PCA_Manifold.ipynb

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   "source": [
    "# 数据降维\n",
    "\n",
    "在统计学和机器学习中，存在所谓“**维数的灾难**”（**the curse of dimensionality**），特别是对于高度非参数的模型，该问题更加严重。\n",
    "\n",
    "比如，如果我们考虑使用高阶多项式进行拟合：$$y_i=p\\left(x_i\\right)+u_i$$如果有$K$个解释变量，那么一阶多项式有$K+1$（包含常数项）个参数，而二阶多项式（包含交叉项）就有$C_K^2+K$个参数......随着多项式阶数的增加，未知参数的个数是指数级增加的，然而样本量是有限的，这就会导致模型的过拟合甚至完全拟合的情况。\n",
    "\n",
    "另一个例子是在匹配（matching）中，如果特征只有一维，那么匹配是非常容易的，然而当维度扩大到比较多维度时，一个样本的周围就很难找到距离近的能够匹配上的样本了。\n",
    "\n",
    "此外，很多不同类型的数据也会有同样的问题，比如图像数据、文本数据、语音数据等，都会存在数据维度太高的问题。比如，文本数据的特征提取最简单的方法是定义某个句子中是否存在某一个词，然而在每种语言中，词汇数量都非常多，如果我们考虑20000个中文词汇，那么每个句子会被翻译成一个20000维的问题，维数非常之高。\n",
    "\n",
    "不同的模型解决以上问题的方法有很多，比如在回归分析中使用正则化的方法等。也有一些其他的**降维**（**dimension reduction**）方法可以在模型训练之前预先完成，常见的方法包括主成分分析、流形学习等。我们这一节简要介绍以下降维的常用方法。"
   ]
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   "source": [
    "# 主成分分析\n",
    "\n",
    "主成分分析是最简单也是非常常用的数据降维方法。\n",
    "\n",
    "考虑一组$D$维数据，对于某一个样本$x_i\\in \\mathbb{R}^D$，我们希望找到一个低维的$m_i\\in\\mathbb{R}^d,d<D$在尽量不损失信息的条件下代表原始的$D$维数据，与此同时还可以将$m_i$通过某种计算方式还原$y_i\\in \\mathbb{R}^D$，由于该过程一定有信息损失，所有$y_i\\neq x_i$，不过我们可以最小化该损失。\n",
    "\n",
    "一般的，我们可以找到一个函数$g\\left(x\\right)$，以及一个函数$h\\left(m\\right)$，通过$m=g\\left(x\\right)$计算降维的结果，并使用$y=h\\left(m\\right)$将其还原。最小化信息损失可以使用距离，比如欧式距离来衡量：$$\\min ||y-x||_2=||h\\left[ g\\left(x\\right)\\right]-x||_2$$\n",
    "\n",
    "主成分分析法通过假设$g\\left(x\\right)$和$h\\left(m\\right)$都是线性函数来构造这两个映射。我们知道，线性函数都可以通过矩阵来表示，从而假设$g\\left(x\\right)=U'x$其中$U$是一个$D\\times d$的矩阵。在主成分分析中，假设$U$的每一列都是相互正交、长度为1的列向量，那么自然有：$$U'U=I_d$$即单位阵。\n",
    "\n",
    "如果$U$是一个$D\\times D$的正交矩阵，那么自然有$U_{-1}=U'$，从而$U'U=UU'=I_D$，而我们这里$U$是一个$D\\times d$的矩阵，不过将$U'x\\in \\mathbb{R}^d$还原回$\\mathbb{R}^D$的自然的矩阵即$$y=UU'x$$\n",
    "\n",
    "带入到以上目标函数中，我们记$X=\\left[x_1',x_2',...,x_N'\\right]$为$N\\times K$的数据矩阵，我们需要最小化：$$\\sum_{i=1}^N ||UU'x_i-x_i||_2^2=\\sum_{i=1}^N \\left(UU'x_i-x_i\\right)'\\left(UU'x_i-x_i\\right)=trace\\left[\\left(XUU'-X\\right)'\\left(XUU'-X\\right)\\right]$$\n",
    "\n",
    "可以计算：$$trace\\left[\\left(XUU'-X\\right)'\\left(XUU'-X\\right)\\right]=trace\\left[UU'X'XUU'-UU'X'X-X'XUU'+X'X\\right] \\\\ =trace\\left[UU'X'XUU'\\right]-trace\\left[UU'X'X\\right]-trace\\left[X'XUU'\\right]+trace\\left[X'X\\right] \\\\ = trace\\left[U'X'XUU'U\\right]-trace\\left[U'X'XU\\right]-trace\\left[U'X'XU\\right]+trace\\left[X'X\\right] \\\\ \n",
    "=trace\\left[U'X'XU\\right]-trace\\left[U'X'XU\\right]-trace\\left[U'X'XU\\right]+trace\\left[X'X\\right] \\\\ = -trace\\left[U'X'XU\\right]+trace\\left[X'X\\right] $$\n",
    "\n",
    "而最后一部分与$U$无关，第一部分实际上就是$Y=XUU'$的每一列的方差之和：$$trace(Y'Y)=trace(UU'X'XUU')=trace(U'X'XUU'U)=trace(U'X'XU)$$所以最小化$x_i$和$y_i$之间的距离，等价于最大化以上的方差之和。\n",
    "\n",
    "之所以最大化方差，直觉上是因为方差的大小可以看做信息量的多少：方差越大，那么包含在随机变量里面的“信息”越多，比如线性回归中，自变量的方差越大，系数的标准误就会越小，线性回归中的$R^2$也是通过对$y$的方差进行分解而得到的。\n",
    "\n",
    "一个简单的例子，比如：$x\\sim N\\left(3,6\\right)$，而$y=1+2x+u, u\\sim N\\left(0,12\\right)$这个系统里面有两个随机性的来源：$x$和$u$，我们现在希望找到包含在$x$和$y$里面的信息量最大的组合，如下图所示，方差最大的方向应该是沿着回归线的方向，为了方便展示，我们将以上数据进行标准化："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "matched-anaheim",
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   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "N = 100\n",
    "x = np.random.normal(3, np.sqrt(6), N)\n",
    "y = 1 + 2 * x + np.random.normal(0, np.sqrt(12), N)\n",
    "x = (x - x.mean()) / x.std()\n",
    "y = (y - y.mean()) / y.std()\n",
    "# 画图\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.patches as mpatches\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (10.0, 10.0)\n",
    "ax = plt.axes()\n",
    "plt.scatter(x, y)\n",
    "ax.arrow(0, 0, 1, 1, head_width=0.1, head_length=0.1, fc='k', ec='k')\n",
    "ax.arrow(0, 0, -0.5, 0.6, head_width=0.1, head_length=0.1, fc='k', ec='k')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "documented-tunisia",
   "metadata": {},
   "source": [
    "从而对于这个2维的数据，最重要的、方差最大的成分应该是沿着回归直线方向的成分。实际上从这点来看，主成分分析无非是一种坐标变换：将坐标变换为方差最大的方向即是最大的主成分。\n",
    "\n",
    "为了完成以上的最大化问题，主要到如果假设$X$的每个变量均值为0，那么$\\Sigma=X'X$就是$X$的协方差矩阵，从而只需要将$\\Sigma$矩阵进行特征值分解：$$\\Sigma=\\Gamma'\\Lambda\\Gamma$$由于$\\Sigma$是实对称矩阵，所以$\\Gamma$可以规范化为一个正交矩阵，而$\\Lambda$为对角矩阵，由于$\\Sigma$是正定矩阵，所以其特征值一定大于0，我们假设$\\Lambda$中的特征值从大到小排列。那么可以构造：$$U=\\Gamma_d$$其中$\\Gamma_d$为$\\Gamma$矩阵的前$d$列。\n",
    "\n",
    "同时注意到，主成分分析过程中每个变量的方差是非常重要的，所以在进行主成分分析之前，不仅仅要中心化，最好还要对每个变量除以其标准差，即进行标准化。\n",
    "\n",
    "比如，以上的x,y数据可以使用如下代码计算主成分："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "respected-buffalo",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "协方差矩阵=\n",
      " [[1.         0.82305528]\n",
      " [0.82305528 1.        ]]\n",
      "特征值=\n",
      " [1.82305528 0.17694472]\n",
      "特征向量=\n",
      " [[ 0.70710678 -0.70710678]\n",
      " [ 0.70710678  0.70710678]]\n"
     ]
    }
   ],
   "source": [
    "X = np.vstack([x, y]).T\n",
    "## 标准化\n",
    "X = (X - X.mean(axis=0)) / X.std(axis=0)\n",
    "## 计算协方差矩阵\n",
    "Sigma = 1 / 100 * X.T @ X\n",
    "print(\"协方差矩阵=\\n\", Sigma)\n",
    "## 计算特征值特征向量\n",
    "v, vec = np.linalg.eig(Sigma)\n",
    "print(\"特征值=\\n\", v)\n",
    "print(\"特征向量=\\n\", vec)\n",
    "## 验证特征值分解\n",
    "vec @ np.diag(v) @ vec.T\n",
    "## 计算主成分\n",
    "U = (vec.T)[:, 0]\n",
    "Comp1 = X @ U\n",
    "U2 = (vec.T)[:, 1]\n",
    "Comp2 = X @ U2\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "considered-pendant",
   "metadata": {},
   "source": [
    "或者，也可以直接使用Scikit-learn中的sklearn.decomposition.PCA来进行："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "accessible-jaguar",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.91152764 0.08847236]\n",
      "0.899217045\n"
     ]
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(n_components=2)\n",
    "pca.fit(X)\n",
    "# 打印出第一个主成分可解释的总方差的比例，即最大特征值占特征值总和的比例，\n",
    "print(pca.explained_variance_ratio_)\n",
    "print(1.79843409 / (1.79843409 + 0.20156591))\n",
    "# 计算主成分\n",
    "Comp = pca.transform(X)\n",
    "# Comp"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fabulous-apollo",
   "metadata": {},
   "source": [
    "接下来我们以实际数据例子来看一下主成分分析降维的用法。以下数据包含了我国18年1月到2020年2月的国债收益率数据："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "portable-cholesterol",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>IB010007</th>\n",
       "      <th>IB010011</th>\n",
       "      <th>SH010107</th>\n",
       "      <th>SH010303</th>\n",
       "      <th>SH010504</th>\n",
       "      <th>SH010512</th>\n",
       "      <th>SH010609</th>\n",
       "      <th>SH010619</th>\n",
       "      <th>SH010706</th>\n",
       "      <th>...</th>\n",
       "      <th>IB200003</th>\n",
       "      <th>IB209901</th>\n",
       "      <th>IB209902</th>\n",
       "      <th>IB209903</th>\n",
       "      <th>IB209904</th>\n",
       "      <th>IB209905</th>\n",
       "      <th>IB209906</th>\n",
       "      <th>IB209907</th>\n",
       "      <th>IB209908</th>\n",
       "      <th>IB209909</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2018-01-02</td>\n",
       "      <td>4.1168</td>\n",
       "      <td>3.8014</td>\n",
       "      <td>4.1168</td>\n",
       "      <td>4.2580</td>\n",
       "      <td>3.9000</td>\n",
       "      <td>3.7726</td>\n",
       "      <td>3.9000</td>\n",
       "      <td>3.8026</td>\n",
       "      <td>4.2265</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2018-01-03</td>\n",
       "      <td>4.0911</td>\n",
       "      <td>3.7837</td>\n",
       "      <td>4.0911</td>\n",
       "      <td>4.2822</td>\n",
       "      <td>3.9052</td>\n",
       "      <td>3.7370</td>\n",
       "      <td>3.9122</td>\n",
       "      <td>3.7873</td>\n",
       "      <td>4.2339</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2018-01-04</td>\n",
       "      <td>4.1428</td>\n",
       "      <td>3.8092</td>\n",
       "      <td>4.1428</td>\n",
       "      <td>4.3109</td>\n",
       "      <td>3.9137</td>\n",
       "      <td>3.7391</td>\n",
       "      <td>3.9216</td>\n",
       "      <td>3.8136</td>\n",
       "      <td>4.2414</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2018-01-05</td>\n",
       "      <td>4.1080</td>\n",
       "      <td>3.7726</td>\n",
       "      <td>4.1080</td>\n",
       "      <td>4.2829</td>\n",
       "      <td>3.9103</td>\n",
       "      <td>3.7046</td>\n",
       "      <td>3.9174</td>\n",
       "      <td>3.7765</td>\n",
       "      <td>4.2314</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2018-01-08</td>\n",
       "      <td>4.0987</td>\n",
       "      <td>3.7356</td>\n",
