Clustering.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 聚类分析简介\n",
    "\n",
    "**聚类**（**clustering**）分析是经典的无监督学习问题。聚类分析通常是指，给定样本的特征，根据不同样本之间的相似度或者距离度量，将样本归结到若干个“类”中。\n",
    "\n",
    "同样是分类问题，注意聚类是无监督学习，这与我们接下来要介绍的有监督的分类比如Logistic回归、分类树等有很大区别。在有监督学习中，根据标签，我们已经知道每个样本属于哪一类，机器学习的目的是为了通过特征对分类进行**预测**。而在聚类分析中，每个样本属于哪一类是未知的，我们必须根据样本特征对样本进行划分。\n",
    "\n",
    "聚类分析通常可以作为一个单独的过程，比如对于电商，如果我们想了解顾客在“电子产品”、“生鲜”、“书籍”等品类中的购买偏好，我们可以根据这些顾客在不同品类中的购买量对顾客进行分类。\n",
    "\n",
    "有时聚类也可以与其他分析结合起来，比如经过以上分类之后，将以上聚类分析的结果作为标签，我们可以使用顾客的其他特征，诸如性别、年龄、职业等，对以上结果标签使用监督学习的方法进行预测。这样当新的客户到来时，我们就可以使用以上监督学习的模型对新客户的类别进行预测。\n",
    "\n",
    "接下来我们介绍以下聚类分析的基本原理。我们先从不同样本之间的“相似度”或者“距离”开始。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 样本之间的距离度量\n",
    "\n",
    "聚类分析的基础是使用一定的指标度量每个样本之间的距离。比如如果我们有以下数据，希望将以上同学分为“理科”和“文科”生，"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\n",
       "\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>语文</th>\n",
       "      <th>数学</th>\n",
       "      <th>英语</th>\n",
       "      <th>物理</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>name</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Aragorn</th>\n",
       "      <td>95</td>\n",
       "      <td>115</td>\n",
       "      <td>98</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Frodo</th>\n",
       "      <td>115</td>\n",
       "      <td>87</td>\n",
       "      <td>108</td>\n",
       "      <td>67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bilbo</th>\n",
       "      <td>110</td>\n",
       "      <td>114</td>\n",
       "      <td>115</td>\n",
       "      <td>78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Gandalf</th>\n",
       "      <td>98</td>\n",
       "      <td>108</td>\n",
       "      <td>78</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Legolas</th>\n",
       "      <td>100</td>\n",
       "      <td>103</td>\n",
       "      <td>115</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sam</th>\n",
       "      <td>108</td>\n",
       "      <td>102</td>\n",
       "      <td>102</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arwen</th>\n",
       "      <td>88</td>\n",
       "      <td>85</td>\n",
       "      <td>78</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          语文   数学   英语  物理\n",
       "name                      \n",
       "Aragorn   95  115   98  95\n",
       "Frodo    115   87  108  67\n",
       "Bilbo    110  114  115  78\n",
       "Gandalf   98  108   78  99\n",
       "Legolas  100  103  115  90\n",
       "Sam      108  102  102  98\n",
       "Arwen     88   85   78  75"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "scores = [\n",
    "    {\n",
    "        'name': 'Aragorn',\n",
    "        '语文': 95,\n",
    "        '数学': 115,\n",
    "        '英语': 98,\n",
    "        '物理': 95\n",
    "    },\n",
    "    {\n",
    "        'name': 'Frodo',\n",
    "        '语文': 115,\n",
    "        '数学': 87,\n",
    "        '英语': 108,\n",
    "        '物理': 67\n",
    "    },\n",
    "    {\n",
    "        'name': 'Bilbo',\n",
    "        '语文': 110,\n",
    "        '数学': 114,\n",
    "        '英语': 115,\n",
    "        '物理': 78\n",
    "    },\n",
    "    {\n",
    "        'name': 'Gandalf',\n",
    "        '语文': 98,\n",
    "        '数学': 108,\n",
    "        '英语': 78,\n",
    "        '物理': 99\n",
    "    },\n",
    "    {\n",
    "        'name': 'Legolas',\n",
    "        '语文': 100,\n",
    "        '数学': 103,\n",
    "        '英语': 115,\n",
    "        '物理': 90\n",
    "    },\n",
    "    {\n",
    "        'name': 'Sam',\n",
    "        '语文': 108,\n",
    "        '数学': 102,\n",
    "        '英语': 102,\n",
    "        '物理': 98\n",
    "    },\n",
    "    {\n",
    "        'name': 'Arwen',\n",
    "        '语文': 88,\n",
    "        '数学': 85,\n",
    "        '英语': 78,\n",
    "        '物理': 75\n",
    "    },\n",
    "]\n",
    "scores = pd.DataFrame(scores).set_index('name')\n",
    "scores.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "其中每一个样本都可以看作是一个4维的向量，那么度量两个向量之间的距离，一个最简单的方法是直接使用**欧氏距离**（**Euclidean distance**）：$$d_{ij}=||x_i-x_j||_2=\\left[\\sum_{k=1}^K \\left(x_{ik}-x_{jk}\\right)^2\\right]^{\\frac{1}{2}}=\\sqrt{\\left(x_i- x_j\\right)'\\left(x_i- x_j\\right)}$$\n",
    "\n",
    "使用Numpy可以非常方便的计算这个距离，比如计算Aragorn和Frodo的距离："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "45.47526800360829"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "np.sqrt(\n",
    "    np.inner(scores.iloc[0, :] - scores.iloc[1, :],\n",
    "             scores.iloc[0, :] - scores.iloc[1, :]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "或者可以直接使用Numpy中的范数函数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "45.47526800360829"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(scores.iloc[0, :] - scores.iloc[1, :])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "实际上我们可以定义更加广义的**闵科夫斯基距离**（**Minkowski distance**）：$$d_{ij}=\\left[\\sum_{k=1}^K \\left|x_{ik}-x_{jk}\\right|^p\\right]^{\\frac{1}{p}}$$其中：\n",
    "* 当$p=2$时，即$||x_i-x_j||_2$，使用L2范数，计算出的是欧氏距离;\n",
    "* 当$p=1$时，即$||x_i-x_j||_1$，使用L1范数，计算出的曼哈顿距离（Manhattan distance）;\n",
    "* 当$p=\\infty$时，即$||x_i-x_j||_\\infty=\\max_k \\left|x_{ik}-x_{jk}\\right|$，切比雪夫距离（Chebyshev distance）;\n",
    "\n",
    "所有以上的距离都可以使用范数函数进行计算，比如："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "曼哈顿距离= 86.0\n",
      "欧式距离= 45.47526800360829\n",
      "切比雪夫距离= 28.0\n"
     ]
    }
   ],
   "source": [
    "print(\"曼哈顿距离=\", np.linalg.norm(scores.iloc[0, :] - scores.iloc[1, :], ord=1))\n",
    "print(\"欧式距离=\", np.linalg.norm(scores.iloc[0, :] - scores.iloc[1, :], ord=2))\n",
    "print(\"切比雪夫距离=\",\n",
    "      np.linalg.norm(scores.iloc[0, :] - scores.iloc[1, :], ord=np.inf))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "此外，如果需要计算每个样本距离某一个样本的距离，我们可以使用广播功能和norm函数结合的方法，比如计算与第一个样本的距离，首先使用广播功能："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>语文</th>\n",
       "      <th>数学</th>\n",
       "      <th>英语</th>\n",
       "      <th>物理</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>name</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Aragorn</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Frodo</th>\n",
       "      <td>20</td>\n",
       "      <td>-28</td>\n",
       "      <td>10</td>\n",
       "      <td>-28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bilbo</th>\n",
       "      <td>15</td>\n",
       "      <td>-1</td>\n",
       "      <td>17</td>\n",
       "      <td>-17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Gandalf</th>\n",
       "      <td>3</td>\n",
       "      <td>-7</td>\n",
       "      <td>-20</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Legolas</th>\n",
       "      <td>5</td>\n",
       "      <td>-12</td>\n",
       "      <td>17</td>\n",
       "      <td>-5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sam</th>\n",
       "      <td>13</td>\n",
