣∣r∣∣22​=1。那么来计算一波
h ⋅ r = ( x h + i y h ) ( x r + i y r ) h ⋅ r = ( x h x r − y h y r ) + i ( x h x r + x r y h ) \bm{h} \cdot \bm{r} = (\bm{x}_h + i \bm{y}_h)(\bm{x}_r + i \bm{y}_r)\\ \bm{h} \cdot \bm{r} = (\bm{x}_h\bm{x}_r - \bm{y}_h\bm{y}_r) + i(\bm{x}_h\bm{x}_r + \bm{x}_r\bm{y}_h) h⋅r=(xh​+iyh​)(xr​+iyr​)h⋅r=(xh​xr​−yh​yr​)+i(xh​xr​+xr​yh​)
然后有
h ⋅ r − t = ( x h x r − y h y r − x t ) + i ( x h x r + x r y h − y t ) \bm{h} \cdot \bm{r} - \bm{t} = (\bm{x}_h\bm{x}_r - \bm{y}_h\bm{y}_r - \bm{x}_t) + i(\bm{x}_h\bm{x}_r + \bm{x}_r\bm{y}_h - \bm{y}_t) h⋅r−t=(xh​xr​−yh​yr​−xt​)+i(xh​xr​+xr​yh​−yt​)
具体运算则是

def RotatE(self, head, relation, tail, mode):
    pi = 3.14159265358979323846
        
    re_head, im_head = torch.chunk(head, 2, dim=2)
    re_tail, im_tail = torch.chunk(tail, 2, dim=2)

    #Make phases of relations uniformly distributed in [-pi, pi]

    phase_relation = relation/(self.embedding_range.item()/pi)

    re_relation = torch.cos(phase_relation)
    im_relation = torch.sin(phase_relation)

    re_score = re_head * re_relation - im_head * im_relation
    im_score = re_head * im_relation + im_head * re_relation
    re_score = re_score - re_tail
    im_score = im_score - im_tail

    score = torch.stack([re_score, im_score], dim = 0)
    score = score.norm(dim = 0)

    score = self.gamma.item() - score.sum(dim = 2)
    return score

文章来源:RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space。

标签:head,图谱,知识,随感,re,score,relation,bm,im
来源: https://blog.csdn.net/ab459548764/article/details/113664676