       "      <td>4.0987</td>\n",
       "      <td>4.2629</td>\n",
       "      <td>3.9036</td>\n",
       "      <td>3.6663</td>\n",
       "      <td>3.9086</td>\n",
       "      <td>3.7403</td>\n",
       "      <td>4.2214</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 1699 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         Date  IB010007  IB010011  SH010107  SH010303  SH010504  SH010512  \\\n",
       "0  2018-01-02    4.1168    3.8014    4.1168    4.2580    3.9000    3.7726   \n",
       "1  2018-01-03    4.0911    3.7837    4.0911    4.2822    3.9052    3.7370   \n",
       "2  2018-01-04    4.1428    3.8092    4.1428    4.3109    3.9137    3.7391   \n",
       "3  2018-01-05    4.1080    3.7726    4.1080    4.2829    3.9103    3.7046   \n",
       "4  2018-01-08    4.0987    3.7356    4.0987    4.2629    3.9036    3.6663   \n",
       "\n",
       "   SH010609  SH010619  SH010706  ...  IB200003  IB209901  IB209902  IB209903  \\\n",
       "0    3.9000    3.8026    4.2265  ...       NaN       NaN       NaN       NaN   \n",
       "1    3.9122    3.7873    4.2339  ...       NaN       NaN       NaN       NaN   \n",
       "2    3.9216    3.8136    4.2414  ...       NaN       NaN       NaN       NaN   \n",
       "3    3.9174    3.7765    4.2314  ...       NaN       NaN       NaN       NaN   \n",
       "4    3.9086    3.7403    4.2214  ...       NaN       NaN       NaN       NaN   \n",
       "\n",
       "   IB209904  IB209905  IB209906  IB209907  IB209908  IB209909  \n",
       "0       NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "1       NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "2       NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "3       NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "4       NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "\n",
       "[5 rows x 1699 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "bond = pd.read_csv(\"csv/bond_interest.csv\")\n",
    "bond.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "intimate-hometown",
   "metadata": {},
   "source": [
    "可以看到以上数据有1699列，实际上都是国债收益率。不同债券的利率会有差异，主要是因为不同债券的到期时间不同，利率期限结构决定了即使都是无风险的国债，也会有利率上的差异。\n",
    "\n",
    "如果需要使用利率数据，如此多的国债可以选择，可能选择哪一个都会有失偏颇。我们可以转而使用主成分分析对其进行降维。由于很多债券是刚刚发行或者已经到期，所以在某些时间某些债券的收益率数据不可用。如果我们使用整个期间段，那么结果会偏重于长期债券。我们不妨以半年为期限，以2018年上半年为例："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "special-panama",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>IB010007</th>\n",
       "      <th>IB010011</th>\n",
       "      <th>SH010107</th>\n",
       "      <th>SH010303</th>\n",
       "      <th>SH010504</th>\n",
       "      <th>SH010512</th>\n",
       "      <th>SH010609</th>\n",
       "      <th>SH010619</th>\n",
       "      <th>SH010706</th>\n",
       "      <th>SH010713</th>\n",
       "      <th>...</th>\n",
       "      <th>BC170021</th>\n",
       "      <th>IB170021</th>\n",
       "      <th>IB170022</th>\n",
       "      <th>BC170023</th>\n",
       "      <th>IB170023</th>\n",
       "      <th>BC170025</th>\n",
       "      <th>IB170025</th>\n",
       "      <th>IB170026</th>\n",
       "      <th>BC170027</th>\n",
       "      <th>IB170027</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2018-01-02</th>\n",
       "      <td>1.145519</td>\n",
       "      <td>1.607523</td>\n",
       "      <td>1.145519</td>\n",
       "      <td>1.235691</td>\n",
       "      <td>1.231931</td>\n",
       "      <td>1.978725</td>\n",
       "      <td>1.178144</td>\n",
       "      <td>1.579299</td>\n",
       "      <td>1.293647</td>\n",
       "      <td>1.136165</td>\n",
       "      <td>...</td>\n",
       "      <td>1.137263</td>\n",
       "      <td>1.137263</td>\n",
       "      <td>1.477363</td>\n",
       "      <td>1.486544</td>\n",
       "      <td>1.486544</td>\n",
       "      <td>1.093421</td>\n",
       "      <td>1.093421</td>\n",
       "      <td>1.466402</td>\n",
       "      <td>1.249744</td>\n",
       "      <td>1.249744</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-01-03</th>\n",
       "      <td>1.042193</td>\n",
       "      <td>1.510075</td>\n",
       "      <td>1.042193</td>\n",
       "      <td>1.329485</td>\n",
       "      <td>1.272207</td>\n",
       "      <td>1.773202</td>\n",
       "      <td>1.273046</td>\n",
       "      <td>1.495568</td>\n",
       "      <td>1.352958</td>\n",
       "      <td>1.245890</td>\n",
       "      <td>...</td>\n",
       "      <td>1.210889</td>\n",
       "      <td>1.210889</td>\n",
       "      <td>1.477363</td>\n",
       "      <td>1.373368</td>\n",
       "      <td>1.373368</td>\n",
       "      <td>1.217759</td>\n",
       "      <td>1.217759</td>\n",
       "      <td>1.466402</td>\n",
       "      <td>1.249744</td>\n",
       "      <td>1.249744</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-01-04</th>\n",
       "      <td>1.250051</td>\n",
       "      <td>1.650466</td>\n",
       "      <td>1.250051</td>\n",
       "      <td>1.440720</td>\n",
       "      <td>1.338043</td>\n",
       "      <td>1.785326</td>\n",
       "      <td>1.346168</td>\n",
       "      <td>1.639499</td>\n",
       "      <td>1.413070</td>\n",
       "      <td>1.354092</td>\n",
       "      <td>...</td>\n",
       "      <td>1.322801</td>\n",
       "      <td>1.322801</td>\n",
       "      <td>1.477363</td>\n",
       "      <td>1.373692</td>\n",
       "      <td>1.373692</td>\n",
       "      <td>1.342098</td>\n",
       "      <td>1.342098</td>\n",
       "      <td>1.466402</td>\n",
       "      <td>1.324070</td>\n",
       "      <td>1.324070</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-01-05</th>\n",
       "      <td>1.110139</td>\n",
       "      <td>1.448964</td>\n",
       "      <td>1.110139</td>\n",
       "      <td>1.332198</td>\n",
       "      <td>1.311709</td>\n",
       "      <td>1.586153</td>\n",
       "      <td>1.313496</td>\n",
       "      <td>1.436463</td>\n",
       "      <td>1.332920</td>\n",
       "      <td>1.284752</td>\n",
       "      <td>...</td>\n",
       "      <td>1.192115</td>\n",
       "      <td>1.192115</td>\n",
       "      <td>1.392740</td>\n",
       "      <td>1.260193</td>\n",
       "      <td>1.260193</td>\n",
       "      <td>1.258377</td>\n",
       "      <td>1.258377</td>\n",
       "      <td>1.385426</td>\n",
       "      <td>1.287650</td>\n",
       "      <td>1.287650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-01-08</th>\n",
       "      <td>1.072749</td>\n",
       "      <td>1.245261</td>\n",
       "      <td>1.072749</td>\n",
       "      <td>1.254683</td>\n",
       "      <td>1.259814</td>\n",
       "      <td>1.365044</td>\n",
       "      <td>1.245042</td>\n",
       "      <td>1.238354</td>\n",
       "      <td>1.252771</td>\n",
       "      <td>1.210839</td>\n",
       "      <td>...</td>\n",
       "      <td>1.100450</td>\n",
       "      <td>1.100450</td>\n",
       "      <td>1.308116</td>\n",
       "      <td>1.139256</td>\n",
       "      <td>1.139256</td>\n",
       "      <td>1.176313</td>\n",
       "      <td>1.176313</td>\n",
       "      <td>1.305260</td>\n",
       "      <td>1.249744</td>\n",
       "      <td>1.249744</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-06-25</th>\n",
       "      <td>-1.001411</td>\n",
       "      <td>-0.612295</td>\n",
       "      <td>-1.001411</td>\n",
       "      <td>-1.082797</td>\n",
       "      <td>-1.289976</td>\n",
       "      <td>-0.305693</td>\n",
       "      <td>-1.321994</td>\n",
       "      <td>-0.626176</td>\n",
       "      <td>-1.194182</td>\n",
       "      <td>-1.302937</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.816410</td>\n",
       "      <td>-0.816410</td>\n",
       "      <td>-0.955563</td>\n",
       "      <td>-0.110526</td>\n",
       "      <td>-0.110526</td>\n",
       "      <td>-1.228396</td>\n",
       "      <td>-1.228396</td>\n",
       "      <td>-1.133740</td>\n",
       "      <td>-1.292178</td>\n",
       "      <td>-1.292178</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-06-26</th>\n",
       "      <td>-1.057295</td>\n",
       "      <td>-0.678911</td>\n",
       "      <td>-1.057295</td>\n",
       "      <td>-1.056054</td>\n",
       "      <td>-1.330252</td>\n",
       "      <td>-0.392867</td>\n",
       "      <td>-1.332885</td>\n",
       "      <td>-0.689112</td>\n",
       "      <td>-1.234256</td>\n",
       "      <td>-1.305223</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.814201</td>\n",
       "      <td>-0.814201</td>\n",