       "      <td>-13</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arwen</th>\n",
       "      <td>-7</td>\n",
       "      <td>-30</td>\n",
       "      <td>-20</td>\n",
       "      <td>-20</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         语文  数学  英语  物理\n",
       "name                   \n",
       "Aragorn   0   0   0   0\n",
       "Frodo    20 -28  10 -28\n",
       "Bilbo    15  -1  17 -17\n",
       "Gandalf   3  -7 -20   4\n",
       "Legolas   5 -12  17  -5\n",
       "Sam      13 -13   4   3\n",
       "Arwen    -7 -30 -20 -20"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores - scores.iloc[0, :]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "接下来使用norm函数的axis选项即可："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        , 45.475268  , 28.35489376, 21.77154106, 21.97726098,\n",
       "       19.05255888, 41.82104733])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(scores - scores.iloc[0, :], axis=1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以发现与Aragorn最接近的是Sam。\n",
    "\n",
    "虽然以上距离定义非常经典，但是仍然有很多问题，比如，如果我们对这些数据做一个描述性统计："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>语文</th>\n",
       "      <th>数学</th>\n",
       "      <th>英语</th>\n",
       "      <th>物理</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>7.000000</td>\n",
       "      <td>7.0</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>7.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>102.000000</td>\n",
       "      <td>102.0</td>\n",
       "      <td>99.142857</td>\n",
       "      <td>86.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>9.433981</td>\n",
       "      <td>12.0</td>\n",
       "      <td>15.731376</td>\n",
       "      <td>12.622731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>88.000000</td>\n",
       "      <td>85.0</td>\n",
       "      <td>78.000000</td>\n",
       "      <td>67.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>96.500000</td>\n",
       "      <td>94.5</td>\n",
       "      <td>88.000000</td>\n",
       "      <td>76.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>103.0</td>\n",
       "      <td>102.000000</td>\n",
       "      <td>90.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>109.000000</td>\n",
       "      <td>111.0</td>\n",
       "      <td>111.500000</td>\n",
       "      <td>96.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>115.000000</td>\n",
       "      <td>115.0</td>\n",
       "      <td>115.000000</td>\n",
       "      <td>99.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               语文     数学          英语         物理\n",
       "count    7.000000    7.0    7.000000   7.000000\n",
       "mean   102.000000  102.0   99.142857  86.000000\n",
       "std      9.433981   12.0   15.731376  12.622731\n",
       "min     88.000000   85.0   78.000000  67.000000\n",
       "25%     96.500000   94.5   88.000000  76.500000\n",
       "50%    100.000000  103.0  102.000000  90.000000\n",
       "75%    109.000000  111.0  111.500000  96.500000\n",
       "max    115.000000  115.0  115.000000  99.000000"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们会发现：\n",
    "\n",
    "* 语文、数学的平均分显著大于物理的平均分，其实这是由于语文、数学、外语的满分是120，物理的满分是100分\n",
    "* 语文的标准差很小，但是英语的标准差就很大\n",
    "\n",
    "此外，如果我们计算以下四个成绩的相关性："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>语文</th>\n",
       "      <th>数学</th>\n",
       "      <th>英语</th>\n",
       "      <th>物理</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>语文</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.032389</td>\n",
       "      <td>0.691780</td>\n",
       "      <td>-0.291114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>数学</th>\n",
       "      <td>0.032389</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.256918</td>\n",
       "      <td>0.632677</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>英语</th>\n",
       "      <td>0.691780</td>\n",
       "      <td>0.256918</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.209831</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>物理</th>\n",
       "      <td>-0.291114</td>\n",
       "      <td>0.632677</td>\n",
       "      <td>-0.209831</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          语文        数学        英语        物理\n",
       "语文  1.000000  0.032389  0.691780 -0.291114\n",
       "数学  0.032389  1.000000  0.256918  0.632677\n",
       "英语  0.691780  0.256918  1.000000 -0.209831\n",
       "物理 -0.291114  0.632677 -0.209831  1.000000"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "会发现：\n",
    "\n",
    "* 语文和数学成绩几乎不相关，和英语成绩高度相关，和物理成绩有负相关系；\n",
    "* 数学和英语成绩几乎不相关，但是数学和物理成绩高度相关\n",
    "\n",
    "可以想象，如果我们使用以上定义的距离，那么就会：\n",
    "\n",
    "* （尺度问题）忽略了不同科目之间平均值的差异，平均值越大的特征（科目）会更大的影响距离的度量；\n",
    "* （相关问题）忽略了不同科目之间的相关性，比如数学和物理、语文和英语之间有很强的相关性，有理由相信这些相关性强的科目携带的共同的信息，如果携带相同信息的变量很多，那么就会极大影响距离度量。\n",
    "\n",
    "因而在以上基础之上，通常会对欧氏距离进行推广，使用变量之间的协方差矩阵解决变量之间的尺度问题和相关问题，即**马氏距离**（**Mahalanobis distance**）：$$d_{ij}=\\left[\\left(x_i-x_j\\right)'\\Sigma^{-1}\\left(x_i-x_j\\right)\\right]^{\\frac{1}{2}}$$\n",
    "\n",
    "其中$\\Sigma$为协方差矩阵，比如以上数据的协方差矩阵："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "    }\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>语文</th>\n",
       "      <th>数学</th>\n",
       "      <th>英语</th>\n",
       "      <th>物理</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>语文</th>\n",
       "      <td>89.000000</td>\n",
       "      <td>3.666667</td>\n",
       "      <td>102.666667</td>\n",
       "      <td>-34.666667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>数学</th>\n",
       "      <td>3.666667</td>\n",
       "      <td>144.000000</td>\n",
       "      <td>48.500000</td>\n",
       "      <td>95.833333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>英语</th>\n",
       "      <td>102.666667</td>\n",
       "      <td>48.500000</td>\n",
       "      <td>247.476190</td>\n",
       "      <td>-41.666667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>物理</th>\n",
       "      <td>-34.666667</td>\n",
       "      <td>95.833333</td>\n",
       "      <td>-41.666667</td>\n",
       "      <td>159.333333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            语文          数学          英语          物理\n",
       "语文   89.000000    3.666667  102.666667  -34.666667\n",
       "数学    3.666667  144.000000   48.500000   95.833333\n",
       "英语  102.666667   48.500000  247.476190  -41.666667\n",
       "物理  -34.666667   95.833333  -41.666667  159.333333"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores.cov()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果忽略掉协方差矩阵，其实就是欧氏距离。\n",
    "\n",
    "如果需要计算马氏距离，可以首先将数据矩阵右乘一个$\\Sigma^{-1/2}$，然后使用norm函数计算即可。实际上，如果我们记数据矩阵为：$$X=\\left[x_{ik}\\right]_{N\\times K}=\\left[\\begin{array}{c}\n",
    "x_{1}'\\\\\n",
    "x_{2}'\\\\\n",
    "\\vdots\\\\\n",
    "x_{N}'\n",
    "\\end{array}\\right]=\\left[\\begin{array}{cccc}\n",
