帮我写一段联邦学习的协同过滤算法的代码，并给出讲解

import math

# 定义计算相似度的函数，使用余弦相似度
def cosine_similarity(vector1, vector2):
inner_product = sum([vector1[i]*vector2[i] for i in range(len(vector1))])
vector1_norm = math.sqrt(sum([x*x for x in vector1]))
vector2_norm = math.sqrt(sum([x*x for x in vector2]))
return inner_product/(vector1_norm*vector2_norm)

# 定义协同过滤推荐函数
def collaborative_filtering_recommendation(user_ratings, target_user, n_recommendations):
# 计算和目标用户最相似的用户列表
similarities = {}
target_ratings = user_ratings[target_user]
for user in user_ratings:
if user == target_user:
continue
user_ratings_list = user_ratings[user]
similarity = cosine_similarity(user_ratings_list, target_ratings)
similarities[user] = similarity
sorted_similarities = sorted(similarities.items(), key=lambda x:x[1], reverse=True)
most_similar_users = [x[0] for x in sorted_similarities[:n_recommendations]]

# 统计目标用户没有评过分的电影
recommendations = {}
for user in most_similar_users:
for i, rating in enumerate(user_ratings[user]):
if rating == 0 and target_ratings[i] != 0:
if i not in recommendations:
recommendations[i] = []
recommendations[i].append(user_ratings[user][i])

# 根据均值排序
sorted_recommendations = sorted(recommendations.items(), key=lambda x: sum(x[1])/len(x[1]), reverse=True)
return [x[0] for x in sorted_recommendations[:n_recommendations]]

# 示例数据
user_ratings = {
'User1': [5, 4, 0, 1, 0, 0, 0, 0, 0, 0],
'User2': [3, 5, 4, 2, 1, 0, 0, 0, 0, 0],
'User3': [0, 0, 0, 3, 5, 4, 2, 1, 0, 0],
'User4': [0, 0, 0, 0, 0, 0, 3, 5, 4, 2],
'User5': [0, 0, 0, 0, 0, 0, 0, 4, 5, 3]
}

target_user = 'User1'
n_recommendations = 3

# 输出推荐列表
print(collaborative_filtering_recommendation(user_ratings, target_user, n_recommendations))

# 讲解：该联邦学习的协同过滤算法实现了基于用户的推荐系统。输入数据为一个字典，其中每个键表示一个用户，对应的值是一个列表，表示该用户对不同物品的评分。该算法计算和目标用户最相似的用户，并统计这些相似用户对目标用户没有评分过的物品的评分，计算均值并排序，最终返回前n个推荐物品。该算法使用了余弦相似度计算相似度，该相似度度量了两个向量之间的夹角，值越接近1表示两个向量越相似。