       "      <td>-1.033417</td>\n",
       "      <td>-0.159030</td>\n",
       "      <td>-0.159030</td>\n",
       "      <td>-1.395010</td>\n",
       "      <td>-1.395010</td>\n",
       "      <td>-1.218765</td>\n",
       "      <td>-1.322652</td>\n",
       "      <td>-1.322652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-06-27</th>\n",
       "      <td>-1.061316</td>\n",
       "      <td>-0.693776</td>\n",
       "      <td>-1.061316</td>\n",
       "      <td>-1.140933</td>\n",
       "      <td>-1.401510</td>\n",
       "      <td>-0.392290</td>\n",
       "      <td>-1.487685</td>\n",
       "      <td>-0.707171</td>\n",
       "      <td>-1.312802</td>\n",
       "      <td>-1.503338</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.871630</td>\n",
       "      <td>-0.871630</td>\n",
       "      <td>-1.043572</td>\n",
       "      <td>-0.159030</td>\n",
       "      <td>-0.159030</td>\n",
       "      <td>-1.616333</td>\n",
       "      <td>-1.616333</td>\n",
       "      <td>-1.218765</td>\n",
       "      <td>-1.310760</td>\n",
       "      <td>-1.310760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-06-28</th>\n",
       "      <td>-1.149766</td>\n",
       "      <td>-0.801134</td>\n",
       "      <td>-1.149766</td>\n",
       "      <td>-1.257207</td>\n",
       "      <td>-1.597469</td>\n",
       "      <td>-0.645729</td>\n",
       "      <td>-1.672045</td>\n",
       "      <td>-0.812246</td>\n",
       "      <td>-1.542830</td>\n",
       "      <td>-1.677069</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.968080</td>\n",
       "      <td>-0.968080</td>\n",
       "      <td>-1.336369</td>\n",
       "      <td>-0.306158</td>\n",
       "      <td>-0.306158</td>\n",
       "      <td>-1.804499</td>\n",
       "      <td>-1.804499</td>\n",
       "      <td>-1.499752</td>\n",
       "      <td>-1.584277</td>\n",
       "      <td>-1.584277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-06-29</th>\n",
       "      <td>-1.308574</td>\n",
       "      <td>-1.016949</td>\n",
       "      <td>-1.308574</td>\n",
       "      <td>-1.413013</td>\n",
       "      <td>-1.983190</td>\n",
       "      <td>-0.880117</td>\n",
       "      <td>-2.071102</td>\n",
       "      <td>-1.026774</td>\n",
       "      <td>-2.043762</td>\n",
       "      <td>-2.088539</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.111283</td>\n",
       "      <td>-1.111283</td>\n",
       "      <td>-1.921964</td>\n",
       "      <td>-0.438412</td>\n",
       "      <td>-0.438412</td>\n",
       "      <td>-2.254604</td>\n",
       "      <td>-2.254604</td>\n",
       "      <td>-2.066585</td>\n",
       "      <td>-1.948470</td>\n",
       "      <td>-1.948470</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>119 rows × 477 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            IB010007  IB010011  SH010107  SH010303  SH010504  SH010512  \\\n",
       "Date                                                                     \n",
       "2018-01-02  1.145519  1.607523  1.145519  1.235691  1.231931  1.978725   \n",
       "2018-01-03  1.042193  1.510075  1.042193  1.329485  1.272207  1.773202   \n",
       "2018-01-04  1.250051  1.650466  1.250051  1.440720  1.338043  1.785326   \n",
       "2018-01-05  1.110139  1.448964  1.110139  1.332198  1.311709  1.586153   \n",
       "2018-01-08  1.072749  1.245261  1.072749  1.254683  1.259814  1.365044   \n",
       "...              ...       ...       ...       ...       ...       ...   \n",
       "2018-06-25 -1.001411 -0.612295 -1.001411 -1.082797 -1.289976 -0.305693   \n",
       "2018-06-26 -1.057295 -0.678911 -1.057295 -1.056054 -1.330252 -0.392867   \n",
       "2018-06-27 -1.061316 -0.693776 -1.061316 -1.140933 -1.401510 -0.392290   \n",
       "2018-06-28 -1.149766 -0.801134 -1.149766 -1.257207 -1.597469 -0.645729   \n",
       "2018-06-29 -1.308574 -1.016949 -1.308574 -1.413013 -1.983190 -0.880117   \n",
       "\n",
       "            SH010609  SH010619  SH010706  SH010713  ...  BC170021  IB170021  \\\n",
       "Date                                                ...                       \n",
       "2018-01-02  1.178144  1.579299  1.293647  1.136165  ...  1.137263  1.137263   \n",
       "2018-01-03  1.273046  1.495568  1.352958  1.245890  ...  1.210889  1.210889   \n",
       "2018-01-04  1.346168  1.639499  1.413070  1.354092  ...  1.322801  1.322801   \n",
       "2018-01-05  1.313496  1.436463  1.332920  1.284752  ...  1.192115  1.192115   \n",
       "2018-01-08  1.245042  1.238354  1.252771  1.210839  ...  1.100450  1.100450   \n",
       "...              ...       ...       ...       ...  ...       ...       ...   \n",
       "2018-06-25 -1.321994 -0.626176 -1.194182 -1.302937  ... -0.816410 -0.816410   \n",
       "2018-06-26 -1.332885 -0.689112 -1.234256 -1.305223  ... -0.814201 -0.814201   \n",
       "2018-06-27 -1.487685 -0.707171 -1.312802 -1.503338  ... -0.871630 -0.871630   \n",
       "2018-06-28 -1.672045 -0.812246 -1.542830 -1.677069  ... -0.968080 -0.968080   \n",
       "2018-06-29 -2.071102 -1.026774 -2.043762 -2.088539  ... -1.111283 -1.111283   \n",
       "\n",
       "            IB170022  BC170023  IB170023  BC170025  IB170025  IB170026  \\\n",
       "Date                                                                     \n",
       "2018-01-02  1.477363  1.486544  1.486544  1.093421  1.093421  1.466402   \n",
       "2018-01-03  1.477363  1.373368  1.373368  1.217759  1.217759  1.466402   \n",
       "2018-01-04  1.477363  1.373692  1.373692  1.342098  1.342098  1.466402   \n",
       "2018-01-05  1.392740  1.260193  1.260193  1.258377  1.258377  1.385426   \n",
       "2018-01-08  1.308116  1.139256  1.139256  1.176313  1.176313  1.305260   \n",
       "...              ...       ...       ...       ...       ...       ...   \n",
       "2018-06-25 -0.955563 -0.110526 -0.110526 -1.228396 -1.228396 -1.133740   \n",
       "2018-06-26 -1.033417 -0.159030 -0.159030 -1.395010 -1.395010 -1.218765   \n",
       "2018-06-27 -1.043572 -0.159030 -0.159030 -1.616333 -1.616333 -1.218765   \n",
       "2018-06-28 -1.336369 -0.306158 -0.306158 -1.804499 -1.804499 -1.499752   \n",
       "2018-06-29 -1.921964 -0.438412 -0.438412 -2.254604 -2.254604 -2.066585   \n",
       "\n",
       "            BC170027  IB170027  \n",
       "Date                            \n",
       "2018-01-02  1.249744  1.249744  \n",
       "2018-01-03  1.249744  1.249744  \n",
       "2018-01-04  1.324070  1.324070  \n",
       "2018-01-05  1.287650  1.287650  \n",
       "2018-01-08  1.249744  1.249744  \n",
       "...              ...       ...  \n",
       "2018-06-25 -1.292178 -1.292178  \n",
       "2018-06-26 -1.322652 -1.322652  \n",
       "2018-06-27 -1.310760 -1.310760  \n",
       "2018-06-28 -1.584277 -1.584277  \n",
       "2018-06-29 -1.948470 -1.948470  \n",
       "\n",
       "[119 rows x 477 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "date = pd.to_datetime(bond['Date'])\n",
    "bond = bond.set_index(date)\n",
    "sub_bond = bond['2018-01-02':'2018-07-01']\n",
    "sub_bond = sub_bond.dropna(axis=1)\n",
    "# 标准化\n",
    "std_sub_bond = (sub_bond.iloc[:, 1:] - sub_bond.iloc[:, 1:].mean(axis=0)\n",
    "                ) / sub_bond.iloc[:, 1:].std(axis=0)\n",
    "std_sub_bond"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "medieval-classics",
   "metadata": {},
   "source": [
    "如此，我们就跳出了一个不包含缺失变量的样本。\n",
    "\n",
    "然后进行主成分分析，我们选取前5个主成分："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "political-bermuda",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.94147679 0.04165834 0.00702729 0.00335977 0.00150169]\n"
     ]
    },
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>IB010007</th>\n",
       "      <th>IB010011</th>\n",
       "      <th>SH010107</th>\n",
       "      <th>SH010303</th>\n",
       "      <th>SH010504</th>\n",
       "      <th>SH010512</th>\n",
       "      <th>SH010609</th>\n",
       "      <th>SH010619</th>\n",
       "      <th>SH010706</th>\n",
       "      <th>...</th>\n",
       "      <th>IB170022</th>\n",
       "      <th>BC170023</th>\n",
       "      <th>IB170023</th>\n",
       "      <th>BC170025</th>\n",
       "      <th>IB170025</th>\n",
       "      <th>IB170026</th>\n",
       "      <th>BC170027</th>\n",
       "      <th>IB170027</th>\n",
       "      <th>Comp1</th>\n",
       "      <th>Comp2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2018-01-02</th>\n",
       "      <td>2018-01-02</td>\n",
       "      <td>4.1168</td>\n",
       "      <td>3.8014</td>\n",