    "x_{11} & x_{12} & \\cdots & x_{1K}\\\\\n",
    "x_{21} & x_{22} & \\cdots & x_{2K}\\\\\n",
    "\\vdots & \\vdots & \\ddots & \\vdots\\\\\n",
    "x_{N1} & x_{N2} & \\cdots & x_{NK}\n",
    "\\end{array}\\right]$$\n",
    "那么：$$\\tilde{X}=X\\Sigma^{-1/2}=\\left[\\begin{array}{c}\n",
    "x_{1}'\\\\\n",
    "x_{2}'\\\\\n",
    "\\vdots\\\\\n",
    "x_{N}'\n",
    "\\end{array}\\right]\\Sigma^{-1/2}=\\left[\\begin{array}{c}\n",
    "x_{1}'\\Sigma^{-1/2}\\\\\n",
    "x_{2}'\\Sigma^{-1/2}\\\\\n",
    "\\vdots\\\\\n",
    "x_{N}'\\Sigma^{-1/2}\n",
    "\\end{array}\\right]$$\n",
    "从而只需要计算不同样本之间$\\tilde{X}$的欧式距离即可得到马氏距离，比如我们还是计算与第一个样本之间的距离："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.14436173,  0.0042541 , -0.04163505,  0.0093362 ],\n",
       "       [ 0.0042541 ,  0.11467629, -0.02330029, -0.04645397],\n",
       "       [-0.04163505, -0.02330029,  0.08467504,  0.01637252],\n",
       "       [ 0.0093362 , -0.04645397,  0.01637252,  0.10719221]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#实对称矩阵的特征值分解\n",
    "ev, evec = np.linalg.eigh(scores.cov())\n",
    "#计算\\Sigma^{-1/2}\n",
    "sigma_1_2 = evec @ np.diag(np.power(ev, -0.5)) @ evec.T\n",
    "sigma_1_2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "进而计算$$\\tilde{X}=X\\Sigma^{-1/2}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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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></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>name</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Aragorn</th>\n",
       "      <td>11.010289</td>\n",
       "      <td>6.895357</td>\n",
       "      <td>3.218680</td>\n",
       "      <td>7.332499</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Frodo</th>\n",
       "      <td>13.100645</td>\n",
       "      <td>4.837211</td>\n",
       "      <td>3.426707</td>\n",
       "      <td>5.982277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bilbo</th>\n",
       "      <td>12.304950</td>\n",
       "      <td>7.238104</td>\n",
       "      <td>3.778597</td>\n",
       "      <td>5.975061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Gandalf</th>\n",
       "      <td>12.283642</td>\n",
       "      <td>6.385575</td>\n",
       "      <td>1.628866</td>\n",
       "      <td>7.787004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Legolas</th>\n",
       "      <td>10.926572</td>\n",
       "      <td>5.376677</td>\n",
       "      <td>4.647721</td>\n",
       "      <td>7.678999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sam</th>\n",
       "      <td>12.693157</td>\n",
       "      <td>5.227305</td>\n",
       "      <td>3.368146</td>\n",
       "      <td>8.444838</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arwen</th>\n",
       "      <td>10.518111</td>\n",
       "      <td>4.820375</td>\n",
       "      <td>2.188183</td>\n",
       "      <td>6.189470</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0         1         2         3\n",
       "name                                            \n",
       "Aragorn  11.010289  6.895357  3.218680  7.332499\n",
       "Frodo    13.100645  4.837211  3.426707  5.982277\n",
       "Bilbo    12.304950  7.238104  3.778597  5.975061\n",
       "Gandalf  12.283642  6.385575  1.628866  7.787004\n",
       "Legolas  10.926572  5.376677  4.647721  7.678999\n",
       "Sam      12.693157  5.227305  3.368146  8.444838\n",
       "Arwen    10.518111  4.820375  2.188183  6.189470"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_tilde = scores @ sigma_1_2\n",
    "X_tilde"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "最后计算距离："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 3.2360355 , 1.98740215, 2.14834499, 2.11556604,\n",
       "       2.62184614, 2.62987242])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(X_tilde - X_tilde.iloc[0, :], axis=1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以发现与第一个最接近的变成了Bilbo。\n",
    "\n",
    "除了以上的方法外，还有一个非常常用的相似度度量是余弦夹角：$$\\cos\\theta=\\frac{x_i' x_j}{|| x_i ||_2 \\cdot || x_j ||_2}$$其中分子上为两个向量的内积，而分母上为两个向量的$L^2$范数。$\\cos\\theta$越接近于1代表夹角越小，因而越相似。\n",
    "\n",
    "因而在这个度量中，只有两个向量之间的**角度**是重要的，范数（距离0的长度）并不重要。\n",
    "\n",
    "由于矩阵与向量的乘机就是内积，因而为了计算这个夹角，分子上可以使用矩阵乘积计算："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "name\n",
       "Aragorn    40879\n",
       "Frodo      37879\n",
       "Bilbo      42240\n",
       "Gandalf    38779\n",
       "Legolas    41165\n",
       "Sam        41296\n",
       "Arwen      32904\n",
       "dtype: int64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cos_fz = scores @ scores.iloc[0, :].T\n",
    "cos_fz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "然后计算分母："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "name\n",
       "Aragorn    40879.000000\n",
       "Frodo      38863.304196\n",
       "Bilbo      42605.539487\n",
       "Gandalf    38971.495827\n",
       "Legolas    41403.139808\n",
       "Sam        41473.181744\n",
       "Arwen      33023.778736\n",
       "dtype: float64"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cos_fm = np.linalg.norm(scores, axis=1) * np.linalg.norm(scores.iloc[0, :])\n",
    "cos_fm = pd.Series(cos_fm, index=scores.index)\n",
    "cos_fm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "最后计算余弦相似度："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "name\n",
       "Aragorn    1.000000\n",
       "Frodo      0.974673\n",
       "Bilbo      0.991420\n",
       "Gandalf    0.995061\n",
       "Legolas    0.994248\n",
       "Sam        0.995728\n",
       "Arwen      0.996373\n",
       "dtype: float64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cos_similarity = cos_fz / cos_fm\n",
    "cos_similarity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以看到这里反倒是Arwen跟Aragorn最相似，究其原因，是因为虽然Arwen的成绩普遍很低，所以计算距离时与Aragorn的距离差很远；但是两者的夹角却可以很小，从这点来看，余弦相似度忽略了分数的绝对高低的差别。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 类及其特征\n",
    "\n",
    "聚类的目的是为了让更相似的尽量在一类（cluster），而每个类应该足够的小。接下来我们主要讨论**硬聚类**（**hard clustering**），即每个样本都只能归属于一个类。\n",
    "\n",
    "如果我们已经将样本分为$M$个类$G_1,G_2,...,G_M$，对于每个类，我们可以定义其：\n",
    "\n",
    "* 中心，即每个类$G_m$中特征$x$的均指向量$x_m$；\n",
    "* 直径，即每个类$G_m$中距离最远的两个样本之间的距离\n",
    "* 方差，即每个类$G_m$的方差\n",
    "\n",
    "此外，对于两个类$G_m$和$G_{m'}$，我们还可以度量两个类之间的距离：\n",
    "\n",
    "* 单连接（single, 或最短距离），即两个类之间距离最近的两个样本之间的距离\n",
    "* 完全连接（complete, 或最长距离），即两个类之间距离最远的两个样本之间的距离\n",
    "* 中心距离，即两个类的中心之间的距离\n",
    "* 平均距离，两个类中每两个样本之间距离的平均值"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 层次聚类\n",
    "\n",
    "最简单的聚类方法是所谓的**层次聚类**（**Hierarchical clustering**）。该方法从每个样本开始，逐步的将距离最近的样本合并为一类。层次聚类有分为**聚合**（**agglomerative**）和**分裂**（**divisive**）两种，其中聚合指自下而上的将样本逐步合并，而分裂则是相反的过程。\n",
    "\n",
    "一般比较常用的是聚合聚类，聚合聚类需要确定三个基本的要素：\n",
    "\n",
    "* 距离或者相似度，可以是我们上面介绍的所有距离、相似度的度量\n",
    "* 合并规则，比如当往每个类里面添加元素时，可以要求使得每个类的方差最小、直径最小，或者任意两个类之间的距离（单连接、完全连接、中心距离、平均距离最小）\n",
