Python Example
Included in the static site for reading. Run locally from the source repository when needed.
"""
第24章：协同过滤推荐系统
Chapter 24: Collaborative Filtering Recommender
"""
import numpy as np
# 用户-物品评分矩阵 (4用户 x 5物品), 0表示未评分
R = np.array([
[5, 3, 0, 1, 0],
[4, 0, 0, 1, 2],
[1, 1, 0, 5, 0],
[0, 0, 4, 4, 5],
])
num_users, num_items = R.shape
num_features = 2
# 初始化用户特征和物品特征
X = np.random.randn(num_items, num_features) # 物品特征
W = np.random.randn(num_users, num_features) # 用户特征
b = np.zeros((1, num_items))
# 训练 (梯度下降)
alpha = 0.01
iterations = 1000
for _ in range(iterations):
# 只计算已评分的误差
for i in range(num_users):
for j in range(num_items):
if R[i, j] > 0:
pred = W[i] @ X[j] + b[0, j]
error = pred - R[i, j]
W[i] -= alpha * error * X[j]
X[j] -= alpha * error * W[i]
b[0, j] -= alpha * error
# 预测完整矩阵
predictions = W @ X.T + b
print("原始评分矩阵:")
print(R)
print("\n预测评分矩阵:")
print(np.round(predictions, 1))
# 为用户0推荐未评分物品
user = 0
unrated = np.where(R[user] == 0)[0]
recommendations = [(j, predictions[user, j]) for j in unrated]
recommendations.sort(key=lambda x: -x[1])
print(f"\n给用户 {user} 的推荐 (未评分物品按预测分排序):")
for item, score in recommendations:
print(f" 物品 {item}: 预测评分 {score:.2f}")