MovieLens/3-LFM_Model.ipynb · weili_yzzcq/UndergraduateGraduationProject

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3-LFM_Model.ipynb 23.34 KB

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 模块和包都是在逐步的探索中所需要的，全部汇总到这里，\n",
    "#    并不是一开始就知道了 ^_^ ^_^ ^_^ \n",
    "# 不熟悉的模块和包，强烈建议查看官方文档说明以及例子\n",
    "# 1、导入模块和包\n",
    "import pandas as pd    # 加载并处理csv文件\n",
    "import datetime        # 利用datetime处理时间戳\n",
    "# cPickle 数据以二进制进行高效的储存到文件\n",
    "import _pickle as cPickle \n",
    "# defaultdict 设置稀疏矩阵的 NULL 位置的默认值\n",
    "from collections import defaultdict \n",
    "# 利用scipy sparse 构建稀疏矩阵\n",
    "import scipy.sparse as ss     \n",
    "import scipy.io as sio    # 利用scipy储存评分矩阵\n",
    "# 利用numpy创建指定长度或形状的矩阵以及矩阵运算\n",
    "import numpy as np \n",
    "# numpy.random中的randn函数生成正态分布的随机数据\n",
    "from numpy.random import random    \n",
    "import time    # 计算训练时迭代的时间\n",
    "import json    # 将模型参数保存和加载 json文件\n",
    "import scipy    # 将储存加载的稀疏评分矩阵转换为numpy矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 4.2.1、LMF模型\n",
    "# ############################################\n",
    "#\n",
    "# 核心算法实现\n",
    "#\n",
    "# @输入参数\n",
    "#     R —— M*N 评分矩阵\n",
    "#     k —— 隐向量的维度\n",
    "#     theta —— 迭代次数\n",
    "#     alpha —— 步长（学习率）\n",
    "#     lamda —— 正则化系数\n",
    "#\n",
    "# @输出参数\n",
    "#     分解之后的 P，Q\n",
    "#     P：初始化用户特征矩阵 M*K\n",
    "#     Q：初始化物品特征矩阵 N*K\n",
    "#\n",
    "# ############################################\n",
    "# 设定模型参数\n",
    "# 18 个电影类型 10、12、14、16、18、20、24、36\n",
    "K = 16\n",
    "# 迭代次数：20、40、60、80、100\n",
    "theta = 80\n",
    "alpha = 0.005\n",
    "lamda = 0.15\n",
    "# 核心算法\n",
    "def LFM_grad_desc( R, K, theta, alpha, lamda ):\n",
    "    # 基本维度参数定义\n",
    "    M = R.shape[0]\n",
    "    N = R.shape[1]\n",
    "    \n",
    "    # P,Q初始值，随机生成\n",
    "    P = np.random.rand(M, K)\n",
    "    Q = np.random.rand(N, K)\n",
    "    Q = Q.T\n",
    "    \n",
    "    # 第一次迭代时间开始\n",
    "    time_start = time.time()\n",
    "    print(\"开始进行{}个step的训练\".format(theta))\n",
    "    each_time_start = time_start\n",
    "        \n",
    "    # 开始迭代\n",
    "    for step in range(theta):\n",
    "        print('The {}-th  step is running'.format(step))\n",
    "        # 对所有的用户u、物品i做遍历，\n",
    "        # 对应的特征向量Pu、Qi梯度下降\n",
    "        for u in range(M):\n",
    "            for i in range(N):\n",
    "                # 对于每一个大于0的评分，\n",
    "                # 求出预测评分误差\n",
    "                if R[u, i] > 0:\n",
    "                    eui = np.dot( P[u,:], Q[:,i] ) - R[u, i]\n",
    "                    \n",
    "                    # 按照梯度下降算法更新当前的Pu、Qi\n",
    "                    for k in range(K):\n",
    "                        P[u][k] = P[u][k] - alpha * ( eui * Q[k][i] + lamda * P[u][k] )\n",
    "                        Q[k][i] = Q[k][i] - alpha * ( eui * P[u][k] + lamda * Q[k][i] )\n",
    "        \n",
    "        # u、i遍历完成，所有特征向量更新完成，\n",
    "        # 可以得到P、Q，可以计算预测评分矩阵\n",
    "        predR = np.dot( P, Q )\n",
    "        \n",
    "        # 计算当前损失函数\n",
    "        cost = 0\n",
    "        for u in range(M):\n",
    "            for i in range(N):\n",