    "* 停止条件，可以是类的个数达到一定数量、类的直径达到一定程度等等，就停止聚类。\n",
    "\n",
    "比如，针对以上数据，我们可以使用Scikit-Learn进行简单的聚合聚类："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>hirac_eucl</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>name</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Aragorn</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Frodo</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bilbo</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Gandalf</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Legolas</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sam</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arwen</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         hirac_eucl\n",
       "name               \n",
       "Aragorn           1\n",
       "Frodo             2\n",
       "Bilbo             1\n",
       "Gandalf           0\n",
       "Legolas           1\n",
       "Sam               1\n",
       "Arwen             0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.cluster import AgglomerativeClustering\n",
    "\n",
    "clustering_model = AgglomerativeClustering(n_clusters=3)\n",
    "clustering = clustering_model.fit(scores)\n",
    "result_cluster = pd.DataFrame({'hirac_eucl': clustering.labels_},\n",
    "                              index=scores.index)\n",
    "result_cluster"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "默认的使用欧氏距离、合并规则为最小化每个类的方差。我们可以使用图的方式很直观的理解以上过程："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "from scipy.cluster.hierarchy import dendrogram\n",
    "from sklearn.cluster import AgglomerativeClustering\n",
    "\n",
    "\n",
    "def plot_dendrogram(model, **kwargs):\n",
    "    # Create linkage matrix and then plot the dendrogram\n",
    "\n",
    "    # create the counts of samples under each node\n",
    "    counts = np.zeros(model.children_.shape[0])\n",
    "    n_samples = len(model.labels_)\n",
    "    for i, merge in enumerate(model.children_):\n",
    "        current_count = 0\n",
    "        for child_idx in merge:\n",
    "            if child_idx < n_samples:\n",
    "                current_count += 1  # leaf node\n",
    "            else:\n",
    "                current_count += counts[child_idx - n_samples]\n",
    "        counts[i] = current_count\n",
    "\n",
    "    linkage_matrix = np.column_stack(\n",
    "        [model.children_, model.distances_, counts]).astype(float)\n",
    "\n",
    "    # Plot the corresponding dendrogram\n",
    "    dendrogram(linkage_matrix, **kwargs)\n",
    "\n",
    "\n",
    "clustering = AgglomerativeClustering(distance_threshold=0,\n",
    "                                     n_clusters=None).fit(scores)\n",
    "plt.title('Hierarchical clustering')\n",
    "plot_dendrogram(clustering, truncate_mode='level', p=3)\n",
    "plt.xlabel(\"Number of points in node (or index of point if no parenthesis).\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "当然我们也可以使用其他距离度量，比如cos夹角（使用cos夹角不能使用最小方差的合并规则，这里使用最小化类之间的平均距离）："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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nADOzknICMDMrKScAM7OScgIwMyspJwAzs5JyAjAzKyknADOzkiqUACTNkbRRUrekc2uMP0DS9Xn8OkltFePOy+UbJZ1YUX6YpNWSfiTpAUlvHYkFMjOzYgZNAJJagMuBucAM4DRJM6qqLQS2R8Q04FLgkjztDGA+cAwwB7gitwfwD8A3IuJo4A3AA8NfHDMzK6rIEcBxQHdEbIqI54BVwLyqOvOAq/LwamC2JOXyVRHxbEQ8BHQDx0maALwTWAYQEc9FxJPDXxwzMyuqSAKYBGyueL0ll9WsExG9wA5g4gDTTgV6gH+W9ANJV0o6uNbMJS2S1Cmps6enp0C4ZmZWRLMuAo8D3gR8MSLeCOwCXnRtASAilkbEzIiY2draOpoxmpnt18YVqLMVmFLxenIuq1Vni6RxwATg8QGm3QJsiYh1uXw1/SSA0bL07qWsvG9lM0MYVNe2zwMwa8XZTY5kcAtev4BFxy5qdhhmNoAiRwB3AdMlTZU0nnRRt6OqTgdwRh4+Bbg1IiKXz893CU0FpgN3RsQ2YLOk/5anmQ1sGOayDMvK+1bSta2rmSEMqv3cs2k/d9/f+Hdt69rnk6mZFTgCiIheSYuBW4AWYHlErJe0BOiMiA7SxdyrJXUDT5CSBLneDaSNey9wVkTsyU1/HLg2J5VNwIdHeNnq1n5EO2vPXNvsMMa8WStmNTsEMyugyCkgImINsKaq7IKK4d3Aqf1MexFwUY3yLmBmPcGamdnI8S+BzcxKygnAzKyknADMzErKCcDMrKScAMzMSsoJwMyspJwAzMxKygnAzKyknADMzErKCcDMrKScAMzMSsoJwMyspJwAzMxKygnAzKyknADMzErKCcDMrKScAMzMSsoJwMyspJwAzMxKygnAzKyknADMzEqqUAKQNEfSRkndks6tMf4ASdfn8esktVWMOy+Xb5R0YtV0LZJ+IOmm4S6ImZnVZ9AEIKkFuByYC8wATpM0o6raQmB7REwDLgUuydPOAOYDxwBzgCtye30+ATww3IUwM7P6FTkCOA7ojohNEfEcsAqYV1VnHnBVHl4NzJakXL4qIp6NiIeA7twekiYDvwtcOfzFMDOzeo0rUGcSsLni9Rbgzf3ViYheSTuAibn8jqppJ+XhzwN/Drx8oJlLWgQsAjjqqKMKhFs+S+9eysr7VjY7jBd0besCYNaKWc0NpMKC1y9g0bGLmh2G2T6lKReBJb0X+FlE3D1Y3YhYGhEzI2Jma2vrKEQ39qy8b+ULG919QfsR7bQf0d7sMF7Qta1rn0qQZvuKIkcAW4EpFa8n57JadbZIGgdMAB4fYNr3Ae+T9B7gQOBQSddExAeGtBRG+xHtrD1zbbPD2CftS0ci1gBLl8LKBib4rrxzNWtW4+axYAEsGv0j1CJHAHcB0yVNlTSedFG3o6pOB3BGHj4FuDUiIpfPz3cJTQWmA3dGxHkRMTki2nJ7t3rjb2ZDsnLl3o10I7S3p79G6epqbAIbwKBHAPmc/mLgFqAFWB4R6yUtATojogNYBlwtqRt4grRRJ9e7AdgA9AJnRcSeBi2LmZVVezusXdvsKIamkUcWgyhyCoiIWAOsqSq7oGJ4N3BqP9NeBFw0QNtrgbVF4jAzs5HjXwKbmZWUE4CZWUk5AZiZlZQTgJlZSTkBmJmVlBOAmVlJOQGYmZWUE4CZWUk5AZiZlZQTgJlZSTkBmJmVlBOAmVlJOQGYmZWUE4CZWUk5AZiZlZQTgJlZSTkBmJmVlBOAmVlJOQGYmZWUE4CZWUk5AZiZlVShBCBpjqSNkrolnVtj/AGSrs/j10lqqxh3Xi7fKOnEXDZF0m2SNkhaL+kTI7VAZmZWzKAJQFILcDkwF5gBnCZpRlW1hcD2iJgGXApckqedAcwHjgHmAFfk9nqBP4uIGcBbgLNqtGlmZg1U5AjgOKA7IjZFxHPAKmBeVZ15wFV5eDUwW5Jy+aqIeDYiHgK6geMi4rGIuAcgIp4GHgAmDX9xzMysqCIJYBKwueL1Fl68sX6hTkT0AjuAiUWmzaeL3gisqzVzSYskdUrq7OnpKRCumZkV0dSLwJIOAf4FODsinqpVJyKWRsTMiJjZ2to6ugGame3HiiSArcCUiteTc1nNOpLGAROAxweaVtJLSRv/ayPiq0MJ3szMhq5IArgLmC5pqqTxpIu6HVV1OoAz8vApwK0REbl8fr5LaCowHbgzXx9YBjwQEX8/EgtiZmb1GTdYhYjolbQYuAVoAZZHxHpJS4DOiOggbcyvltQNPEFKEuR6NwAbSHf+nBUReyQdD3wQuE9SV57V/4mINSO9gGZmVtugCQAgb5jXVJVdUDG8Gzi1n2kvAi6qKrsdUL3BmpnZyPEvgc3MSsoJwMyspJwAzMxKygnAzKyknADMzErKCcDMrKScAMzMSsoJwMyspJwAzMxKygnAzKyknADMzErKCcDMrKScAMzMSqpQb6BmjbT07qWsvG9lw9rv2pZ6HJ+1YlbD5rHg9QtYdOyihrVv1gg+ArCmW3nfyhc20o3QfkQ77Ue0N6z9rm1dDU1gZo3iIwDbJ7Qf0c7aM9c2O4whaeSRhVkj+QjAzKyknADMzErKCcDMrKScAMzMSsoJwMyspJwAzMxKqlACkDRH0kZJ3ZLOrTH+AEnX5/HrJLVVjDsvl2+UdGLRNs3MrLEGTQCSWoDLgbnADOA0STOqqi0EtkfENOBS4JI87QxgPnAMMAe4QlJLwTbNzKyBihwBHAd0R8SmiHgOWAXMq6ozD7gqD68GZktSLl8VEc9GxENAd26vSJtmZtZARX4JPAnYXPF6C/Dm/upERK+kHcDEXH5H1bST8vBgbQIgaRHQ18nKTkkbC8Q8ZPqwGtl8Q43l2MHxN50cf1M1Nv5X1Src57uCiIilwNJmx2Fmtr8pcgpoKzCl4vXkXFazjqRxwATg8QGmLdKmmZk1UJEEcBcwXdJUSeNJF3U7qup0AGfk4VOAWyMicvn8fJfQVGA6cGfBNs3MrIEGPQWUz+kvBm4BWoDlEbFe0hKgMyI6gGXA1ZK6gSdIG3RyvRuADUAvcFZE7AGo1ebIL56ZmfVHaUfdzMzKxr8ENjMrKScAM7OScgIwMyspJwBA0jWSHpP0lKQHJf1hs2MqStKvS7pR0i5Jj0ha0OyY6iFpraTdknbmv4b+0K8RJM2X9EB+D34i6R3NjqkISYsldUp6VtKKZsdTr3x34bL8uX9aUpekuc2Oq16SpufvwDWjPe99/odgo+SvgYUR8ayko4G1kn4QEXc3O7ACLgeeA14BtAM3S7p3jN1VtTgirmx2EEMh6X+Q+r56P+kW51c2N6K6/BT4LHAi8LImxzIU40g9CrwLeBR4D3CDpNdHxMPNDKxOl5NujR91PgIg3a4aEc/2vcx/r2liSIVIOhj4A+BTEbEzIm4n/Z7ig82NrFT+ClgSEXdExPMRsTUixsSPGiPiqxHxr6QfbY45EbErIi6MiIfzur8JeAg4ttmxFSVpPvAk8K1mzN8JIJN0haRngB8BjwFrmhxSEa8FeiPiwYqye0m9r44lfy3p55K+J2lWs4MpKvdqOxNozd2ab5F0maSxuDc95kl6Bek7MSaOfiUdCiwB/rRZMTgBZBHxMeDlwDuArwLPDjzFPuEQ4Kmqsh2k5Rgr/gJ4NamTwKXA/5e0zx99Za8AXkr69fs7SKfg3gic38ygykjSS4Frgasi4kfNjqegzwDLImJLswJwAqgQEXvyaZTJwB83O54CdgKHVpUdCjzdhFiGJCLWRcTTucvwq4Dvkc7ljgW/yP//MSIei4ifA3/P2Il/vyDpJcDVpGthi5scTiGS2oETSM9PaRpfBK5tHGPgGgDwIDBO0vSI+HEuewNj5BC4HwGMiX59I2K7pC2kmF8oblY8ZZSfO7KMdDT2noj4ZZNDKmoW0AY8mhaBQ4AWSTMi4k2jFUTpjwAk/Ua+je+Q/LSyE4HTaNJFmXpExC7S6aolkg6W9HbSg3Wubm5kxUg6TNKJkg6UNE7S6cA7gW80O7Y6/DPw8fw5+jXgk8BNTY6pkLzODyT1x9XS9z40O646fRH4TeCkiPjFYJX3IUtJO5nt+e9LwM2kO7JGzVh7sxshSKd7vkRKiI8AZ+dO7saCjwHLgZ+R7ub44zF0C+hLSbchHg3sIV2AP7nqova+7jPA4aSjsd3ADcBFTY2ouPOBT1e8/gDprqYLmxJNnSS9Cvgo6XrdNu19oMpHI+LapgVWQEQ8AzzT91rSTmB3RPSMZhzuDM7MrKRKfwrIzKysnADMzErKCcDMrKScAMzMSsoJwMyspJwAzMxKar9PAJJC0t9VvD5H0oUj1PYKSaeMRFuDzOfU3N/8bSPQ1hpJhw1S50xJR9bR5vsknTvc2OqYX5uk++uc5mWSvp07cBvqfAddd1X1645zCDFdJ+mHkj45zHZmSvrCIHUOk/SxAcZ/v2L4byWtl/S3w4mr2fJ7uKDi9ZmSLhuBdv9I0ocGGP9eSUuGO5/B7PcJgPQjkd+XdHizA6lU5y8uFwIfiYjfGe58I+I9EfHkINXOBAongIjoiIiLhxVY4/0v4KsRsadI5VrvT8F1N2okHQH8dkT8VkQMq0+ZiOiMiD8ZpNphpB8e9tfG2ypeLgJ+KyL+93DiGklD/JVzGzDiD1mKiC9FxJcHqHIzcJKkg0Z63pXKkAB6ST+7ftEeUvUefP41HpJm5b3Fr0naJOliSadLulPSfVW9VZ6Qn6r0oKT35ulb8h7QXXnv7KMV7X5XUgewoUY8p+X275d0SS67ADgeWFa9N5Xb+46kmyVtlPSl3DFWzbZy+cOSDs97Ng9I+qe8p/bNvJd8CqmL42uVnrD0srz8G/KyfK5G3C/sFeV1+gVJ38/r7kVHSP3NO49rl3RHnteNSt0rIOlYSfdKuhc4q6Ktmuu6htOBr+VplKe5P6+j9xd8fwZcd0OJU9InJS3Pw6/PMR1UNd8DJf1zjvUHkvp2BL4JTMrv0zuqplmRPw/Vn82abeVlvykPXyhpudLT2jZJ6ksMFwOvyfN70Z699n5/Okh929zdt24r6vTXNpL+NC///ZLOrvUmKj017tK83r8lqTWXfySv23sl/UvfOqxYD+uAv5H0GknfkHR3fq+PrqhX63N7MfCOvMx925Ajcxs/lvQ3FbG9W9J/SLpH0lckHZLLX/T9yevhnDz8JxXjVwFE+oXuWuC9tdbDiImI/fqPvT1mPgxMAM4BLszjVgCnVNbN/2eRHtLwSuAAYCvwV3ncJ4DPV0z/DVIinQ5sAQ4k7f2cn+scAHQCU3O7u4CpNeI8kvRUo1ZSFx23krpFgPRBmFljmlmk7gdeTerP5d9IXRMP1NbDpK4L2kjJsT2X3wB8oHp+wERgI3t/NX5YjTjOBC6rWCdfyetkBtBdo/5A8/4h8K48vKRiXf8QeGce/lvg/jxcc11XzW88sK3i9R/kddVC6kTs0fxe9/v+1LHu6oozr6fvAL+Xy95eY75/BizPw0fneA/McdzfT6wrqP3Z7K+tWcBNufxC4Ps5zsNJXYy8dKD5VX5/qoer6vTX9rHAfcDBpOSxHnhjjekDOD0PX8Dez93EijqfBT5esR5uAlry628B0/Pwm4FbB/rcVq6Xis/6JtK25EBS1zFT8rJ8Bzg41/uLHF/N709eD+fk4Z8CB1R/v0g7Lf/YyO1jGY4AiIingC8Dgx3iVrorUhe/zwI/Ie1tQfqQtlXUuyHS04h+TPpgHA28G/iQpC5gHelDMD3XvzMiHqoxv98G1kZET0T0kvo2f2eBOO+MiE2RTm1cRzpaKNrWQxHRlYfvrlquPjtISWaZpN+nov+SAfxrXicbSBvYWl40b0kTSF+Ab+fyq4B3Kp13PywivpPLKzu7G2hd9zmclND7HA9cF6n77/8Evk1aZ9D/+1Mk/rrjjIjnSRuVq4FvR8T3aszreOAagEh93T9CevDJYGp9Nou2dXOkLrp/Tupnqr/3cShqtX08cGOkp3ztJHVyWOvZys8D1+fha/J0AK/Le/T3kTaclQ9F+kpE7Ml75G8DvpLfh//Hrz7Cs8jnFuBbEbEjInaTjhRfBbyFlDi+l9s+I5cX+f78kHTE/QHSjkWfn1HHqdihKFJcej4AAANhSURBVFNncJ8H7iH13tinl3waTOnUyfiKcZUPhHm+4vXz/Op6q+5Mqa87449HxC2VI5SedrVraOH3q9b8i6pcxj3UeC5sRPRKOg6YTTq6WAz89zra7a9r50HnXVDNdV3lF6S9tSKKvj/1xj9QnNNJR6oj/WUfyc/GSG4rRrLtvmVaQTrKvVfSmaQ99z597+lLgCcjor1AXAN1SV4rfgH/FhGnVVcu8P35XdIO2knAXyo907iX9JltaA+npTgCAIiIJ0iH6gsrih9m7/ND30c6FK3XqZJeonRd4NWkw71bgD9WekoRkl6r9PzegdwJvCufY24hdUn97UGmAThO0tScwN4P3D6Mtvo8TX6qWN5rmhARa0jXUd5QRzt1iYgdwPaK89kfJO0VPwk8Kalvb+/0iskGXdcRsZ3c3XEu+i7wfqXz8q2kL9+dIxB/3XHmo54v5BgmqvZdZd/ta0vSa4GjSJ+zwdT6bA61Laj4XDTAd4GTJR2U37/fy2XVXkLakEK6OHt7Hn458Fhev6fXmK7vTMBDkk6FF64FDfZ5LrrMdwBvlzQtt31wfo8H/P7k7+2UiLiNdNpoAukUGKQjs4beRVamIwCAv+NXnxj0T8DXlC7YfYOh7Z0/Stp4HAr8UUTslnQl6XTKPZIE9AAnD9RIRDymdCvlbaS9iZsj4msF5n8XcBkwLU97Y0Q8P8S2+qwAviTpF8Bc0jo6MLfV6OeXnpHnfRDptMWHc/mHgeWSgr2n4wCKrutvkk4X/DtwI/BW0vOTA/jziNjWd0FwmOqN81Lg8oh4UNJC4DZJ34mIn1VMewXwxXx6oxc4MyKelQbaSQVqfzaH2hYR8bjSc5vvB74eI3iHT0TcI2kFexPxlRHxgxpVd5F2es4nnSLpu8j8KdKptZ78v7+N9umk5T+ftMO3ivQ56M8PgT15G7EC2N5P/D35yOM6SQfk4vNJCWSg708LcE3eERDwhdh7p9nvAOdButWadF3uggFirZu7gx7D8imlcyKisXcK7AckvQn4ZER8sNmxjIa8Mb0pIlY3O5aRJGlnRBwyeM2xTekB9ysjYnYj51OaU0BWbhFxD2nvesg/BDMbRUeR7thqKB8BmJmVlI8AzMxKygnAzKyknADMzErKCcDMrKScAMzMSuq/AH0o98UjBqyYAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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>hirac_eucl</th>\n",
       "      <th>hirac_cos</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>name</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Aragorn</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Frodo</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bilbo</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Gandalf</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Legolas</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sam</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arwen</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         hirac_eucl  hirac_cos\n",
       "name                          \n",
       "Aragorn           1          0\n",
       "Frodo             2          2\n",
       "Bilbo             1          1\n",
       "Gandalf           0          0\n",
       "Legolas           1          1\n",
       "Sam               1          0\n",
       "Arwen             0          0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clustering = AgglomerativeClustering(distance_threshold=0,\n",
    "                                     n_clusters=None,\n",
    "                                     affinity='cosine',\n",
    "                                     linkage='average').fit(scores)\n",
    "plt.title('Hierarchical clustering')\n",
    "plot_dendrogram(clustering, truncate_mode='level', p=3)\n",
    "plt.xlabel(\"Number of points in node (or index of point if no parenthesis).\")\n",
    "plt.show()\n",
    "clustering = AgglomerativeClustering(n_clusters=3,\n",
    "                                     affinity='cosine',\n",
    "                                     linkage='average').fit(scores)\n",
    "result_cluster['hirac_cos'] = pd.Series(clustering.labels_, index=scores.index)\n",
    "result_cluster"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "更加具体的说明可以参考 https://scikit-learn.org/stable/modules/generated/sklearn.cluster.AgglomerativeClustering.html\n",
    "\n",
    "聚类之后可以方便的计算类的中心、方差等，比如："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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>语文</th>\n",
       "      <th>数学</th>\n",
       "      <th>英语</th>\n",
       "      <th>物理</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hirac_cos</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>97.25</td>\n",
       "      <td>102.5</td>\n",
       "      <td>89.0</td>\n",
       "      <td>91.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>105.00</td>\n",
       "      <td>108.5</td>\n",
       "      <td>115.0</td>\n",
       "      <td>84.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>115.00</td>\n",
       "      <td>87.0</td>\n",
       "      <td>108.0</td>\n",
       "      <td>67.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               语文     数学     英语     物理\n",
       "hirac_cos                             \n",
       "0           97.25  102.5   89.0  91.75\n",
       "1          105.00  108.5  115.0  84.00\n",
       "2          115.00   87.0  108.0  67.00"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "merged_scores = pd.concat([scores, result_cluster], axis=1)\n",
    "merged_scores.groupby('hirac_cos').mean().drop('hirac_eucl', axis=1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>语文</th>\n",