       "      <td>4.1168</td>\n",
       "      <td>4.2580</td>\n",
       "      <td>3.9000</td>\n",
       "      <td>3.7726</td>\n",
       "      <td>3.9000</td>\n",
       "      <td>3.8026</td>\n",
       "      <td>4.2265</td>\n",
       "      <td>...</td>\n",
       "      <td>4.3700</td>\n",
       "      <td>3.7699</td>\n",
       "      <td>3.7699</td>\n",
       "      <td>3.9000</td>\n",
       "      <td>3.9000</td>\n",
       "      <td>4.4226</td>\n",
       "      <td>3.9000</td>\n",
       "      <td>3.9000</td>\n",
       "      <td>30.360802</td>\n",
       "      <td>5.108068</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-01-03</th>\n",
       "      <td>2018-01-03</td>\n",
       "      <td>4.0911</td>\n",
       "      <td>3.7837</td>\n",
       "      <td>4.0911</td>\n",
       "      <td>4.2822</td>\n",
       "      <td>3.9052</td>\n",
       "      <td>3.7370</td>\n",
       "      <td>3.9122</td>\n",
       "      <td>3.7873</td>\n",
       "      <td>4.2339</td>\n",
       "      <td>...</td>\n",
       "      <td>4.3700</td>\n",
       "      <td>3.7349</td>\n",
       "      <td>3.7349</td>\n",
       "      <td>3.9150</td>\n",
       "      <td>3.9150</td>\n",
       "      <td>4.4226</td>\n",
       "      <td>3.9000</td>\n",
       "      <td>3.9000</td>\n",
       "      <td>30.397110</td>\n",
       "      <td>3.527838</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-01-04</th>\n",
       "      <td>2018-01-04</td>\n",
       "      <td>4.1428</td>\n",
       "      <td>3.8092</td>\n",
       "      <td>4.1428</td>\n",
       "      <td>4.3109</td>\n",
       "      <td>3.9137</td>\n",
       "      <td>3.7391</td>\n",
       "      <td>3.9216</td>\n",
       "      <td>3.8136</td>\n",
       "      <td>4.2414</td>\n",
       "      <td>...</td>\n",
       "      <td>4.3700</td>\n",
       "      <td>3.7350</td>\n",
       "      <td>3.7350</td>\n",
       "      <td>3.9300</td>\n",
       "      <td>3.9300</td>\n",
       "      <td>4.4226</td>\n",
       "      <td>3.9100</td>\n",
       "      <td>3.9100</td>\n",
       "      <td>31.795481</td>\n",
       "      <td>3.452123</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-01-05</th>\n",
       "      <td>2018-01-05</td>\n",
       "      <td>4.1080</td>\n",
       "      <td>3.7726</td>\n",
       "      <td>4.1080</td>\n",
       "      <td>4.2829</td>\n",
       "      <td>3.9103</td>\n",
       "      <td>3.7046</td>\n",
       "      <td>3.9174</td>\n",
       "      <td>3.7765</td>\n",
       "      <td>4.2314</td>\n",
       "      <td>...</td>\n",
       "      <td>4.3600</td>\n",
       "      <td>3.6999</td>\n",
       "      <td>3.6999</td>\n",
       "      <td>3.9199</td>\n",
       "      <td>3.9199</td>\n",
       "      <td>4.4126</td>\n",
       "      <td>3.9051</td>\n",
       "      <td>3.9051</td>\n",
       "      <td>29.245293</td>\n",
       "      <td>2.162864</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-01-08</th>\n",
       "      <td>2018-01-08</td>\n",
       "      <td>4.0987</td>\n",
       "      <td>3.7356</td>\n",
       "      <td>4.0987</td>\n",
       "      <td>4.2629</td>\n",
       "      <td>3.9036</td>\n",
       "      <td>3.6663</td>\n",
       "      <td>3.9086</td>\n",
       "      <td>3.7403</td>\n",
       "      <td>4.2214</td>\n",
       "      <td>...</td>\n",
       "      <td>4.3500</td>\n",
       "      <td>3.6625</td>\n",
       "      <td>3.6625</td>\n",
       "      <td>3.9100</td>\n",
       "      <td>3.9100</td>\n",
       "      <td>4.4027</td>\n",
       "      <td>3.9000</td>\n",
       "      <td>3.9000</td>\n",
       "      <td>26.808093</td>\n",
       "      <td>0.932411</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-06-25</th>\n",
       "      <td>2018-06-25</td>\n",
       "      <td>3.5828</td>\n",
       "      <td>3.3982</td>\n",
       "      <td>3.5828</td>\n",
       "      <td>3.6598</td>\n",
       "      <td>3.5744</td>\n",
       "      <td>3.3769</td>\n",
       "      <td>3.5786</td>\n",
       "      <td>3.3996</td>\n",
       "      <td>3.9161</td>\n",
       "      <td>...</td>\n",
       "      <td>4.0825</td>\n",
       "      <td>3.2760</td>\n",
       "      <td>3.2760</td>\n",
       "      <td>3.6199</td>\n",
       "      <td>3.6199</td>\n",
       "      <td>4.1015</td>\n",
       "      <td>3.5580</td>\n",
       "      <td>3.5580</td>\n",
       "      <td>-19.833129</td>\n",
       "      <td>7.707087</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-06-26</th>\n",
       "      <td>2018-06-26</td>\n",
       "      <td>3.5689</td>\n",
       "      <td>3.3861</td>\n",
       "      <td>3.5689</td>\n",
       "      <td>3.6667</td>\n",
       "      <td>3.5692</td>\n",
       "      <td>3.3618</td>\n",
       "      <td>3.5772</td>\n",
       "      <td>3.3881</td>\n",
       "      <td>3.9111</td>\n",
       "      <td>...</td>\n",
       "      <td>4.0733</td>\n",
       "      <td>3.2610</td>\n",
       "      <td>3.2610</td>\n",
       "      <td>3.5998</td>\n",
       "      <td>3.5998</td>\n",
       "      <td>4.0910</td>\n",
       "      <td>3.5539</td>\n",
       "      <td>3.5539</td>\n",
       "      <td>-20.812740</td>\n",
       "      <td>7.560393</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-06-27</th>\n",
       "      <td>2018-06-27</td>\n",
       "      <td>3.5679</td>\n",
       "      <td>3.3834</td>\n",
       "      <td>3.5679</td>\n",
       "      <td>3.6448</td>\n",
       "      <td>3.5600</td>\n",
       "      <td>3.3619</td>\n",
       "      <td>3.5573</td>\n",
       "      <td>3.3848</td>\n",
       "      <td>3.9013</td>\n",
       "      <td>...</td>\n",
       "      <td>4.0721</td>\n",
       "      <td>3.2610</td>\n",
       "      <td>3.2610</td>\n",
       "      <td>3.5731</td>\n",
       "      <td>3.5731</td>\n",
       "      <td>4.0910</td>\n",
       "      <td>3.5555</td>\n",
       "      <td>3.5555</td>\n",
       "      <td>-21.981982</td>\n",
       "      <td>8.135084</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-06-28</th>\n",
       "      <td>2018-06-28</td>\n",
       "      <td>3.5459</td>\n",
       "      <td>3.3639</td>\n",
       "      <td>3.5459</td>\n",
       "      <td>3.6148</td>\n",
       "      <td>3.5347</td>\n",
       "      <td>3.3180</td>\n",
       "      <td>3.5336</td>\n",
       "      <td>3.3656</td>\n",
       "      <td>3.8726</td>\n",
       "      <td>...</td>\n",
       "      <td>4.0375</td>\n",
       "      <td>3.2155</td>\n",
       "      <td>3.2155</td>\n",
       "      <td>3.5504</td>\n",
       "      <td>3.5504</td>\n",
       "      <td>4.0563</td>\n",
       "      <td>3.5187</td>\n",
       "      <td>3.5187</td>\n",
       "      <td>-26.681830</td>\n",
       "      <td>8.258614</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-06-29</th>\n",
       "      <td>2018-06-29</td>\n",
       "      <td>3.5064</td>\n",
       "      <td>3.3247</td>\n",
       "      <td>3.5064</td>\n",
       "      <td>3.5746</td>\n",
       "      <td>3.4849</td>\n",
       "      <td>3.2774</td>\n",
       "      <td>3.4823</td>\n",
       "      <td>3.3264</td>\n",
       "      <td>3.8101</td>\n",
       "      <td>...</td>\n",
       "      <td>3.9683</td>\n",
       "      <td>3.1746</td>\n",
       "      <td>3.1746</td>\n",
       "      <td>3.4961</td>\n",
       "      <td>3.4961</td>\n",
       "      <td>3.9863</td>\n",
       "      <td>3.4697</td>\n",
       "      <td>3.4697</td>\n",
       "      <td>-34.349807</td>\n",
       "      <td>10.523319</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>119 rows × 480 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                  Date  IB010007  IB010011  SH010107  SH010303  SH010504  \\\n",
       "Date                                                                       \n",
       "2018-01-02  2018-01-02    4.1168    3.8014    4.1168    4.2580    3.9000   \n",
       "2018-01-03  2018-01-03    4.0911    3.7837    4.0911    4.2822    3.9052   \n",
       "2018-01-04  2018-01-04    4.1428    3.8092    4.1428    4.3109    3.9137   \n",
       "2018-01-05  2018-01-05    4.1080    3.7726    4.1080    4.2829    3.9103   \n",
       "2018-01-08  2018-01-08    4.0987    3.7356    4.0987    4.2629    3.9036   \n",
       "...                ...       ...       ...       ...       ...       ...   \n",
       "2018-06-25  2018-06-25    3.5828    3.3982    3.5828    3.6598    3.5744   \n",
       "2018-06-26  2018-06-26    3.5689    3.3861    3.5689    3.6667    3.5692   \n",
