首先，将每个组的成员数加起来，得到 * k * 项：

df2['count'] = df1.groupby('group')['user'].count()

然后合并df1和df2，这样我们就有了一个帧，其中每行包含每个用户的所有必要参数：

joined = df1.join(df2[['x2', 'p2', 'threshold', 'count']], on='group')
print(joined)

>>>      user               x1  group               x2     p2  threshold  count
0  user 1  [0.2, 0.3, 0.5]      1  [0.5, 0.1, 0.4]  0.342        0.6      2
1  user 2  [0.3, 0.3, 0.4]      0  [0.4, 0.2, 0.4]  0.231        0.9      2
2  user 3  [0.4, 0.4, 0.2]      0  [0.4, 0.2, 0.4]  0.231        0.9      2
3  user 4  [0.2, 0.1, 0.7]      2  [0.5, 0.1, 0.4]  0.411        0.8      1
4  user 5  [0.5, 0.3, 0.2]      1  [0.5, 0.1, 0.4]  0.342        0.6      2

现在定义计算S分数的函数：

def l_delta(z1, z2):
    return [a1 - a2 for (a1, a2) in zip(z1, z2)]

def inner(z1, z2):
    return sum([a1 * a2 for (a1, a2) in zip(z1, z2)])

def s_score(row):
    delta = l_delta(row['x2'], row['x1'])
    num = inner(delta, delta)
    return 1/row['count'] + num / row['p2']

最后，将这些函数应用于联接矩阵中的每一行：

joined['s_score'] = joined.apply(s_score, axis=1)
print(joined[['user', 's_score']])

结果：

user   s_score
0  user 1  0.909357
1  user 2  0.586580
2  user 3  0.846320
3  user 4  1.437956
4  user 5  0.733918

答案与@The Photon类似，其中我们（1）合并df 1和df 2，（2）用groupby计算k（3）计算（x2-x1）与自身的内积

import pandas as pd
import numpy as np

df1 = pd.DataFrame({'user': ['user 1', 'user 2', 'user 3', 'user 4', 'user 5'],
                    'x1': [[0.2, 0.3, 0.5],[0.3, 0.3, 0.4],[0.4, 0.4, 0.2],[0.2, 0.1, 0.7],[0.5,0.3,0.2]],
                    'group': [1, 0, 0, 2, 1]})

df2 = pd.DataFrame({'group': [0, 1, 2],
                    'x2': [[0.4, 0.2, 0.4],[0.5, 0.1, 0.4], [0.5, 0.1, 0.4]],
                    'p2': [0.231, 0.342, 0.411],
                    'threshold': [0.9, 0.6, 0.8]})

#merge df1 and df2 into a single table
merged_df = df1.merge(df2)

#calculate the number of unique users per group (k)
merged_df['k'] = merged_df.groupby('group')['user'].transform('nunique')

#calculate x2-x1 for each user (convert to numpy array for vectorized subtraction)
x2_sub_x1 = merged_df['x2'].apply(np.array)-merged_df['x1'].apply(np.array)

#calculate (x2-x1)T(x2-x1) for each user (same as squaring each term and summing)
numerator = x2_sub_x1.pow(2).apply(sum)

#calculate S from your formula and add it as a column to the merged table
merged_df['S'] = (1/merged_df['k'])+(numerator/merged_df['p2'])

最终合并表

user    x1  group   x2  p2  threshold   k   S
0   user 1  [0.2, 0.3, 0.5] 1   [0.5, 0.1, 0.4] 0.342   0.6 2   0.909357
1   user 5  [0.5, 0.3, 0.2] 1   [0.5, 0.1, 0.4] 0.342   0.6 2   0.733918
2   user 2  [0.3, 0.3, 0.4] 0   [0.4, 0.2, 0.4] 0.231   0.9 2   0.586580
3   user 3  [0.4, 0.4, 0.2] 0   [0.4, 0.2, 0.4] 0.231   0.9 2   0.846320
4   user 4  [0.2, 0.1, 0.7] 2   [0.5, 0.1, 0.4] 0.411   0.8 1   1.437956