Complex_Network_Analysis/链路预测_数据集划分.ipynb

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    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#随机抽样\" data-toc-modified-id=\"随机抽样-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>随机抽样</a></span><ul class=\"toc-item\"><li><span><a href=\"#代码\" data-toc-modified-id=\"代码-1.1\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>代码</a></span></li><li><span><a href=\"#测试\" data-toc-modified-id=\"测试-1.2\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>测试</a></span></li></ul></li><li><span><a href=\"#逐项遍历\" data-toc-modified-id=\"逐项遍历-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>逐项遍历</a></span></li><li><span><a href=\"#K-fold-交叉检验\" data-toc-modified-id=\"K-fold-交叉检验-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>K-fold 交叉检验</a></span></li><li><span><a href=\"#滚雪球抽样\" data-toc-modified-id=\"滚雪球抽样-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>滚雪球抽样</a></span></li><li><span><a href=\"#熟识者抽样\" data-toc-modified-id=\"熟识者抽样-5\"><span class=\"toc-item-num\">5&nbsp;&nbsp;</span>熟识者抽样</a></span></li><li><span><a href=\"#随机游走采样\" data-toc-modified-id=\"随机游走采样-6\"><span class=\"toc-item-num\">6&nbsp;&nbsp;</span>随机游走采样</a></span></li><li><span><a href=\"#基于路径抽样\" data-toc-modified-id=\"基于路径抽样-7\"><span class=\"toc-item-num\">7&nbsp;&nbsp;</span>基于路径抽样</a></span></li></ul></div>"
   ]
  },
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   "source": [
    "* 为了测试算法的性能， 需要对数据集进行划分\n",
    "\n",
    "\n",
    "\n",
    "* 划分方法的不同，算法的表现也不同\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 随机抽样\n",
    "\n",
    "*  最常用的方法\n",
    "\n",
    "* 含有 M 条边， 假设划分的比例为 p, M 条 已知边中随机选择 pM 条边构成测试集， 保证每条边被选进测试集的概率相同。\n",
    "\n",
    "* 有时会有一些限制条件： 抽样之后网络的连通性\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 代码\n",
    "\n",
    "* 参照 《链路预测》 书完成\n",
    "\n",
    "* 原书有较为完整 Matlab 代码\n",
    "\n"
   ]
  },
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   "cell_type": "code",
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     "start_time": "2019-10-30T02:06:45.446015Z"
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   "outputs": [],
   "source": [
    "from scipy import sparse\n",
    "import networkx as nx\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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     "end_time": "2019-10-30T01:48:10.597034Z",
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   "source": [
    "def spones(array):\n",
    "    \"\"\"\n",
    "    将矩阵中的非零元素全部替换为 1 \n",
    "    \"\"\"\n",
    "    sparse_array = sparse.csr_matrix(array)  # 转换为稀疏矩阵\n",
    "    sparse_array.data.fill(1)  # 稀疏矩阵全部替换为 1\n",
    "    array = sparse_array.toarray()  # 返回密集矩阵\n",
    "\n",
    "    return array\n",
    "\n",
    "\n",
    "def DivideNet(MatrixAdajacency, ratioTrain):\n",
    "    \"\"\"\n",
    "    划分训练集和测试集\n",
    "    \n",
    "    保证网络训练集连通\n",
    "    \"\"\"\n",
    "\n",
    "    # 测试集的连边数目\n",
    "    num_testlinks = int(\n",
    "        (1 - ratioTrain) * np.count_nonzero(MatrixAdajacency) / 2)\n",