       "2018-06-27  2018-06-27    3.5679    3.3834    3.5679    3.6448    3.5600   \n",
       "2018-06-28  2018-06-28    3.5459    3.3639    3.5459    3.6148    3.5347   \n",
       "2018-06-29  2018-06-29    3.5064    3.3247    3.5064    3.5746    3.4849   \n",
       "\n",
       "            SH010512  SH010609  SH010619  SH010706  ...  IB170022  BC170023  \\\n",
       "Date                                                ...                       \n",
       "2018-01-02    3.7726    3.9000    3.8026    4.2265  ...    4.3700    3.7699   \n",
       "2018-01-03    3.7370    3.9122    3.7873    4.2339  ...    4.3700    3.7349   \n",
       "2018-01-04    3.7391    3.9216    3.8136    4.2414  ...    4.3700    3.7350   \n",
       "2018-01-05    3.7046    3.9174    3.7765    4.2314  ...    4.3600    3.6999   \n",
       "2018-01-08    3.6663    3.9086    3.7403    4.2214  ...    4.3500    3.6625   \n",
       "...              ...       ...       ...       ...  ...       ...       ...   \n",
       "2018-06-25    3.3769    3.5786    3.3996    3.9161  ...    4.0825    3.2760   \n",
       "2018-06-26    3.3618    3.5772    3.3881    3.9111  ...    4.0733    3.2610   \n",
       "2018-06-27    3.3619    3.5573    3.3848    3.9013  ...    4.0721    3.2610   \n",
       "2018-06-28    3.3180    3.5336    3.3656    3.8726  ...    4.0375    3.2155   \n",
       "2018-06-29    3.2774    3.4823    3.3264    3.8101  ...    3.9683    3.1746   \n",
       "\n",
       "            IB170023  BC170025  IB170025  IB170026  BC170027  IB170027  \\\n",
       "Date                                                                     \n",
       "2018-01-02    3.7699    3.9000    3.9000    4.4226    3.9000    3.9000   \n",
       "2018-01-03    3.7349    3.9150    3.9150    4.4226    3.9000    3.9000   \n",
       "2018-01-04    3.7350    3.9300    3.9300    4.4226    3.9100    3.9100   \n",
       "2018-01-05    3.6999    3.9199    3.9199    4.4126    3.9051    3.9051   \n",
       "2018-01-08    3.6625    3.9100    3.9100    4.4027    3.9000    3.9000   \n",
       "...              ...       ...       ...       ...       ...       ...   \n",
       "2018-06-25    3.2760    3.6199    3.6199    4.1015    3.5580    3.5580   \n",
       "2018-06-26    3.2610    3.5998    3.5998    4.0910    3.5539    3.5539   \n",
       "2018-06-27    3.2610    3.5731    3.5731    4.0910    3.5555    3.5555   \n",
       "2018-06-28    3.2155    3.5504    3.5504    4.0563    3.5187    3.5187   \n",
       "2018-06-29    3.1746    3.4961    3.4961    3.9863    3.4697    3.4697   \n",
       "\n",
       "                Comp1      Comp2  \n",
       "Date                              \n",
       "2018-01-02  30.360802   5.108068  \n",
       "2018-01-03  30.397110   3.527838  \n",
       "2018-01-04  31.795481   3.452123  \n",
       "2018-01-05  29.245293   2.162864  \n",
       "2018-01-08  26.808093   0.932411  \n",
       "...               ...        ...  \n",
       "2018-06-25 -19.833129   7.707087  \n",
       "2018-06-26 -20.812740   7.560393  \n",
       "2018-06-27 -21.981982   8.135084  \n",
       "2018-06-28 -26.681830   8.258614  \n",
       "2018-06-29 -34.349807  10.523319  \n",
       "\n",
       "[119 rows x 480 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(n_components=5)\n",
    "pca.fit(std_sub_bond)\n",
    "# 打印出第一个主成分可解释的总方差的比例，即最大特征值占特征值总和的比例，\n",
    "print(pca.explained_variance_ratio_)\n",
    "# 计算主成分\n",
    "Comp = pca.transform(std_sub_bond)\n",
    "# 放入dataframe中\n",
    "sub_bond['Comp1'] = Comp[:, 0]\n",
    "sub_bond['Comp2'] = Comp[:, 1]\n",
    "sub_bond"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fundamental-laptop",
   "metadata": {},
   "source": [
    "可以发现第一个主成分基本上已经包含了94%的信息，前两个主成分更是包含了98%的信息，剩下的成分信息已经非常少。\n",
    "\n",
    "值得注意的是，生成的主成分的符号是没有意义的：特征向量的符号是没有意义的，所以实际得到的主成分完全有可能与实际数据负相关，在使用主成分时需要特别注意。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "thousand-treaty",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(sub_bond['IB010007'],sub_bond['Comp1'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "buried-somerset",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(sub_bond['IB010007'],sub_bond['Comp2'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "becoming-royalty",
   "metadata": {},
   "source": [
    "可以看到第一个主成分和某个债券的利率已经是非常高度相关了。\n",
    "\n",
    "最后，在使用主成分时，结合计量经济学，还有几点需要提醒：\n",
    "\n",
    "* 主成分非常适合多个不相同但是类似的度量，如果不同变量之间差异极大，主成分分析也需要更多的主成分才能比较好的保留信息\n",
    "* 主成分分析得到的主成分是方差最大的一部分信息，然而实际研究中，最有用的信息不一定是方差最大的信息。一个简单的例子，债券利率中方差最大的一部分信息一定是市场的利率，然而不同到期时间的债券之间收益率的差别，虽然方差微小，然而作为固定收益分析的重要工具，肯定不能说这些信息没用，甚至这些信息才是最有用的。\n",
    "* 基于以上原因，因果推断中慎用主成分：我们使用控制变量的主要原因就是为了得到那部分虽然微小但是足以说明因果性的那部分信息，主成分完全有可能把这部分信息过滤掉。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "nearby-amber",
   "metadata": {},
   "source": [
    "# 多维缩放\n",
    "\n",
    "**多维缩放**（**multiple dimensional scaling, MDS**）与主成分分析紧密相关的一个方法，不过多维缩放提供了降维方法的另一个视角：**嵌入**（**embedding**）。\n",
    "\n",
    "所谓嵌入，即从高维空间向低维空间的一个映射，而这个映射需要尽量保持高维空间的距离。比如地图就是现实生活中最常用的嵌入应用。一个城市的路网是三维的，会有高架桥、隧道等等，然而对于我们出行而言，实际上并不需要一个三维地图，我们将路网映射到一张二维的平面地图上，仍然不会损失太多的信息。而且重要的是，在这张地图上，两个点之间的距离是比例于现实世界的距离的。\n",
    "\n",
    "现在，我们仍然考虑$x_i\\in \\mathbb{R}^D, i=1,...,N$，以及$N\\times D$维的矩阵$X=\\left[x_1',x_2',...,x_N'\\right]'$。我们可以定义这$N$个点的一个距离矩阵$$D=[d_{ij}]$$其中$d_{ij}$为$x_i$和$x_j$之间的距离。\n",
    "\n",
    "实际上，除了欧式距离：$$d_{ij}=\\sqrt{\\left(x_i-x_j\\right)'\\left(x_i-x_j\\right)}$$之外，还有很多其他的距离定义方式，使用不同的距离定义方式会得到不同的结果。一般的，MDS算法寻求找到一个映射$x_i\\rightarrow y_i$使得：$$\\sum_{i,j=1,...,N}\\left[dist\\left(x_i,x_j\\right)-dist\\left(y_i,y_j\\right)\\right]$$\n",
    "\n",
    "\n",
    "不过，由于欧式距离可以通过内积定义，分析起来非常方便，我们以欧式距离定义为例。\n",
    "\n",
    "现在，我们要找到样本在$d$维空间的映射，即将每一个$x_i$找到一个$y_i$的对应，并且使得$$||x_i-x_j||_2\\approx ||y_i-y_j||_2$$我们不妨假设$y_i$是中心化的，即假设：$\\sum _{i=1}^N y_i=0$，我们可以计算一个$N\\times N$的内积矩阵：$$\\Omega = Y\\times Y'$$其中$Y=\\left[y_1',y_2',...,y_N'\\right]'$为$N\\times d$的矩阵。\n",
    "\n",
    "可以发现，矩阵$\\Omega$的第$i$行第$j$列就是$y_i$和$y_j$的内积，那么$y_i,y_j$之间的距离应该为$$||y_i-y_j||^2_2=\\left(y_i-y_j\\right)'\\left(y_i-y_j\\right)'=\\Omega_{jj}+\\Omega_{ii}-2\\Omega_{ij}$$我们要求：$||y_i-y_j||_2\\approx ||x_i-x_j||_2$不妨取以上的等号成立，那么我们可以通过$x_i,x_j$之间的距离矩阵$D$反过来计算出$\\Omega$矩阵。\n",
    "\n",
    "当我们计算得到$\\Omega$矩阵之后，可以通过特征值分解：$$\\Omega=\\Gamma'\\Lambda\\Gamma$$同样该矩阵是一个实对称的正定矩阵，假设所有的特征值从大到小排列，我们选$\\Lambda$的前$d$行$d$列为$\\Lambda^*$，以及$\\Gamma$的前$d$行为$\\Gamma^*$，并根据：$$Y=\\Gamma^{*'}\\Lambda^{*\\frac{1}{2}}$$就可以计算嵌入的$Y$了。\n",
    "\n",
    "虽然出发点不同、计算方法不同，不过如果我们使用了欧氏距离来度量原始数据之间的距离，那么多位缩放和主成分分析实际上是等价的。不过多位缩放技术给我们打开了降维方法的一扇大门：通过嵌入的方法将高维空间映射到低维空间。接下来的流形学习就是在此基础上进行拓展的。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "another-membrane",
   "metadata": {},
   "source": [
    "# 流形学习\n",
    "\n",
    "**流形**（**manifold**）是一个几何学的术语，指的是在局部与欧式空间同胚的空间，即在局部与欧式空间类似的一个空间。比如对于地球而言，虽然是一个球体，但是在一个小的范围内，我们可以把一小块土地看成是一个二维平面，可以使用欧式距离来进行距离测算，而不用复杂的球面距离。\n",
    "\n",
    "这启发了流形学习，即也许高维空间中的数据并不是真的非常高维，而是有低维的结构，如果我们能够找到这样的结构，在每个局部都看成是一个低维空间，再一块块的将这个高维空间的结构映射到低维空间，那么就完成了降维。\n",
    "\n",
    "以上思想可以用下图表示：\n",
    "\n",
    "![](pic/manifold.png \"流形学习\")\n",
    "\n",
    "像上图的这种S型曲面，实际上是一个在三维空间中的一个低维空间，我们可以想象是一张纸巾飘在空中：虽然纸巾在空中可以有各种各样的姿态，但是其本质还是一个二维平面。流形学习的目的就是为了将这样的一个三维空间的复杂集合映射到一个低维空间中去。\n",
    "\n",
    "可以看到，上图中的MDS算法并不能够很好的完成这项任务：MDS试图还原所有的点到点的欧式距离，这就会把三维空间中的形态信息带入到二维空间中去，然而这种形态信息可能是不必要的，所以MDS没能会很好的将额外的维度压缩掉。而我们接下来要讲的Isomap等算法可以很好的完成这个任务。\n",
    "\n",
    "Isomap算法建立在MDS基础之上，区别在于：MDS算法要求经过嵌入操作后，所有的两个点之间的距离都要与高维空间中的距离相似。而**Isomap**（**isometric mapping**）即**等距映射**（或者等度量映射），并不寻求所有的点和点之间的距离与高维空间中的距离相似，而是只要在每一个局部保持等距离即可。\n",
    "\n",
    "比如，在上面的S形曲面中，虽然位于S右上和左下的两个点在三维空间中似乎看起来距离并不算太长，但是如果考虑到沿着S形曲面从右上走到左下，实际上要经过两个大的“弯道”，其在二维S形曲面上的面积实际上是非常远的。\n",
    "\n",
    "如果使用MDS算法，将会在嵌入的二维空间中模仿三维空间中的距离，所以得到的嵌入结果仍然是一个S形的。然而如果使用Isomap算法，S右上和左下的两个点之间的距离并不会被直接度量，而是一个局部一个局部的拼凑起来，那么这两个点之间的距离就要沿着S形曲面从头到尾走一遍了，距离就比较长了。\n",
    "\n",
    "为了计算这个等距映射，可以考虑给定对于每一个点，都找到与其距离（比如欧氏距离）最近的$k$个点，假设每个点只与最近的$k$个点连通，这样，每个点之间就形成了一个**图**（**graph**）。\n",
    "\n",
    "比如，如果我们考虑我国的所有城市，MDS的做法相当于坐飞机：任意的两个城市之间可以用直线连接起来。而Isomap的做法相当于坐火车：火车不可能跳跃，比如不可能从上海直接跳跃到南京去，从上海出发一定要先经过苏州、无锡、常州才能到达南京。所以我们只考虑每个城市有火车相通的临近城市，并使用城市之间的铁路连接构成一个“临近连接图”。\n",
    "\n",
    "给定这个临近连接图，从任意一点A到任意一点B，如果经过每个节点，下一步只能走进最近的$k$个节点，那么就有很多中不同的路径，我们将A和B之间的距离定义为其最短路径。比如，我们如果想要从上海到南京，可以上海-苏州-无锡-常州-南京，也可以上海-嘉兴-杭州-湖州-宜兴-南京，然而我们知道第二条路线更远：绕过了太湖！所以上海和南京之间的距离并非由这两个点之间的欧式距离决定的，而是由上海-苏州-无锡-常州-南京的铁路距离决定的。\n",
    "\n",
    "图上的最短路径问题可以使用Dijkstra算法求解，是计算机领域十分成熟的算法。这样，我们就将所有点和点之间的距离使用这种“近邻连接图”的方式定义出了一个全新的距离。\n",
    "\n",
    "使用该距离，继续使用MDS算法，就得到了一个新的嵌入结果。这个算法即Isomap。\n",
    "\n",