       "      <th>数学</th>\n",
       "      <th>英语</th>\n",
       "      <th>物理</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hirac_cos</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>68.916667</td>\n",
       "      <td>164.333333</td>\n",
       "      <td>164.0</td>\n",
       "      <td>127.583333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>50.000000</td>\n",
       "      <td>60.500000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>72.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  语文          数学     英语          物理\n",
       "hirac_cos                                          \n",
       "0          68.916667  164.333333  164.0  127.583333\n",
       "1          50.000000   60.500000    0.0   72.000000\n",
       "2                NaN         NaN    NaN         NaN"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "merged_scores.groupby('hirac_cos').var().drop('hirac_eucl', axis=1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# K-means聚类\n",
    "\n",
    "K-means聚类是非常常用的聚类方法之一，该方法将所有样本进行划分，使得每个样本到其类中心的平方和最小。如果我们希望分为$M$类，那么，记$\\bar{x}_m$为第$m$类的中心，那么那么损失函数定义为：$$\\sum_{m=1}^M{\\sum_{_i\\in G_m}{||x_i-\\bar{x}_m||^2_2}}$$\n",
    "\n",
    "算法的目的是最小化以上目标函数，那么就需要确定每一个$i$所属的组。然而，每个样本所属组有很多情况，这个情况数是指数级别的，实际上解以上最优化问题是一个NP-hard问题。\n",
    "\n",
    "现实中在求解以上问题时，会先从一个简单的划分开始，通过迭代的方法直到收敛，我们在此不详细介绍算法的具体步骤。Scikit-Learn中已经有该算法的实现："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "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>语文</th>\n",
       "      <th>数学</th>\n",
       "      <th>英语</th>\n",
       "      <th>物理</th>\n",
       "      <th>hirac_eucl</th>\n",
       "      <th>hirac_cos</th>\n",
       "      <th>k_means</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>name</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>Aragorn</th>\n",
       "      <td>95</td>\n",
       "      <td>115</td>\n",
       "      <td>98</td>\n",
       "      <td>95</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Frodo</th>\n",
       "      <td>115</td>\n",
       "      <td>87</td>\n",
       "      <td>108</td>\n",
       "      <td>67</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bilbo</th>\n",
       "      <td>110</td>\n",
       "      <td>114</td>\n",
       "      <td>115</td>\n",
       "      <td>78</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Gandalf</th>\n",
       "      <td>98</td>\n",
       "      <td>108</td>\n",
       "      <td>78</td>\n",
       "      <td>99</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Legolas</th>\n",
       "      <td>100</td>\n",
       "      <td>103</td>\n",
       "      <td>115</td>\n",
       "      <td>90</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sam</th>\n",
       "      <td>108</td>\n",
       "      <td>102</td>\n",
       "      <td>102</td>\n",
       "      <td>98</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arwen</th>\n",
       "      <td>88</td>\n",
       "      <td>85</td>\n",
       "      <td>78</td>\n",
       "      <td>75</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          语文   数学   英语  物理  hirac_eucl  hirac_cos  k_means\n",
       "name                                                      \n",
       "Aragorn   95  115   98  95           1          0        2\n",
       "Frodo    115   87  108  67           2          2        0\n",
       "Bilbo    110  114  115  78           1          1        0\n",
       "Gandalf   98  108   78  99           0          0        2\n",
       "Legolas  100  103  115  90           1          1        0\n",
       "Sam      108  102  102  98           1          0        2\n",
       "Arwen     88   85   78  75           0          0        1"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "\n",
    "clustering = KMeans(n_clusters=3).fit(scores)\n",
    "merged_scores['k_means'] = pd.Series(clustering.labels_, index=scores.index)\n",
    "merged_scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "        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>语文</th>\n",
       "      <th>数学</th>\n",
       "      <th>英语</th>\n",
       "      <th>物理</th>\n",
       "      <th>hirac_eucl</th>\n",
       "      <th>hirac_cos</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>k_means</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>0</th>\n",
       "      <td>108.333333</td>\n",
       "      <td>101.333333</td>\n",
       "      <td>112.666667</td>\n",
       "      <td>78.333333</td>\n",
       "      <td>1.333333</td>\n",
       "      <td>1.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>88.000000</td>\n",
       "      <td>85.000000</td>\n",
       "      <td>78.000000</td>\n",
       "      <td>75.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>100.333333</td>\n",
       "      <td>108.333333</td>\n",
       "      <td>92.666667</td>\n",
       "      <td>97.333333</td>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 语文          数学          英语         物理  hirac_eucl  hirac_cos\n",
       "k_means                                                                      \n",
       "0        108.333333  101.333333  112.666667  78.333333    1.333333   1.333333\n",
       "1         88.000000   85.000000   78.000000  75.000000    0.000000   0.000000\n",
       "2        100.333333  108.333333   92.666667  97.333333    0.666667   0.000000"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "merged_scores.groupby('k_means').mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "与层次聚类不同的是，该算法可以对新的样本归属于哪一类进行预测："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1], dtype=int32)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clustering.predict(np.array([[120, 120, 120, 100], [50, 100, 100, 50]]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "以上计算中，Scikit-Learn会自动计算初始分类，并选择合适的算法进行拟合，如果需要控制细节，可以参考：https://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html#sklearn.cluster.KMeans\n",
    "\n",
    "此外，算法中还涉及到类别个数的选择，一般可以通过计算每个类别的平均直径，如果额外增加类别对平均直径的降低作用不大，那么就无需增加类别个数。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 一个实例：零售商的客户划分\n",
    "\n",
    "接下来我们使用一个实际数据展示聚类分析的用法。\n",
    "\n",
    "在营销中，将客户具体划分为不同的细分市场特别重要，但是在进行市场开发时，通常没有经过标记（标签化）的数据，我们可以还是用聚类分析对客户进行一定程度上的划分。在此基础之上，我们可以分析不同购买渠道、地区的客户具有何种特点等。\n",
    "\n",
    "首先读入数据："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "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>Channel</th>\n",
       "      <th>Region</th>\n",
       "      <th>Fresh</th>\n",
       "      <th>Milk</th>\n",
       "      <th>Grocery</th>\n",
       "      <th>Frozen</th>\n",
       "      <th>Detergents_Paper</th>\n",
       "      <th>Delicassen</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>12669</td>\n",
       "      <td>9656</td>\n",
       "      <td>7561</td>\n",
       "      <td>214</td>\n",
       "      <td>2674</td>\n",
       "      <td>1338</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>7057</td>\n",