    "    # 将邻接矩阵中所有的边找出来 存储到 linklist 中\n",
    "    linklist = [list(i) for i in np.argwhere(np.triu(MatrixAdajacency))]\n",
    "    # 为每条边都设置标志位 ， 判断是否能够删除\n",
    "    MatrixAdajacency_test = np.zeros(shape=(np.shape(MatrixAdajacency)[0],\n",
    "                                            np.shape(MatrixAdajacency)[1]))\n",
    "\n",
    "    while (np.count_nonzero(MatrixAdajacency_test) < num_testlinks):\n",
    "\n",
    "        ### 随机选择一条边\n",
    "        link_index = int(np.random.rand(1) * len(linklist))\n",
    "        uid1 = linklist[link_index][0]  # 边两端的节点 1\n",
    "        uid2 = linklist[link_index][1]\n",
    "\n",
    "        ### 判断所选边两端节点 uid1 和 uid2 是否可达， 若可达则放入测试集， 否则重新选边\n",
    "        # 将这条边从网络中挖去，\n",
    "        MatrixAdajacency[uid1, uid2] = 0\n",
    "        MatrixAdajacency[uid2, uid1] = 0\n",
    "\n",
    "        tempvector = MatrixAdajacency[uid1]  # 取出 uid1  一步可达的点 构成一维向量\n",
    "        sign = 0  # 标记此边是否可以被移除，  sign = 0 表示不可， sign = 1 表示可以\n",
    "        uid1TOuid2 = np.dot(tempvector,\n",
    "                            MatrixAdajacency) + tempvector  # 表示 uid1 2步内可达的点\n",
    "\n",
    "        if uid1TOuid2[0, uid2] > 0:\n",
    "            sign = 1  # 两步即可到达\n",
    "        else:\n",
    "\n",
    "            count = 1\n",
    "            while (len((spones(uid1TOuid2) - tempvector).nonzero()[0]) != 0):\n",
    "                # 直到可达的点到达稳定状态， 仍然不能到达 uid2， 此边就不能删除\n",
    "                tempvector = spones(uid1TOuid2)\n",
    "                uid1TOuid2 = np.dot(\n",
    "                    tempvector, MatrixAdajacency) + tempvector  # 表示 K 步 内可达的点\n",
    "                count += 1\n",
    "                if uid1TOuid2[0, uid2] > 0:\n",
    "                    sign = 1  # 某步内可以到达\n",
    "                    break\n",
    "\n",
    "                if count >= MatrixAdajacency.shape[0]:\n",
    "                    print(\"不可达\" + str([uid1, uid2]))\n",
    "                    sign = 0\n",
    "\n",
    "        ### 如果边可以删除， 将其放入测试集中， 并从 link 集中删除\n",
    "        if sign == 1:\n",
    "            linklist.pop(link_index)\n",
    "            MatrixAdajacency_test[uid1, uid2] = 1\n",
    "\n",
    "        ### 如果不可以删除， 恢复原始矩阵， 也从 link 集中删除\n",
    "        else:\n",
    "            linklist.pop(link_index)\n",
    "            MatrixAdajacency[uid1, uid2] = 1\n",
    "            MatrixAdajacency[uid2, uid1] = 1\n",
    "\n",
    "    MatrixAdajacency_Train = MatrixAdajacency\n",
    "    MatrixAdajacency_Test = MatrixAdajacency_test + MatrixAdajacency_test.T\n",
    "\n",
    "    print('    训练集计划边数：' +\n",
    "          str(np.count_nonzero(MatrixAdajacency) - num_testlinks))\n",
    "    print('    训练集实际边数：' + str(np.count_nonzero(MatrixAdajacency_Train)))\n",
    "    print('    测试集计划边数：' + str(num_testlinks))\n",
    "    print('    测试集实际边数：' + str(np.count_nonzero(MatrixAdajacency_Test)))\n",
    "\n",
    "    return MatrixAdajacency_Train, MatrixAdajacency_Test\n",
    "\n",
    "\n",
    "def check_symmetric(a, tol=1e-8):\n",
    "    \"\"\"\n",
    "    检查是否是 对称矩阵\n",