    "下面，作为例子，我们使用一份百度迁徙数据提供的某个年份春运时城市和城市之间的迁徙人数对我国城市进行一个“迁徙距离”的度量。\n",
    "\n",
    "首先载入数据："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "aquatic-sudan",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>start</th>\n",
       "      <th>end</th>\n",
       "      <th>num</th>\n",
       "      <th>singleNum</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>北京_北京</td>\n",
       "      <td>河北_保定</td>\n",
       "      <td>1919</td>\n",
       "      <td>1919</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>北京_北京</td>\n",
       "      <td>河北_廊坊</td>\n",
       "      <td>1211</td>\n",
       "      <td>1211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>北京_北京</td>\n",
       "      <td>河北_张家口</td>\n",
       "      <td>1127</td>\n",
       "      <td>1127</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>江苏_苏州</td>\n",
       "      <td>上海_上海</td>\n",
       "      <td>969</td>\n",
       "      <td>969</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>广东_深圳</td>\n",
       "      <td>广西_玉林</td>\n",
       "      <td>902</td>\n",
       "      <td>902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3995</th>\n",
       "      <td>山东_青岛</td>\n",
       "      <td>山西_长治</td>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3996</th>\n",
       "      <td>广西_南宁</td>\n",
       "      <td>浙江_温州</td>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3997</th>\n",
       "      <td>广西_南宁</td>\n",
       "      <td>河南_郑州</td>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3998</th>\n",
       "      <td>江苏_泰州</td>\n",
       "      <td>安徽_淮北</td>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3999</th>\n",
       "      <td>江苏_宿迁</td>\n",
       "      <td>安徽_六安</td>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>4000 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      start     end   num  singleNum\n",
       "0     北京_北京   河北_保定  1919       1919\n",
       "1     北京_北京   河北_廊坊  1211       1211\n",
       "2     北京_北京  河北_张家口  1127       1127\n",
       "3     江苏_苏州   上海_上海   969        969\n",
       "4     广东_深圳   广西_玉林   902        902\n",
       "...     ...     ...   ...        ...\n",
       "3995  山东_青岛   山西_长治     9          9\n",
       "3996  广西_南宁   浙江_温州     9          9\n",
       "3997  广西_南宁   河南_郑州     9          9\n",
       "3998  江苏_泰州   安徽_淮北     9          9\n",
       "3999  江苏_宿迁   安徽_六安     9          9\n",
       "\n",
       "[4000 rows x 4 columns]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import json\n",
    "with open('csv/migration.json') as f:\n",
    "    migration_str = f.read()\n",
    "migration_json = json.loads(migration_str)\n",
    "mig_data = pd.DataFrame(migration_json['allLine'])\n",
    "mig_data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "hidden-setting",
   "metadata": {},
   "source": [
    "注意以上的数据并不是一个足够好的数据：可能存在南宁到温州，但是没有温州到南宁的数据，为此，我们先把所有的城市列表整理出来，然后形成一个城市×城市的新的空数据集："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "married-trace",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>zeros</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>start</th>\n",
       "      <th>end</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"5\" valign=\"top\">宁夏_固原</th>\n",
       "      <th>宁夏_固原</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>湖北_襄阳</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>黑龙江_黑河</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>天津_天津</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>新疆_喀什</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"5\" valign=\"top\">黑龙江_大兴安岭</th>\n",
       "      <th>辽宁_铁岭</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>黑龙江_哈尔滨</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>四川_内江</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>海南_临高</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>黑龙江_大兴安岭</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>117649 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                   zeros\n",
       "start    end            \n",
       "宁夏_固原    宁夏_固原       0.0\n",
       "         湖北_襄阳       0.0\n",
       "         黑龙江_黑河      0.0\n",
       "         天津_天津       0.0\n",
       "         新疆_喀什       0.0\n",
       "...                  ...\n",
       "黑龙江_大兴安岭 辽宁_铁岭       0.0\n",
       "         黑龙江_哈尔滨     0.0\n",
       "         四川_内江       0.0\n",
       "         海南_临高       0.0\n",
       "         黑龙江_大兴安岭    0.0\n",
       "\n",
       "[117649 rows x 1 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "del mig_data['singleNum']\n",
    "city_set = set(mig_data['start'])\n",
    "city_set2 = set(mig_data['end'])\n",
    "city_set.update(city_set2)\n",
    "city_index = pd.Series(list(city_set))\n",
    "mid_data_matrix = pd.DataFrame(np.zeros((len(city_set), len(city_set))))\n",
    "mid_data_matrix = mid_data_matrix.set_index(city_index)\n",
    "mid_data_matrix = mid_data_matrix.T.set_index(city_index)\n",
    "mid_data_matrix = mid_data_matrix.stack()\n",
    "mid_data_matrix = pd.DataFrame({'zeros': mid_data_matrix})\n",
    "mid_data_matrix.index.names = ['start', 'end']\n",
    "mid_data_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "romantic-board",
   "metadata": {},
   "source": [
    "可以看到数据集中总共有343个城市，从而上面的matrix共有343×343=117649行。\n",
    "\n",
    "接下来将迁徙数据设定索引："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "juvenile-blind",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>num</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>start</th>\n",
       "      <th>end</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"5\" valign=\"top\">上海_上海</th>\n",
       "      <th>云南_昆明</th>\n",
       "      <td>29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>云南_曲靖</th>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>内蒙古_乌兰察布</th>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>北京_北京</th>\n",
       "      <td>144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>台湾_台北</th>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>黑龙江_牡丹江</th>\n",
       "      <th>北京_北京</th>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>黑龙江_黑河</th>\n",
       "      <th>内蒙古_呼伦贝尔</th>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">黑龙江_齐齐哈尔</th>\n",
       "      <th>内蒙古_兴安盟</th>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>内蒙古_呼伦贝尔</th>\n",
       "      <td>61</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>北京_北京</th>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>4000 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                   num\n",
       "start    end          \n",
       "上海_上海    云南_昆明      29\n",
       "         云南_曲靖      10\n",
       "         内蒙古_乌兰察布   11\n",
       "         北京_北京     144\n",
       "         台湾_台北      23\n",
       "...                ...\n",
       "黑龙江_牡丹江  北京_北京       9\n",
       "黑龙江_黑河   内蒙古_呼伦贝尔   15\n",
       "黑龙江_齐齐哈尔 内蒙古_兴安盟    18\n",
       "         内蒙古_呼伦贝尔   61\n",
       "         北京_北京      13\n",
       "\n",
       "[4000 rows x 1 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mig_data = mig_data.set_index(['start', 'end'])\n",
    "mig_data = mig_data.sort_index()\n",
    "mig_data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adjacent-arkansas",
   "metadata": {},
   "source": [
    "然后将两者合并，从而获得了一个117649行的新数据，如果两个地方之间没有迁徙数据，那么就是NaN："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "great-collapse",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "</style>\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>num</th>\n",
       "      <th>zeros</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>start</th>\n",
       "      <th>end</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"5\" valign=\"top\">上海_上海</th>\n",
       "      <th>上海_上海</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>云南_临沧</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>云南_丽江</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>云南_大理</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>云南_文山</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"5\" valign=\"top\">黑龙江_齐齐哈尔</th>\n",
       "      <th>黑龙江_绥化</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>黑龙江_鸡西</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>黑龙江_鹤岗</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>黑龙江_黑河</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>黑龙江_齐齐哈尔</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>117649 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                   num  zeros\n",
       "start    end                 \n",