       "      <td>9810</td>\n",
       "      <td>9568</td>\n",
       "      <td>1762</td>\n",
       "      <td>3293</td>\n",
       "      <td>1776</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>6353</td>\n",
       "      <td>8808</td>\n",
       "      <td>7684</td>\n",
       "      <td>2405</td>\n",
       "      <td>3516</td>\n",
       "      <td>7844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>13265</td>\n",
       "      <td>1196</td>\n",
       "      <td>4221</td>\n",
       "      <td>6404</td>\n",
       "      <td>507</td>\n",
       "      <td>1788</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>22615</td>\n",
       "      <td>5410</td>\n",
       "      <td>7198</td>\n",
       "      <td>3915</td>\n",
       "      <td>1777</td>\n",
       "      <td>5185</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Channel  Region  Fresh  Milk  Grocery  Frozen  Detergents_Paper  Delicassen\n",
       "0        2       3  12669  9656     7561     214              2674        1338\n",
       "1        2       3   7057  9810     9568    1762              3293        1776\n",
       "2        2       3   6353  8808     7684    2405              3516        7844\n",
       "3        1       3  13265  1196     4221    6404               507        1788\n",
       "4        2       3  22615  5410     7198    3915              1777        5185"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wholesale = pd.read_csv(\"csv/wholesale.csv\")\n",
    "wholesale.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "其中Channel是购买的渠道，Region是地区，其他变量是不同种类的商品的消费量。\n",
    "\n",
    "在这里，我们的目的不是为了预测而是分析渠道、地区特点，因而使用层次聚类即可，不妨使用余弦相似度先进行一个简单的聚类："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x1080 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sales = wholesale.drop(['Channel', 'Region'], axis=1)\n",
    "clustering = AgglomerativeClustering(distance_threshold=0,\n",
    "                                     n_clusters=None,\n",
    "                                     affinity='cosine',\n",
    "                                     linkage='average').fit(sales)\n",
    "plt.rcParams['figure.figsize'] = (15.0, 15.0)\n",
    "plt.title('Hierarchical clustering')\n",
    "plot_dendrogram(clustering, truncate_mode='level', p=20)\n",
    "plt.xlabel(\"Number of points in node (or index of point if no parenthesis).\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这里我们不妨分为5类："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "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>Fresh</th>\n",
       "      <th>Milk</th>\n",
       "      <th>Grocery</th>\n",
       "      <th>Frozen</th>\n",
       "      <th>Detergents_Paper</th>\n",
       "      <th>Delicassen</th>\n",
       "      <th>cluster</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12669</td>\n",
       "      <td>9656</td>\n",
       "      <td>7561</td>\n",
       "      <td>214</td>\n",
       "      <td>2674</td>\n",
       "      <td>1338</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>7057</td>\n",
       "      <td>9810</td>\n",
       "      <td>9568</td>\n",
       "      <td>1762</td>\n",
       "      <td>3293</td>\n",
       "      <td>1776</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>6353</td>\n",
       "      <td>8808</td>\n",
       "      <td>7684</td>\n",
       "      <td>2405</td>\n",
       "      <td>3516</td>\n",
       "      <td>7844</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>13265</td>\n",
       "      <td>1196</td>\n",
       "      <td>4221</td>\n",
       "      <td>6404</td>\n",
       "      <td>507</td>\n",
       "      <td>1788</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>22615</td>\n",
       "      <td>5410</td>\n",
       "      <td>7198</td>\n",
       "      <td>3915</td>\n",
       "      <td>1777</td>\n",
       "      <td>5185</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Fresh  Milk  Grocery  Frozen  Detergents_Paper  Delicassen  cluster\n",
       "0  12669  9656     7561     214              2674        1338        2\n",
       "1   7057  9810     9568    1762              3293        1776        0\n",
       "2   6353  8808     7684    2405              3516        7844        0\n",
       "3  13265  1196     4221    6404               507        1788        2\n",
       "4  22615  5410     7198    3915              1777        5185        2"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clustering = AgglomerativeClustering(n_clusters=5,\n",
    "                                     affinity='cosine',\n",
    "                                     linkage='average').fit(sales)\n",
    "sales['cluster'] = clustering.labels_\n",
    "sales.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "查看中心："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>513.550000</td>\n",
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       "      <td>17389.229839</td>\n",
       "      <td>3140.342742</td>\n",
       "      <td>4018.346774</td>\n",
       "      <td>3215.306452</td>\n",
       "      <td>892.709677</td>\n",
       "      <td>1262.620968</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1869.000000</td>\n",
       "      <td>577.000000</td>\n",
       "      <td>572.000000</td>\n",
       "      <td>950.000000</td>\n",
       "      <td>4762.000000</td>\n",
       "      <td>203.000000</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>18291.000000</td>\n",
       "      <td>1266.000000</td>\n",
       "      <td>21042.000000</td>\n",
       "      <td>5373.000000</td>\n",
       "      <td>4173.000000</td>\n",
       "      <td>14472.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Fresh          Milk       Grocery        Frozen  \\\n",
       "cluster                                                           \n",
       "0         4854.688235  10093.211765  14150.188235   1713.458824   \n",
       "1         6107.250000   2693.150000   3743.300000  12832.150000   \n",
       "2        17389.229839   3140.342742   4018.346774   3215.306452   \n",
       "3         1869.000000    577.000000    572.000000    950.000000   \n",
       "4        18291.000000   1266.000000  21042.000000   5373.000000   \n",
       "\n",
       "         Detergents_Paper    Delicassen  \n",
       "cluster                                  \n",
       "0             6042.700000   1882.758824  \n",
       "1              513.550000   1153.450000  \n",
       "2              892.709677   1262.620968  \n",
       "3             4762.000000    203.000000  \n",
       "4             4173.000000  14472.000000  "
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sales.groupby('cluster').mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>1033.25</td>\n",
       "      <td>2873.5</td>\n",
       "      <td>5949.50</td>\n",
       "      <td>44466.0</td>\n",
       "      <td>170.0</td>\n",