    "                if R[u, i] > 0:\n",
    "                    cost += ( np.dot( P[u,:], Q[:,i] ) - R[u, i] ) ** 2\n",
    "                    # 加上正则化项\n",
    "                    for k in range(K):\n",
    "                        cost += lamda * ( P[u][k] ** 2 + Q[k][i] ** 2 )\n",
    "                        each_cost = np.sqrt(cost / K)\n",
    "        \n",
    "        # 学习率递减 / learning rate improve 3th\n",
    "        alpha = alpha * 0.93\n",
    "        # 每次迭代时间结束\n",
    "        each_time_tick = time.time()\n",
    "        # 每次迭代消耗的时间\n",
    "        each_cost_time = each_time_tick - each_time_start\n",
    "        # 更新计算每次迭代的时间\n",
    "        each_time_start = each_time_tick\n",
    "        print(\"完成第{}个step的训练, each_cost={}, 耗时{:.4f}秒\".format( step + 1, cost, each_cost_time))\n",
    "        \n",
    "        if cost < 0.0001:\n",
    "            break\n",
    "    # 计算训练数据集消耗的总时间\n",
    "    time_end = time.time()\n",
    "    total_cost_time = time_end - time_start\n",
    "    print(\"结束了{}个step的训练，总耗时{:.4f}秒\".format(theta, total_cost_time))    \n",
    "    return P, Q.T, cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.matrix"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 加载评分矩阵\n",
    "data_path = \"./../dataset/ml-25m/\"\n",
    "user_item_score = sio.mmread(data_path + \"user_item_score\")\n",
    "# todense() 转换为矩阵 numpy \n",
    "R = scipy.sparse.csc_matrix.todense(user_item_score)\n",
    "type(R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "开始进行100个step的训练\n",
      "The 0-th  step is running\n",
      "完成第1个step的训练, each_cost=7184.14612003106, 耗时20.3322秒\n",
      "The 1-th  step is running\n",
      "完成第2个step的训练, each_cost=6695.706017622515, 耗时20.1422秒\n",
      "The 2-th  step is running\n",
      "完成第3个step的训练, each_cost=6308.151316812769, 耗时20.2222秒\n",
      "The 3-th  step is running\n",
      "完成第4个step的训练, each_cost=5994.669948825578, 耗时20.2682秒\n",
      "The 4-th  step is running\n",
      "完成第5个step的训练, each_cost=5737.061884935879, 耗时20.4552秒\n",
      "The 5-th  step is running\n",
      "完成第6个step的训练, each_cost=5522.54060775252, 耗时20.1332秒\n",
      "The 6-th  step is running\n",
      "完成第7个step的训练, each_cost=5341.867813744572, 耗时20.1732秒\n",
      "The 7-th  step is running\n",
      "完成第8个step的训练, each_cost=5188.210800808784, 耗时20.2842秒\n",
      "The 8-th  step is running\n",
      "完成第9个step的训练, each_cost=5056.414306819959, 耗时20.1532秒\n",
      "The 9-th  step is running\n",
      "完成第10个step的训练, each_cost=4942.521010529235, 耗时20.2352秒\n",
      "The 10-th  step is running\n",
      "完成第11个step的训练, each_cost=4843.44689524589, 耗时20.1842秒\n",
      "The 11-th  step is running\n",
      "完成第12个step的训练, each_cost=4756.756146745573, 耗时20.1402秒\n",
      "The 12-th  step is running\n",
      "完成第13个step的训练, each_cost=4680.50178156784, 耗时20.1692秒\n",
      "The 13-th  step is running\n",
      "完成第14个step的训练, each_cost=4613.110719698109, 耗时20.2102秒\n",
      "The 14-th  step is running\n",
      "完成第15个step的训练, each_cost=4553.299540870965, 耗时20.1762秒\n",
      "The 15-th  step is running\n",
      "完成第16个step的训练, each_cost=4500.011820099368, 耗时20.0301秒\n",
      "The 16-th  step is running\n",
