柚子快报邀请码778899分享：07
LFM--梯度下降法--实现基于模型的协同过滤0.引入依赖1.数据准备2.算法的实现3.测试
LFM--梯度下降法--实现基于模型的协同过滤
0.引入依赖
import numpy as np # 数值计算、矩阵运算、向量运算import pandas as pd # 数值分析、科学计算
1.数据准备
# 定义评分矩阵 RR = np.array([[4, 0, 2, 0, 1], [0, 2, 3, 0, 0], [1, 0, 2, 4, 0], [5, 0, 0, 3, 1], [0, 0, 1, 5, 1], [0, 3, 2, 4, 1], ])# R.shape # (6, 5)# R.shape[0] # 6# R.shape[1] # 5# len(R) # 6# len(R[0]) # 5
2.算法的实现
"""@输入参数：R：M*N 的评分矩阵K：隐特征向量维度max_iter: 最大迭代次数alpha：步长lamda：正则化系数@输出：分解之后的 P，QP：初始化用户特征矩阵 M*KQ：初始化物品特征矩阵 N*K，Q 的转置是 K*N"""# 给定超参数K = 5max_iter = 5000alpha = 0.0002lamda = 0.004# 核心算法def LMF_grad_desc(R, K=2, max_iter=1000, alpha=0.0001, lamda=0.002): # 定义基本维度参数 M = len(R) N = len(R[0]) # P、Q 的初始值随机生成 P = np.random.rand(M, K) Q = np.random.rand(N, K) Q = Q.T # 开始迭代 for steps in range(max_iter): # 对所有的用户 u，物品 i 做遍历，然后对对应的特征向量 Pu、Qi 做梯度下降 for u in range(M): for i in range(N): # 对于每一个大于 0 的评分，求出预测评分误差 e_ui if R[u][i] > 0: e_ui = np.dot(P[u,:], Q[:,i]) - R[u][i] # 代入公式，按照梯度下降算法更新当前的 Pu、Qi for k in range(K): P[u][k] = P[u][k] - alpha * (2 * e_ui * Q[k][i] + 2 * lamda * P[u][k]) Q[k][i] = Q[k][i] - alpha * (2 * e_ui * P[u][k] + 2 * lamda * Q[k][i]) # u,i 遍历完成，所有的特征向量更新完成，可以得到 P、Q，可以计算预测评分矩阵 predR = np.dot(P, Q) # 计算当前损失函数（所有的预测误差平方后求和） cost = 0 for u in range(M): for i in range(N): # 对于每一个大于 0 的评分，求出预测评分误差后，将所有的预测误差平方后求和 if R[u][i] > 0: cost += (np.dot(P[u,:], Q[:,i]) - R[u][i]) ** 2 # 加上正则化项 for k in range(K): cost += lamda * (P[u][k] ** 2 + Q[k][i] ** 2) if cost < 0.0001: # 当前损失函数小于给定的值，退出迭代 break return P, Q.T, cost
3.测试
P, Q, cost = LMF_grad_desc(R, K, max_iter, alpha, lamda)print(P)print(Q)print(cost)predR = P.dot(Q.T)print(R)predR
当 K = 2 时，输出结果如下：
[[1.44372596 1.29573962] [1.82185633 0.0158696 ] [1.5331521 0.16327061] [0.31364667 1.9008297 ] [1.03622742 2.03603634] [1.34107967 0.93406796]][[ 0.4501051 2.55477489] [ 1.18869845 1.20910294] [ 1.54255106 -0.23514326] [ 2.33556583 1.21026575] [ 0.43753164 0.34555928]]1.0432768290554293[[4 0 2 0 1] [0 2 3 0 0] [1 0 2 4 0] [5 0 0 3 1] [0 0 1 5 1] [0 3 2 4 1]]array([[3.96015147, 3.2828374 , 1.92233657, 4.9401063 , 1.07943065], [0.86057008, 2.18482578, 2.80657478, 4.27427181, 0.80260368], [1.10719924, 2.0198665 , 2.32657341, 3.77837848, 0.72722223], [4.99736596, 2.6711301 , 0.03684871, 3.03305153, 0.79407969], [5.66802576, 3.69353946, 1.11967348, 4.8843224 , 1.15695354], [2.98996017, 2.72352365, 1.84904408, 4.2626503 , 0.90954065]])
当 K = 5 时，输出结果如下：
[[ 0.77991893 0.95803701 0.75945903 0.74581653 0.58070622] [ 1.51777367 0.66949331 0.89818609 0.23566984 0.56583223] [ 0.03567022 0.58391558 1.42477223 0.87262652 -0.52553017] [ 1.24101793 0.86257736 0.73772417 0.18181617 0.97014545] [ 0.58789616 0.53522492 0.48830352 1.80622908 0.81202167] [ 1.08640318 0.87660384 0.68935314 0.84506882 0.92284071]][[ 1.64469428 1.10535565 0.56686066 0.38656745 1.56519511] [ 0.61680687 0.57188343 0.49729111 0.9623455 0.43969708] [ 0.99260822 0.6007452 1.14768173 -0.16998497 -0.14094479] [ 0.47070988 0.85347655 1.43546859 1.8185161 0.29759968] [ 0.07923314 0.49412497 0.53285806 0.23753882 -0.05146021]]0.7478305665280703[[4 0 2 0 1] [0 2 3 0 0] [1 0 2 4 0] [5 0 0 3 1] [0 0 1 5 1] [0 3 2 4 1]]array([[3.9694342 , 2.37968507, 2.01268221, 3.8040546 , 1.08714641], [4.72218838, 2.2412959 , 2.81976984, 3.17210672, 0.95653992], [1.02652007, 1.67315396, 1.94711343, 3.99085212, 1.28488146], [5.0014878 , 2.22716585, 2.42906339, 2.99867943, 0.91091753], [3.80452512, 3.00679363, 1.04401937, 4.96078887, 0.95850804], [4.91762916, 2.73324389, 2.1224277 , 4.06049468, 1.03980543]])
柚子快报邀请码778899分享：07
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