    "    \"\"\"\n",
    "    return np.allclose(a, a.T, atol=tol)"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-------\n",
    "\n",
    "##  测试\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-30T01:50:33.094625Z",
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   "outputs": [],
   "source": [
    "edge_lst = []\n",
    "with open(\"lit-bm-13.txt\",\"r\") as file_txt: # 蛋白质相互作用数据集\n",
    "    for i, line in enumerate(file_txt.readlines()):\n",
    "        edge_tpl =  str(line.split()[0]), str(line.split()[1]),{'weight': 1}\n",
    "        edge_lst.append(edge_tpl)\n",
    "\n",
    "F = nx.from_edgelist(edge_lst)\n",
    "df = nx.to_pandas_adjacency(F)\n",
    "data = np.matrix(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-30T01:51:53.336804Z",
     "start_time": "2019-10-30T01:51:15.749890Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    训练集邻接矩阵：(3391, 3391)\n",
      "    训练集计划边数：7963\n",
      "    训练集实际边数：8427\n",
      "    测试集邻接矩阵：(3391, 3391)\n",
      "    测试集计划边数：464\n",
      "    测试集实际边数：433.5\n"
     ]
    }
   ],
   "source": [
    "train , test = DivideNet(data.copy(), 0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-30T01:54:38.670800Z",
     "start_time": "2019-10-30T01:54:38.330680Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "check_symmetric(train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-30T02:03:11.024981Z",
     "start_time": "2019-10-30T02:03:11.011926Z"
    }
   },
   "outputs": [],
   "source": [
    "def Cn(MatrixAdjacency_Train):\n",
    "    \"\"\"\n",
    "    共同邻居算法\n",
    "    \"\"\"\n",
    "    Matrix_similarity = np.dot(MatrixAdjacency_Train,MatrixAdjacency_Train)\n",
    "    return Matrix_similarity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-30T02:03:55.569518Z",
     "start_time": "2019-10-30T02:03:54.633235Z"
    }
   },
   "outputs": [],
   "source": [
    "Matrix_similarity = Cn(train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-30T02:04:05.811579Z",
     "start_time": "2019-10-30T02:04:05.804025Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 2.,  0.,  1., ...,  0.,  0.,  0.],\n",
       "        [ 0.,  1.,  1., ...,  0.,  0.,  0.],\n",
       "        [ 1.,  1., 18., ...,  0.,  0.,  0.],\n",
       "        ...,\n",
       "        [ 0.,  0.,  0., ...,  1.,  0.,  0.],\n",
       "        [ 0.,  0.,  0., ...,  0.,  1.,  0.],\n",
       "        [ 0.,  0.,  0., ...,  0.,  0.,  1.]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Matrix_similarity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-30T02:08:06.332461Z",
     "start_time": "2019-10-30T02:08:06.268813Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "43303"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.count_nonzero(Matrix_similarity)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-30T02:07:05.139027Z",