      "完成第17个step的训练, each_cost=4452.3708933942535, 耗时20.0931秒\n",
      "The 17-th  step is running\n",
      "完成第18个step的训练, each_cost=4409.643823278805, 耗时20.0371秒\n",
      "The 18-th  step is running\n",
      "完成第19个step的训练, each_cost=4371.213604775869, 耗时19.9981秒\n",
      "The 19-th  step is running\n",
      "完成第20个step的训练, each_cost=4336.557510163626, 耗时20.2792秒\n",
      "The 20-th  step is running\n",
      "完成第21个step的训练, each_cost=4305.2300591306785, 耗时20.0861秒\n",
      "The 21-th  step is running\n",
      "完成第22个step的训练, each_cost=4276.849510727165, 耗时20.2592秒\n",
      "The 22-th  step is running\n",
      "完成第23个step的训练, each_cost=4251.087062896268, 耗时20.1442秒\n",
      "The 23-th  step is running\n",
      "完成第24个step的训练, each_cost=4227.658152378136, 耗时19.9751秒\n",
      "The 24-th  step is running\n",
      "完成第25个step的训练, each_cost=4206.315397610044, 耗时20.1872秒\n",
      "The 25-th  step is running\n",
      "完成第26个step的训练, each_cost=4186.842836900698, 耗时20.2592秒\n",
      "The 26-th  step is running\n",
      "完成第27个step的训练, each_cost=4169.051195217331, 耗时20.1212秒\n",
      "The 27-th  step is running\n",
      "完成第28个step的训练, each_cost=4152.773973430475, 耗时20.2552秒\n",
      "The 28-th  step is running\n",
      "完成第29个step的训练, each_cost=4137.864199421404, 耗时20.2362秒\n",
      "The 29-th  step is running\n",
      "完成第30个step的训练, each_cost=4124.191715055672, 耗时20.1882秒\n",
      "The 30-th  step is running\n",
      "完成第31个step的训练, each_cost=4111.640899502374, 耗时20.2672秒\n",
      "The 31-th  step is running\n",
      "完成第32个step的训练, each_cost=4100.108749793947, 耗时20.2312秒\n",
      "The 32-th  step is running\n",
      "完成第33个step的训练, each_cost=4089.503255369964, 耗时20.1382秒\n",
      "The 33-th  step is running\n",
      "完成第34个step的训练, each_cost=4079.7420157346173, 耗时20.2942秒\n",
      "The 34-th  step is running\n",
      "完成第35个step的训练, each_cost=4070.7510600972223, 耗时20.0161秒\n",
      "The 35-th  step is running\n",
      "完成第36个step的训练, each_cost=4062.4638355714046, 耗时20.1642秒\n",
      "The 36-th  step is running\n",
      "完成第37个step的训练, each_cost=4054.8203366367793, 耗时20.3982秒\n",
      "The 37-th  step is running\n",
      "完成第38个step的训练, each_cost=4047.76635346846, 耗时20.0691秒\n",
      "The 38-th  step is running\n",
      "完成第39个step的训练, each_cost=4041.2528206828383, 耗时20.0051秒\n",
      "The 39-th  step is running\n",
      "完成第40个step的训练, each_cost=4035.235251225995, 耗时20.1902秒\n",
      "The 40-th  step is running\n",
      "完成第41个step的训练, each_cost=4029.673242718526, 耗时20.0821秒\n",
      "The 41-th  step is running\n",
      "完成第42个step的训练, each_cost=4024.5300456719806, 耗时20.3022秒\n",
      "The 42-th  step is running\n",
      "完成第43个step的训练, each_cost=4019.7721847165067, 耗时20.0191秒\n",
      "The 43-th  step is running\n",
      "完成第44个step的训练, each_cost=4015.3691253955744, 耗时20.0331秒\n",
      "The 44-th  step is running\n",
      "完成第45个step的训练, each_cost=4011.2929802492527, 耗时20.0411秒\n",
      "The 45-th  step is running\n",
      "完成第46个step的训练, each_cost=4007.5182488779724, 耗时20.0421秒\n",
      "The 46-th  step is running\n",
      "完成第47个step的训练, each_cost=4004.021587480309, 耗时20.1412秒\n",
      "The 47-th  step is running\n",
