%matplotlib inline 

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns

准备数据

用户-物品矩阵

X = np.array([[0.11, 0.2, 0], [0.81, 0, 0], [0, 0.88, 0.74], [0, 0, 0.42]])
m = X.shape[0]
n = X.shape[1]
X

array([[0.11, 0.2 , 0.  ],
       [0.81, 0.  , 0.  ],
       [0.  , 0.88, 0.74],
       [0.  , 0.  , 0.42]])

物品-用户矩阵

Y = X.T
Y

array([[0.11, 0.81, 0.  , 0.  ],
       [0.2 , 0.  , 0.88, 0.  ],
       [0.  , 0.  , 0.74, 0.42]])

Item-Based 基于物品

物品相似度矩阵I

Y_2norm = np.linalg.norm(Y, ord=2, axis=1).reshape(n, 1)
Y_T_2norm = np.linalg.norm(Y.T, ord=2, axis=0).reshape(1, n)

I = np.dot(Y, Y.T) / np.dot(Y_2norm, Y_T_2norm)
I = np.round(I, 3)
I

array([[1.   , 0.03 , 0.   ],
       [0.03 , 1.   , 0.848],
       [0.   , 0.848, 1.   ]])

用户物品推荐矩阵P

I_1norm = np.linalg.norm(I, ord=1, axis=1).reshape(n, 1)
P = np.dot(I, Y) / I_1norm
P = np.round(P, 3)
P = P.T
P

array([[0.113, 0.108, 0.092],
       [0.786, 0.013, 0.   ],
       [0.026, 0.803, 0.804],
       [0.   , 0.19 , 0.227]])

User-Based 基于用户

用户相似度矩阵U

X_2norm = np.linalg.norm(X, ord=2, axis=1).reshape(m, 1)
X_T_2norm = np.linalg.norm(X.T, ord=2, axis=0).reshape(1, m)

U = np.dot(X, X.T) / np.dot(X_2norm, X_T_2norm)
U = np.round(U, 3)
U

array([[1.   , 0.482, 0.671, 0.   ],
       [0.482, 1.   , 0.   , 0.   ],
       [0.671, 0.   , 1.   , 0.644],
       [0.   , 0.   , 0.644, 1.   ]])

用户物品推荐矩阵P

U_1norm = np.linalg.norm(U, ord=1, axis=1).reshape(m, 1)
P = np.dot(U, X) / U_1norm
P = np.round(P, 3)
P

array([[0.232, 0.367, 0.231],
       [0.582, 0.065, 0.   ],
       [0.032, 0.438, 0.436],
       [0.   , 0.345, 0.545]])