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    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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pmT8a9n5XWtkfAdb3ra/rxpaFqjrSfT8K/CO9B9+3j52e6b4f7aYvp/sy34xLmr2qvt39g/lf4MP86CX3ssmb5CR6pfnJqvqHbnhZH+eZMq+EY93l/C5wG/Byeqc6Vs+w/6eyddufDTy8DDJv6U6jVVX9APhbTsBxXmllvx/Y1F1tP5neRZZdS5wJgCQ/meTUY8vA64F76OU7dqX8UuCfuuVdwBu7q+3nAY/1vcQftflm3AO8Psnp3cv613djIzHt2sav0DvOx/Ju6951sRHYBHyZET9uuvPAHwXuq6r39W1atsd5tszL+VgnGUtyWrf8E8Dr6F1ruA24uJs2/TgfO/4XA5/vXmHNdl9Glfnf+54EhN41hv7jPJzHxkKvKi/VF72r01+jd27uHUudpy/X2fSu6N8JHDiWjd45wc8BXwf+FTijfnRV/truftwNjI8o5430Xo7/kN55vssWkhH4LXoXsiaBN4847ye6PHd1/xjO7Jv/ji7v/cD5S/G4AV5J7xTNXcAd3dcFy/w4z5Z52R5r4MXAV7ts9wBXd+Nn0yvrSeDTwCnd+DO79clu+9lz3ZcRZv58d5zvAW7gR+/YGdpjw1+XIEkNWGmncSRJC2DZS1IDLHtJaoBlL0kNsOwlqQGWvSQ1wLKXpAb8H5TjNtSxeAxkAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(10):\n",
    "    plt.figure(i)\n",
    "    plt.scatter([i for i in range(3391)],np.array(Matrix_similarity[:,i* 200]).ravel())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "\n",
    "-----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-30T02:27:58.608878Z",
     "start_time": "2019-10-30T02:27:58.602199Z"
    }
   },
   "source": [
    "# 逐项遍历\n",
    "\n",
    "> 类似于机器学习中的 留一取样\n",
    "\n",
    "* 规模较小的网络中， 更加精确的办法是 逐项遍历\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "*  每次从网络中选取一条边作为测试边， 其余的边构成训练集。 一条测试边进行测试得到一个预测精度， 遍历网络中的所有 M 条边。得到一个预测精度的平均值\n",
    "\n",
    "\n",
    "\n",
    "* 计算复杂度特别高， 只适合小网络\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# K-fold 交叉检验\n",
    "\n",
    "* 将样本集随机分成 k 份， 选择其中的一份作为测试集，其余的 k-1 作为训练集\n",
    "\n",
    "\n",
    "\n",
    "* 试验重复 k 次， 计算精度的平均值\n",
    "\n",
    "\n",
    "\n",
    "* 保证了每条边都能作为测试边， 随机采样的做不到\n",
    "\n",
    "\n",
    "\n",
    "* 常用 10折检验\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 滚雪球抽样\n",
    "\n",
    "> 类似于 广度优先搜索\n",
    "\n",
    "\n",
    "* 初始的时候，随机选择一个或者一组节点构成样本集， 之后遍历样本集的每一个节点的所有邻居节点\n",
    "\n",
    "\n",
    "\n",
    "* 重复上述过程，直到样本集中的样本数量达到要求\n",
    "\n",
    "\n",
    "\n",
    "* 这种抽样的方法得到的是节点\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 熟识者抽样\n",
    "\n",
    "\n",
    "* 倾向于把 度小的节点之间的连边放入到训练集，度大的节点之间的连边放入到测试集\n",
    "\n",
    "\n",
    "* 上述倾向也可以人为调整反过来"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 随机游走采样\n",
    "\n",
    "\n",
    "> 通过一个粒子在网络上随机游走进行抽样\n",
    "\n",
    "* 1. 随机选择一个节点， 并放置一个粒子\n",
    "\n",
    "\n",
    "\n",
    "* 2. 粒子随机游走到当前节点的一个邻居节点， 粒子经过的边放入到训练集中\n",
    "\n",
    "\n",
    "\n",
    "* 3. 重复2 ， 直到训练集中的边的数目满足要求\n",
    "\n",
    "\n",
    "**保证训练集的连通性， 但是可能会丢失一些节点**\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 基于路径抽样\n",
    "\n",
    "\n",
    "> 一般而言， 一条链路上如果包含的信息越多， 挑选出来的概率越大\n",
    "\n",
    "\n",
    "* 每一步随机选择两个节点， 一个视为信息报传输的起点， 一个视为终点。\n",
    "\n",
    "\n",
    "\n",
    "* 信息包选择一条最短路径从起点到终点\n",
    "\n",
    "\n",
    "\n",
    "* 每条边被信息包经过一次分数加1 \n",
    "\n",
    "\n",
    "\n",
    "* 分数值大于一定的阈值的边可以被加入到训练集\n",
    "\n",
    "\n",
    "\n",
    "**最短路径上出现次数最多的边被选入到训练集之中**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "language": "python",
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    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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