       "上海_上海    上海_上海     NaN    0.0\n",
       "         云南_临沧     NaN    0.0\n",
       "         云南_丽江     NaN    0.0\n",
       "         云南_大理     NaN    0.0\n",
       "         云南_文山     NaN    0.0\n",
       "...                ...    ...\n",
       "黑龙江_齐齐哈尔 黑龙江_绥化    NaN    0.0\n",
       "         黑龙江_鸡西    NaN    0.0\n",
       "         黑龙江_鹤岗    NaN    0.0\n",
       "         黑龙江_黑河    NaN    0.0\n",
       "         黑龙江_齐齐哈尔  NaN    0.0\n",
       "\n",
       "[117649 rows x 2 columns]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mig_data = pd.merge(mig_data,\n",
    "                    mid_data_matrix,\n",
    "                    how='outer',\n",
    "                    left_index=True,\n",
    "                    right_index=True)\n",
    "mig_data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "prescribed-trainer",
   "metadata": {},
   "source": [
    "接着整理为迁徙矩阵："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "buried-tackle",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>0.0</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>343 rows × 343 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "end       上海_上海  云南_临沧  云南_丽江  云南_大理  云南_文山  云南_昆明  云南_昭通  云南_普洱  云南_曲靖  \\\n",
       "start                                                                     \n",
       "上海_上海       0.0    0.0    0.0    0.0    0.0   29.0    0.0    0.0   10.0   \n",
       "云南_临沧       0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0   \n",
       "云南_丽江       0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0   \n",
       "云南_大理       0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0   \n",
       "云南_文山       0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0   \n",
       "...         ...    ...    ...    ...    ...    ...    ...    ...    ...   \n",
       "黑龙江_绥化      0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0   \n",
       "黑龙江_鸡西      0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0   \n",
       "黑龙江_鹤岗      0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0   \n",
       "黑龙江_黑河      0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0   \n",
       "黑龙江_齐齐哈尔    0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0   \n",
       "\n",
       "end       云南_楚雄  ...  黑龙江_双鸭山  黑龙江_哈尔滨  黑龙江_大兴安岭  黑龙江_大庆  黑龙江_牡丹江  黑龙江_绥化  \\\n",
       "start            ...                                                        \n",
       "上海_上海       0.0  ...      0.0     55.0       0.0     0.0     12.0     0.0   \n",
       "云南_临沧       0.0  ...      0.0      0.0       0.0     0.0      0.0     0.0   \n",
       "云南_丽江       0.0  ...      0.0      0.0       0.0     0.0      0.0     0.0   \n",
       "云南_大理       0.0  ...      0.0      0.0       0.0     0.0      0.0     0.0   \n",
       "云南_文山       0.0  ...      0.0      0.0       0.0     0.0      0.0     0.0   \n",
       "...         ...  ...      ...      ...       ...     ...      ...     ...   \n",
       "黑龙江_绥化      0.0  ...      0.0      0.0       0.0     0.0      0.0     0.0   \n",
       "黑龙江_鸡西      0.0  ...      0.0      0.0       0.0     0.0      0.0     0.0   \n",
       "黑龙江_鹤岗      0.0  ...      0.0      0.0       0.0     0.0      0.0     0.0   \n",
       "黑龙江_黑河      0.0  ...      0.0      0.0       0.0     0.0      0.0     0.0   \n",
       "黑龙江_齐齐哈尔    0.0  ...      0.0      0.0       0.0     0.0      0.0     0.0   \n",
       "\n",
       "end       黑龙江_鸡西  黑龙江_鹤岗  黑龙江_黑河  黑龙江_齐齐哈尔  \n",
       "start                                       \n",
       "上海_上海        0.0     0.0     0.0      11.0  \n",
       "云南_临沧        0.0     0.0     0.0       0.0  \n",
       "云南_丽江        0.0     0.0     0.0       0.0  \n",
       "云南_大理        0.0     0.0     0.0       0.0  \n",
       "云南_文山        0.0     0.0     0.0       0.0  \n",
       "...          ...     ...     ...       ...  \n",
       "黑龙江_绥化       0.0     0.0     0.0       0.0  \n",
       "黑龙江_鸡西       0.0     0.0     0.0       0.0  \n",
       "黑龙江_鹤岗       0.0     0.0     0.0       0.0  \n",
       "黑龙江_黑河       0.0     0.0     0.0       0.0  \n",
       "黑龙江_齐齐哈尔     0.0     0.0     0.0       0.0  \n",
       "\n",
       "[343 rows x 343 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mig_data = mig_data.fillna(0)\n",
    "mig_data = mig_data['num']\n",
    "mig_data = mig_data.unstack()\n",
    "mig_data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "front-affair",
   "metadata": {},
   "source": [
    "计算距离矩阵。注意距离的定义要求A到B的距离等于B到A的距离。所以我们首先要将其变为一个对称矩阵（$X+X'$就是一个对称矩阵了），此外两个城市之间的迁徙人数越多则距离越近，所以我们需要进行一定的转换："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "under-summit",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>end</th>\n",
       "      <th>上海_上海</th>\n",
       "      <th>云南_临沧</th>\n",
       "      <th>云南_丽江</th>\n",
       "      <th>云南_大理</th>\n",
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       "      <th>云南_楚雄</th>\n",
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       "      <th></th>\n",
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       "  <tbody>\n",
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       "      <th>上海_上海</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>4.815940</td>\n",
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       "      <td>7.902833</td>\n",
       "      <td>6.703885</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>...</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>5.890157</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>6.620358</td>\n",
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       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>6.660380</td>\n",
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       "    <tr>\n",
       "      <th>云南_临沧</th>\n",
       "      <td>7.902833</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>...</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
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       "      <th>云南_丽江</th>\n",
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       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
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       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
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       "    <tr>\n",
       "      <th>云南_大理</th>\n",
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       "      <td>7.902833</td>\n",
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       "      <td>7.902833</td>\n",
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       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
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       "    <tr>\n",
       "      <th>云南_文山</th>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
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       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
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       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>黑龙江_绥化</th>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
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       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
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       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>黑龙江_鸡西</th>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>...</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>黑龙江_鹤岗</th>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>...</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>黑龙江_黑河</th>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>...</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>7.902833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>黑龙江_齐齐哈尔</th>\n",
       "      <td>6.660380</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>...</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>7.902833</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>343 rows × 343 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "end          上海_上海     云南_临沧     云南_丽江     云南_大理     云南_文山     云南_昆明  \\\n",
       "start                                                                  \n",
       "上海_上海     0.000000  7.902833  7.902833  7.902833  7.902833  4.815940   \n",
       "云南_临沧     7.902833  0.000000  7.902833  7.902833  7.902833  7.902833   \n",
       "云南_丽江     7.902833  7.902833  0.000000  7.902833  7.902833  7.902833   \n",
       "云南_大理     7.902833  7.902833  7.902833  0.000000  7.902833  7.902833   \n",
       "云南_文山     7.902833  7.902833  7.902833  7.902833  0.000000  7.902833   \n",