      "完成第48个step的训练, each_cost=4000.7816040284333, 耗时20.1122秒\n",
      "The 48-th  step is running\n",
      "完成第49个step的训练, each_cost=3997.7786758073457, 耗时20.2952秒\n",
      "The 49-th  step is running\n",
      "完成第50个step的训练, each_cost=3994.994786512198, 耗时20.1662秒\n",
      "The 50-th  step is running\n",
      "完成第51个step的训练, each_cost=3992.4133804966477, 耗时20.0531秒\n",
      "The 51-th  step is running\n",
      "完成第52个step的训练, each_cost=3990.0192320972783, 耗时20.2692秒\n",
      "The 52-th  step is running\n",
      "完成第53个step的训练, each_cost=3987.798328244492, 耗时20.0541秒\n",
      "The 53-th  step is running\n",
      "完成第54个step的训练, each_cost=3985.737762809731, 耗时19.9531秒\n",
      "The 54-th  step is running\n",
      "完成第55个step的训练, each_cost=3983.825641343104, 耗时20.2512秒\n",
      "The 55-th  step is running\n",
      "完成第56个step的训练, each_cost=3982.0509950320325, 耗时20.0951秒\n",
      "The 56-th  step is running\n",
      "完成第57个step的训练, each_cost=3980.4037028597595, 耗时20.1552秒\n",
      "The 57-th  step is running\n",
      "完成第58个step的训练, each_cost=3978.8744210708855, 耗时20.0381秒\n",
      "The 58-th  step is running\n",
      "完成第59个step的训练, each_cost=3977.454519163193, 耗时19.9701秒\n",
      "The 59-th  step is running\n",
      "完成第60个step的训练, each_cost=3976.136021717613, 耗时20.7072秒\n",
      "The 60-th  step is running\n",
      "完成第61个step的训练, each_cost=3974.911555462766, 耗时21.1342秒\n",
      "The 61-th  step is running\n",
      "完成第62个step的训练, each_cost=3973.774301040534, 耗时21.4352秒\n",
      "The 62-th  step is running\n",
      "完成第63个step的训练, each_cost=3972.717949001522, 耗时21.9913秒\n",
      "The 63-th  step is running\n",
      "完成第64个step的训练, each_cost=3971.736659612095, 耗时20.4042秒\n",
      "The 64-th  step is running\n",
      "完成第65个step的训练, each_cost=3970.8250261033218, 耗时20.3252秒\n",
      "The 65-th  step is running\n",
      "完成第66个step的训练, each_cost=3969.978041031154, 耗时22.4593秒\n",
      "The 66-th  step is running\n",
      "完成第67个step的训练, each_cost=3969.191065454544, 耗时21.2312秒\n",
      "The 67-th  step is running\n",
      "完成第68个step的训练, each_cost=3968.4598006692486, 耗时22.0943秒\n",
      "The 68-th  step is running\n",
      "完成第69个step的训练, each_cost=3967.780262262157, 耗时23.7684秒\n",
      "The 69-th  step is running\n",
      "完成第70个step的训练, each_cost=3967.148756275817, 耗时23.1733秒\n",
      "The 70-th  step is running\n",
      "完成第71个step的训练, each_cost=3966.5618572954418, 耗时21.5352秒\n",
      "The 71-th  step is running\n",
      "完成第72个step的训练, each_cost=3966.016388286782, 耗时21.7832秒\n",
      "The 72-th  step is running\n",
      "完成第73个step的训练, each_cost=3965.5094020338347, 耗时25.1984秒\n",
      "The 73-th  step is running\n",
      "完成第74个step的训练, each_cost=3965.038164036912, 耗时20.8662秒\n",
      "The 74-th  step is running\n",
      "完成第75个step的训练, each_cost=3964.600136747566, 耗时20.7082秒\n",
      "The 75-th  step is running\n",
      "完成第76个step的训练, each_cost=3964.1929650267293, 耗时20.5312秒\n",
      "The 76-th  step is running\n",
      "完成第77个step的训练, each_cost=3963.8144627243587, 耗时21.4362秒\n",
      "The 77-th  step is running\n",
      "完成第78个step的训练, each_cost=3963.4626002876507, 耗时20.4922秒\n",
      "The 78-th  step is running\n",
