PyTorch：距离度量

比眉伴天荒 2023-01-15 09:28 225阅读 0赞

# 两个张量之间的欧氏距离 #

即m\*e和n\*e张量之间的欧式距离

### 理论分析 ###

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3BpcGlzb3JyeQ_size_16_color_FFFFFF_t_70][]

### 算法实现 ###

import torch

def euclidean\_dist(x, y):  
    """  
    Args:  
      x: pytorch Variable, with shape \[m, d\]  
      y: pytorch Variable, with shape \[n, d\]  
    Returns:  
      dist: pytorch Variable, with shape \[m, n\]  
    """  
    m = x.size(0)  
    n = y.size(0)  
    e = x.size(1)

\# 方式1  
    a1 = torch.sum((x \*\* 2), 1, keepdim=True).expand(m, n)  
    b2 = (y \*\* 2).sum(1).expand(m, n)  
    dist = (a1 + b2 - 2 \* (x @ y.T)).float().sqrt()  
    print(dist)

\# 方式2  
    x1 = x.unsqueeze(1).expand(m, n, e)  
    y1 = y.expand(m, n, e)  
    dist = (x1 - y1).pow(2).sum(2).float().sqrt()  
    print(dist)

\# 方式3  
    dist = torch.zeros((m, n))  
    for i, xi in enumerate(x):  
        for j, yi in enumerate(y):  
            \# 方式2.1  
            \# dist\[i\]\[j\] = ((xi - yi) \*\* 2).sum().float().sqrt()  
            \# 方式2.2  
            dist\[i\]\[j\] = torch.pairwise\_distance(torch.unsqueeze(xi, 0), torch.unsqueeze(yi, 0), p=2)  
    print(dist)

\# 方式4  
    dist = torch.zeros((m, n))  
    for i, xi in enumerate(x):  
        dist\[i\] = torch.pairwise\_distance(xi, y, p=2)  
    print(dist)  
    return dist

a = torch.tensor(\[\[1, 2\], \[3, 4\], \[5, 6\]\])  
b = torch.tensor(\[\[2, 3\], \[4, 5\], \[5, 6\], \[8, 9\]\])  
dist = euclidean\_dist(a, b)

tensor(\[\[1.4142, 4.2426, 5.6569, 9.8995\],  
        \[1.4142, 1.4142, 2.8284, 7.0711\],  
        \[4.2426, 1.4142, 0.0000, 4.2426\]\])

\[[矩阵之间欧式距离的快捷计算方法（无循环）][Link 1]\]

### m\*e和m\*e张量之间的欧式距离pairwise\_distance ###

import torch.nn.functional as F  
distance = F.pairwise\_distance(rep\_a, rep\_b, p=2)

其中rep\_a和rep\_b为\[batch\_size,hidden\_dim\]，两个维度必须相同，或者第一个维度为\[hidden\_dim\]会自动进行广播操作（且最多只能有两个维度？）

\[torch.nn.[PairwiseDistance][](p=2.0, eps=1e-06, keepdim=False)\]

### 使用numpy完成相同操作 ###

import numpy as np

a = np.array(\[\[1, 2\], \[3, 4\], \[5, 6\]\])  
b = np.array(\[\[2, 3\], \[4, 5\], \[5, 6\], \[8, 9\]\])  
dist = np.sqrt(np.sum(a \*\* 2, 1, keepdims=True).repeat(b.shape\[0\], axis=1) +  
               np.sum(b \*\* 2, 1, keepdims=True).repeat(a.shape\[0\], axis=1).transpose() - a.dot(b.transpose()) \* 2)  
print(dist)

\[\[1.41421356 4.24264069 5.65685425 9.89949494\]  
 \[1.41421356 1.41421356 2.82842712 7.07106781\]  
 \[4.24264069 1.41421356 0.         4.24264069\]\]

[\-柚子皮-][-_-]

## 单个张量内部向量两两之间的欧氏距离 ##

def self\_euclidean\_dist(embeddings):  
    \# 方式1（类似euclidean\_dist(x, y)方式2）  
    m, m, e = len(embeddings), len(embeddings), embeddings.shape\[1\]  
    t1 = embeddings.unsqueeze(1).expand(m, m, e)  
    t2 = embeddings.unsqueeze(0).expand(m, m, e)  
    dist = (t1 - t2).pow(2).sum(2).float().sqrt()  
    print(dist)  
    return dist

a = torch.tensor(\[\[1, 2\], \[3, 4\], \[5, 6\]\])  
self\_euclidean\_dist(a)  
from: [\-柚子皮-][-_-]

ref:

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3BpcGlzb3JyeQ_size_16_color_FFFFFF_t_70]: /images/20221022/dbfc20fb5c214cd39a874cb9f5d9fea9.png
[Link 1]: https://blog.csdn.net/IT_forlearn/article/details/100022244
[PairwiseDistance]: https://pytorch.org/docs/stable/generated/torch.nn.PairwiseDistance.html
[-_-]: https://me.csdn.net/pipisorry