what

余弦相似度是一种用于度量向量相似性的metric。

$$cos\theta =\frac{A.B}{|A|.|B|}$$

• A.B：向量的内积
• |A|：向量的模长
• $cos\theta$：的范围$ [ -1 , 1 ] $

why

余弦相似度的计算复杂度很低，对于稀疏向量而言，只用考虑非零向量

How

math库实现

python">import numpy as np
import mathdef cosine_similarity(vec1, vec2) -> float:norm_vec1, norm_vec2 = 0, 0dot_product = 0for v1, v2 in zip(vec1, vec2):dot_product += v1 * v2norm_vec1 += v1 * v1norm_vec2 += v2 * v2norm_vec1 = math.sqrt(norm_vec1)norm_vec2 = math.sqrt(norm_vec2)return dot_product / (norm_vec1 * norm_vec2)if __name__ == '__main__':print(cosine_similarity([1, 2, 3], [-1, -2, -3]))

numpy实现

python">import numpy as npdef cosine_similarity(vec1, vec2) -> float:norm_vec1 = np.linalg.norm(vec1)norm_vec2 = np.linalg.norm(vec2)return np.dot(vec1, vec2) / (norm_vec1 * norm_vec2)if __name__ == '__main__':print(cosine_similarity([1, 2, 3], [1, 2, 3]))

pytorch实现

python">import torch
import torch.nn.functional as Fvec1 = torch.FloatTensor([1, 2, 3, 4])
vec2 = torch.FloatTensor([5, 6, 7, 8])cos_sim = F.cosine_similarity(vec1, vec2, dim=0)
print(cos_sim)