      "完成第79个step的训练, each_cost=3963.1354933138455, 耗时21.5272秒\n",
      "The 79-th  step is running\n",
      "完成第80个step的训练, each_cost=3962.8313919701122, 耗时21.0362秒\n",
      "The 80-th  step is running\n",
      "完成第81个step的训练, each_cost=3962.5486712119236, 耗时21.3222秒\n",
      "The 81-th  step is running\n",
      "完成第82个step的训练, each_cost=3962.2858217349108, 耗时21.8132秒\n",
      "The 82-th  step is running\n",
      "完成第83个step的训练, each_cost=3962.041441603485, 耗时20.5022秒\n",
      "The 83-th  step is running\n",
      "完成第84个step的训练, each_cost=3961.814228501214, 耗时20.3642秒\n",
      "The 84-th  step is running\n",
      "完成第85个step的训练, each_cost=3961.6029725564276, 耗时20.3362秒\n",
      "The 85-th  step is running\n",
      "完成第86个step的训练, each_cost=3961.406549696865, 耗时20.3242秒\n",
      "The 86-th  step is running\n",
      "完成第87个step的训练, each_cost=3961.2239154932086, 耗时20.6962秒\n",
      "The 87-th  step is running\n",
      "完成第88个step的训练, each_cost=3961.0540994543785, 耗时21.6992秒\n",
      "The 88-th  step is running\n",
      "完成第89个step的训练, each_cost=3960.8961997392776, 耗时22.3333秒\n",
      "The 89-th  step is running\n",
      "完成第90个step的训练, each_cost=3960.7493782546003, 耗时21.1702秒\n",
      "The 90-th  step is running\n",
      "完成第91个step的训练, each_cost=3960.612856108184, 耗时21.6382秒\n",
      "The 91-th  step is running\n",
      "完成第92个step的训练, each_cost=3960.4859093930313, 耗时21.8322秒\n",
      "The 92-th  step is running\n",
      "完成第93个step的训练, each_cost=3960.367865275005, 耗时21.5122秒\n",
      "The 93-th  step is running\n",
      "完成第94个step的训练, each_cost=3960.258098364243, 耗时22.4533秒\n",
      "The 94-th  step is running\n",
      "完成第95个step的训练, each_cost=3960.1560273468167, 耗时22.6403秒\n",
      "The 95-th  step is running\n",
      "完成第96个step的训练, each_cost=3960.0611118591023, 耗时23.5823秒\n",
      "The 96-th  step is running\n",
      "完成第97个step的训练, each_cost=3959.972849586388, 耗时23.6164秒\n",
      "The 97-th  step is running\n",
      "完成第98个step的训练, each_cost=3959.8907735690022, 耗时23.6214秒\n",
      "The 98-th  step is running\n",
      "完成第99个step的训练, each_cost=3959.8144497015364, 耗时23.3513秒\n",
      "The 99-th  step is running\n",
      "完成第100个step的训练, each_cost=3959.7434744102243, 耗时22.9733秒\n",
      "结束了100个step的训练，总耗时2080.8960秒\n"
     ]
    }
   ],
   "source": [
    "# 开始训练 LFM 模型\n",
    "P, Q, ess = LFM_grad_desc( R, K, theta, alpha, lamda )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 通过训练的 P和 Q 计算出预测评分矩阵\n",
    "pred_R = np.dot( P, Q.T )\n",
    "# 将预测评分矩阵保存\n",
    "sio.mmwrite(data_path + \"pred_R\", pred_R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[3.5 0.  0.  ... 0.  0.  0. ]\n",
      " [0.  4.  0.  ... 0.  0.  0. ]\n",
      " [0.  0.  1.  ... 0.  0.  0. ]\n",
      " ...\n",
      " [0.  0.  0.  ... 0.  0.  0. ]\n",
      " [0.  0.  0.  ... 0.  0.  0. ]\n",
      " [0.  0.  0.  ... 0.  0.  0. ]]\n",
      "[[4.42265701 3.70424086 2.92530286 ... 3.28586296 3.66743726 3.31891823]\n",
      " [4.91853062 3.86737123 3.000895   ... 4.35648991 4.17886201 3.463823  ]\n",
      " [3.38731123 3.08068239 2.71844636 ... 3.45452348 3.02973188 3.00132094]\n",
      " ...\n",
      " [5.41812968 5.07058586 4.3197803  ... 4.66438458 4.63318126 3.63906152]\n",