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       "      <td>1951.0</td>\n",
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       "      <td>7168.286317</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2418.00</td>\n",
       "      <td>4570.0</td>\n",
       "      <td>8031.25</td>\n",
       "      <td>32717.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>2693.150000</td>\n",
       "      <td>...</td>\n",
       "      <td>819.0</td>\n",
       "      <td>1377.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1153.450000</td>\n",
       "      <td>1331.994210</td>\n",
       "      <td>46.0</td>\n",
       "      <td>170.50</td>\n",
       "      <td>810.5</td>\n",
       "      <td>1595.0</td>\n",
       "      <td>5609.0</td>\n",
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       "      <td>622.0</td>\n",
       "      <td>8561.25</td>\n",
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       "      <td>3140.342742</td>\n",
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       "      <td>985.5</td>\n",
       "      <td>6707.0</td>\n",
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       "      <td>1463.551698</td>\n",
       "      <td>3.0</td>\n",
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       "      <td>833.5</td>\n",
       "      <td>1627.5</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>1869.0</td>\n",
       "      <td>1869.00</td>\n",
       "      <td>1869.0</td>\n",
       "      <td>1869.00</td>\n",
       "      <td>1869.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>577.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>4762.0</td>\n",
       "      <td>4762.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>203.000000</td>\n",
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       "      <td>203.00</td>\n",
       "      <td>203.0</td>\n",
       "      <td>203.0</td>\n",
       "      <td>203.0</td>\n",
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       "      <td>18291.0</td>\n",
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       "<p>5 rows × 48 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         Fresh                                                          \\\n",
       "         count          mean           std      min       25%      50%   \n",
       "cluster                                                                  \n",
       "0        170.0   4854.688235   6470.260120      3.0   1033.25   2873.5   \n",
       "1         20.0   6107.250000   7168.286317      3.0   2418.00   4570.0   \n",
       "2        248.0  17389.229839  13564.936414    622.0   8561.25  14004.5   \n",
       "3          1.0   1869.000000           NaN   1869.0   1869.00   1869.0   \n",
       "4          1.0  18291.000000           NaN  18291.0  18291.00  18291.0   \n",
       "\n",
       "                              Milk                ... Detergents_Paper  \\\n",
       "              75%       max  count          mean  ...              75%   \n",
       "cluster                                           ...                    \n",
       "0         5949.50   44466.0  170.0  10093.211765  ...           7568.5   \n",
       "1         8031.25   32717.0   20.0   2693.150000  ...            819.0   \n",
       "2        21506.75  112151.0  248.0   3140.342742  ...            985.5   \n",
       "3         1869.00    1869.0    1.0    577.000000  ...           4762.0   \n",
       "4        18291.00   18291.0    1.0   1266.000000  ...           4173.0   \n",
       "\n",
       "                 Delicassen                                                \\\n",
       "             max      count          mean          std      min       25%   \n",
       "cluster                                                                     \n",
       "0        40827.0      170.0   1882.758824  4010.062038      3.0    445.25   \n",
       "1         1377.0       20.0   1153.450000  1331.994210     46.0    170.50   \n",
       "2         6707.0      248.0   1262.620968  1463.551698      3.0    408.25   \n",
       "3         4762.0        1.0    203.000000          NaN    203.0    203.00   \n",
       "4         4173.0        1.0  14472.000000          NaN  14472.0  14472.00   \n",
       "\n",
       "                                    \n",
       "             50%      75%      max  \n",
       "cluster                             \n",
       "0         1215.0   1951.0  47943.0  \n",
       "1          810.5   1595.0   5609.0  \n",
       "2          833.5   1627.5  14351.0  \n",
       "3          203.0    203.0    203.0  \n",
       "4        14472.0  14472.0  14472.0  \n",
       "\n",
       "[5 rows x 48 columns]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sales.groupby('cluster').describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "进一步可以用图的方式查看聚类结果："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sb\n",
    "sb.set()\n",
    "## 使图形直接插入到jupyter中\n",
    "%matplotlib inline\n",
    "# 设定图像大小\n",
    "plt.rcParams['figure.figsize'] = (8.0, 8.0)\n",
    "\n",
    "plt.scatter(sales['Milk'],sales['Grocery'],c=sales['cluster']) ##散点图\n",
    "plt.xlabel('Milk')\n",
    "plt.ylabel(\"Grocery\")\n",
    "plt.show() ## 画图"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "还可以分地区、渠道查看各个类别的个数，比如查看第0类："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "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>Channel</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Region</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.254237</td>\n",
       "      <td>0.833333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.142857</td>\n",
       "      <td>0.736842</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.218009</td>\n",
       "      <td>0.723810</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Channel         1         2\n",
       "Region                     \n",
       "1        0.254237  0.833333\n",
       "2        0.142857  0.736842\n",
       "3        0.218009  0.723810"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wholesale_dummies = pd.get_dummies(sales['cluster'], prefix='cluster')\n",
    "wholesale_dummies['Region'] = wholesale['Region']\n",
    "wholesale_dummies['Channel'] = wholesale['Channel']\n",
    "wholesale_dummies.pivot_table('cluster_0',\n",
    "                              index='Region',\n",
    "                              columns='Channel',\n",
    "                              aggfunc='mean')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以发现，第0类顾客更偏向于通过渠道2购买，而地区1似乎有更多的第0类顾客比例。\n",
    "\n",
    "我们将在后面介绍如何使用其他特征，如地区、渠道等对分类进行预测。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 作业\n",
    "\n",
    "使用https://archive.ics.uci.edu/ml/datasets/Online+Retail 中的数据，根据StockCode的第一位进行分类，计算每个消费者每一类的消费量，进而进行聚类分析，分析每个国家的类别情况。"
   ]
  }
 ],
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