       "...            ...       ...       ...       ...       ...       ...   \n",
       "黑龙江_绥化    7.902833  7.902833  7.902833  7.902833  7.902833  7.902833   \n",
       "黑龙江_鸡西    7.902833  7.902833  7.902833  7.902833  7.902833  7.902833   \n",
       "黑龙江_鹤岗    7.902833  7.902833  7.902833  7.902833  7.902833  7.902833   \n",
       "黑龙江_黑河    7.902833  7.902833  7.902833  7.902833  7.902833  7.902833   \n",
       "黑龙江_齐齐哈尔  6.660380  7.902833  7.902833  7.902833  7.902833  7.902833   \n",
       "\n",
       "end          云南_昭通     云南_普洱     云南_曲靖     云南_楚雄  ...   黑龙江_双鸭山   黑龙江_哈尔滨  \\\n",
       "start                                             ...                       \n",
       "上海_上海     7.902833  7.902833  6.703885  7.902833  ...  7.902833  5.890157   \n",
       "云南_临沧     7.902833  7.902833  7.902833  7.902833  ...  7.902833  7.902833   \n",
       "云南_丽江     7.902833  7.902833  7.902833  7.902833  ...  7.902833  7.902833   \n",
       "云南_大理     7.902833  7.902833  7.902833  7.902833  ...  7.902833  7.902833   \n",
       "云南_文山     7.902833  7.902833  7.902833  7.902833  ...  7.902833  7.902833   \n",
       "...            ...       ...       ...       ...  ...       ...       ...   \n",
       "黑龙江_绥化    7.902833  7.902833  7.902833  7.902833  ...  7.902833  7.902833   \n",
       "黑龙江_鸡西    7.902833  7.902833  7.902833  7.902833  ...  7.902833  7.902833   \n",
       "黑龙江_鹤岗    7.902833  7.902833  7.902833  7.902833  ...  7.902833  7.902833   \n",
       "黑龙江_黑河    7.902833  7.902833  7.902833  7.902833  ...  7.902833  7.902833   \n",
       "黑龙江_齐齐哈尔  7.902833  7.902833  7.902833  7.902833  ...  7.902833  7.902833   \n",
       "\n",
       "end       黑龙江_大兴安岭    黑龙江_大庆   黑龙江_牡丹江    黑龙江_绥化    黑龙江_鸡西    黑龙江_鹤岗  \\\n",
       "start                                                                  \n",
       "上海_上海     7.902833  7.902833  6.620358  7.902833  7.902833  7.902833   \n",
       "云南_临沧     7.902833  7.902833  7.902833  7.902833  7.902833  7.902833   \n",
       "云南_丽江     7.902833  7.902833  7.902833  7.902833  7.902833  7.902833   \n",
       "云南_大理     7.902833  7.902833  7.902833  7.902833  7.902833  7.902833   \n",
       "云南_文山     7.902833  7.902833  7.902833  7.902833  7.902833  7.902833   \n",
       "...            ...       ...       ...       ...       ...       ...   \n",
       "黑龙江_绥化    7.902833  7.902833  7.902833  0.000000  7.902833  7.902833   \n",
       "黑龙江_鸡西    7.902833  7.902833  7.902833  7.902833  0.000000  7.902833   \n",
       "黑龙江_鹤岗    7.902833  7.902833  7.902833  7.902833  7.902833  0.000000   \n",
       "黑龙江_黑河    7.902833  7.902833  7.902833  7.902833  7.902833  7.902833   \n",
       "黑龙江_齐齐哈尔  7.902833  7.902833  7.902833  7.902833  7.902833  7.902833   \n",
       "\n",
       "end         黑龙江_黑河  黑龙江_齐齐哈尔  \n",
       "start                         \n",
       "上海_上海     7.902833  6.660380  \n",
       "云南_临沧     7.902833  7.902833  \n",
       "云南_丽江     7.902833  7.902833  \n",
       "云南_大理     7.902833  7.902833  \n",
       "云南_文山     7.902833  7.902833  \n",
       "...            ...       ...  \n",
       "黑龙江_绥化    7.902833  7.902833  \n",
       "黑龙江_鸡西    7.902833  7.902833  \n",
       "黑龙江_鹤岗    7.902833  7.902833  \n",
       "黑龙江_黑河    0.000000  7.902833  \n",
       "黑龙江_齐齐哈尔  7.902833  0.000000  \n",
       "\n",
       "[343 rows x 343 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 取log，相当于百分比距离\n",
    "dist = (np.log(1 + mig_data) + np.log(1 + mig_data.T)) / 2\n",
    "# 迁徙人数越多，距离越近，所以取相反数；为了保证距离为正，加上所有距离的最大值\n",
    "dist = dist.max().max() - dist + 1\n",
    "# 自己到自己的距离为0，需要额外处理：\n",
    "EYE = pd.DataFrame(np.eye(dist.shape[0])).set_index(dist.index).T.set_index(\n",
    "    dist.index)\n",
    "dist = dist - dist.iloc[0, 0] * EYE\n",
    "dist"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "located-glory",
   "metadata": {},
   "source": [
    "接下来就可以使用Scikit-learn中的Isomap进行训练了。\n",
    "\n",
    "在使用该方法时，需要提供：\n",
    "\n",
    "* n_neighbors:将最近的多少个点视为邻居？\n",
    "* n_components：嵌入到多少维的空间？\n",
    "* metric：使用何种距离度量？对于一般数据集而言，欧氏距离、马氏距离等都可以使用，或者可以设定为\"precomputed\"，即已经计算好的距离矩阵\n",
    "\n",
    "注意如果我们是一个$N\\times K$的数据集，即$N$个样本点，$K$个特征，我们完全可以使用Isomap对象自动计算$N\\times N$的距离矩阵。不过在这里，我们上面的数据是已经计算好的$N\\times N$的距离矩阵，所以只需要设定为\"precomputed\"即可。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "violent-atlanta",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>end</th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>start</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>上海_上海</th>\n",
       "      <td>-1.992665</td>\n",
       "      <td>0.106905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>云南_临沧</th>\n",
       "      <td>6.413352</td>\n",
       "      <td>5.949499</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>云南_丽江</th>\n",
       "      <td>3.539024</td>\n",
       "      <td>1.778862</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>云南_大理</th>\n",
       "      <td>1.303765</td>\n",
       "      <td>0.068470</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>云南_文山</th>\n",
       "      <td>-1.682454</td>\n",
       "      <td>6.540387</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>黑龙江_绥化</th>\n",
       "      <td>-3.573274</td>\n",
       "      <td>-1.383274</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>黑龙江_鸡西</th>\n",
       "      <td>1.786944</td>\n",
       "      <td>-4.978355</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>黑龙江_鹤岗</th>\n",
       "      <td>2.005302</td>\n",
       "      <td>-5.047238</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>黑龙江_黑河</th>\n",
       "      <td>1.633626</td>\n",
       "      <td>-5.201434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>黑龙江_齐齐哈尔</th>\n",
       "      <td>-2.991813</td>\n",
       "      <td>-5.025370</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>343 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "end              x         y\n",
       "start                       \n",
       "上海_上海    -1.992665  0.106905\n",
       "云南_临沧     6.413352  5.949499\n",
       "云南_丽江     3.539024  1.778862\n",
       "云南_大理     1.303765  0.068470\n",
       "云南_文山    -1.682454  6.540387\n",
       "...            ...       ...\n",
       "黑龙江_绥化   -3.573274 -1.383274\n",
       "黑龙江_鸡西    1.786944 -4.978355\n",
       "黑龙江_鹤岗    2.005302 -5.047238\n",
       "黑龙江_黑河    1.633626 -5.201434\n",
       "黑龙江_齐齐哈尔 -2.991813 -5.025370\n",
       "\n",
       "[343 rows x 2 columns]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.manifold import Isomap\n",
    "\n",
    "embedding = Isomap(n_neighbors=8, n_components=2, metric=\"precomputed\")\n",
    "coordinates = embedding.fit_transform(dist)\n",
    "dist['x'] = coordinates[:, 0]\n",
    "dist['y'] = coordinates[:, 1]\n",
    "dist.iloc[:, -2:]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "extensive-visiting",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 2000x2000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (20.0, 20.0)\n",
    "plt.scatter(dist['x'],dist['y'], marker=\"x\")\n",
    "city_list=[\"上海_上海\",\"北京_北京\",\"广东_广州\",\"广东_深圳\"]\n",
    "plt.scatter(dist['x'][city_list],dist['y'][city_list], color='black')\n",
    "city_list=[\"浙江_杭州\",\"江苏_南京\",\"湖南_长沙\"]\n",
    "plt.scatter(dist['x'][city_list],dist['y'][city_list], color='red')\n",
    "city_list=[\"山东_济南\",\"河北_石家庄\",\"辽宁_沈阳\",\"新疆_乌鲁木齐\"]\n",
    "plt.scatter(dist['x'][city_list],dist['y'][city_list], color='orange')\n",
    "city_list=[\"陕西_西安\"]\n",
    "plt.scatter(dist['x'][city_list],dist['y'][city_list], color='blue')\n",
    "city_list=[\"陕西_渭南\"]\n",
    "plt.scatter(dist['x'][city_list],dist['y'][city_list], color='green')\n",
    "city_list=[\"四川_成都\"]\n",
    "plt.scatter(dist['x'][city_list],dist['y'][city_list], color='pink')\n",
    "city_list=[\"湖北_武汉\"]\n",
    "plt.scatter(dist['x'][city_list],dist['y'][city_list], color='yellow')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "usual-abuse",
   "metadata": {},
   "source": [
    "此外，还有**局部线性嵌入**（**locally linear embedding, LLE**）的方法。Isomap是保持局部的距离结构，而LLE则是保持局部的线性关系。所谓线性关系，即在某个点$x$的邻域中，找到另外的几个临近的样本$x_1,x_2,x_3,..,x_k$使得：$$x=\\omega_1 x_1+\\omega_2 x_2+\\cdots+\\omega_k x_k$$LLE要求如果在高维空间中有如上的线性结构，那么嵌入到低维空间中仍然保持这样的线性结构。在此我们不再赘述。"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "31f2aee4e71d21fbe5cf8b01ff0e069b9275f58929596ceb00d14d90e3e16cd6"
  },
  "kernelspec": {
   "display_name": "Anaconda",
   "language": "python",
   "name": "anaconda"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}