      " [4.277156   2.99367351 2.93057628 ... 4.03656947 3.45455137 2.62244854]\n",
      " [4.77669697 3.37390768 3.54481507 ... 4.35588632 3.9031377  3.24295518]]\n"
     ]
    }
   ],
   "source": [
    "# 查看原始评分矩阵\n",
    "print(R)\n",
    "# 查看预测评分矩阵\n",
    "print(pred_R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.06593345  0.32186047  0.4976257  ... -0.09958345  0.1584439\n",
      "   0.6848624 ]\n",
      " [ 0.36620279  0.31416959  0.41308537 ...  0.66331463  0.98444888\n",
      "   0.28672297]\n",
      " [ 0.78441498  0.69788196  0.28960103 ...  0.50051075  0.58106854\n",
      "   0.47003226]\n",
      " ...\n",
      " [ 0.9332154   0.70923459  0.33642715 ...  0.93963462  0.46401874\n",
      "   0.96817776]\n",
      " [ 0.06704608  0.67819881  0.64192002 ...  0.66981962  0.52080464\n",
      "   0.81221157]\n",
      " [ 0.61845541  0.46915964  0.55543854 ...  0.47280961  0.95707288\n",
      "   0.1364307 ]]\n",
      "====================================================\n",
      "[[ 1.79483818e-01  4.74321878e-01  7.15267388e-01 ...  9.94582543e-01\n",
      "   6.72835420e-01  6.69857406e-01]\n",
      " [ 7.75868717e-01  5.20468549e-01  2.46878674e-01 ...  1.99141891e-01\n",
      "  -2.17662902e-04  5.55480437e-01]\n",
      " [ 8.38112305e-01  4.71472199e-01  7.13348754e-01 ...  7.16759635e-01\n",
      "   8.27744758e-03  1.50912311e-01]\n",
      " ...\n",
      " [ 6.13879168e-01  2.04580626e-01  2.17737030e-01 ...  8.83554850e-01\n",
      "   8.03421987e-01  4.04945353e-01]\n",
      " [ 4.09148213e-01  5.65906870e-01  5.99735544e-01 ...  4.57723593e-01\n",
      "   6.36497808e-01  7.06303908e-01]\n",
      " [ 7.85503549e-01  6.11208292e-01  6.75776174e-02 ...  2.75305690e-02\n",
      "   5.44494915e-02  1.32462090e-01]]\n"
     ]
    }
   ],
   "source": [
    "# 查看训练后的 P 和 Q 矩阵\n",
    "print(P)\n",
    "print(\"====================================================\")\n",
    "print(Q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [],
   "source": [
    "# LFM模型评测指标\n",
    "# RMSE 和 MAE\n",
    "def calc_evaluation(R, pred_R):\n",
    "    mae_sum = 0.0\n",
    "    rmse_sum = 0.0\n",
    "    # 基本维度参数定义\n",
    "    M = R.shape[0]\n",
    "    N = R.shape[1]\n",
    "    T = 0\n",
    "    \n",
    "    for user in range(M):\n",
    "        for item in range(N):\n",
    "            if R[user, item] > 0:\n",
    "                T += 1\n",
    "                ess = R[user, item] - pred_R[user, item]\n",
    "                mae_sum += abs(ess)\n",
    "                rmse_sum += ess**2\n",
    "    \n",
    "    # 计算总的 MAE 指标\n",
    "    MAE = mae_sum / T\n",
    "    # Root Mean Square Error RMSE\n",
    "    RMSE = np.sqrt(rmse_sum / T)\n",
    "    return MAE, RMSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the MAE of LFM: 0.5479792516762387\n",
      "the RMSE OF LFM: 0.7009523875427962\n"
     ]
    }
   ],
   "source": [
    "MAE, RMSE = calc_evaluation(R, pred_R)\n",
    "print(\"the MAE of LFM:\", MAE)\n",
    "print(\"the RMSE OF LFM:\", RMSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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 },
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