Chap06-Decision_Tree/Chap06-Decision_Tree.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chap06 - Decision Tree"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Desicion Tree**(이하, 결정 트리 또는 의사결정나무)는 **분류**와 **회귀**에 사용할 수 있는 머신러닝 알고리즘이다. \n",
    "\n",
    "이번 장에서는 결정 트리의 훈련, 시각화, 예측 방법에 대해 알아보고, 결정 트리 중 Scikit-Learn의 CART 알고리즘을 알아보고 트리에 규제를 적용하는 방법과 회귀 문제에 적용하는 방법에 대해 알아 보도록 하자."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Set Up"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "\n",
    "# 일관된 출력을 위해 유사난수 초기화\n",
    "np.random.seed(42)\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sn\n",
    "sn.set()\n",
    "plt.rcParams['axes.labelsize'] = 14\n",
    "plt.rcParams['xtick.labelsize'] = 12\n",
    "plt.rcParams['ytick.labelsize'] = 12\n",
    "\n",
    "# 한글출력\n",
    "# matplotlib.rc('font', family='AppleGothic')  # MacOS\n",
    "matplotlib.rc('font', family='Malgun Gothic')  # Windows\n",
    "plt.rcParams['axes.unicode_minus'] = False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.1 결정 트리 학습과 시각화\n",
    "\n",
    "다음 예제는 붓꽃(iris) 데이터셋을 Scikit-Learn의 [`DecisionTreeClassifier`](http://scikit-learn.org/stable/modules/generated/sklearn.tree.DecisionTreeClassifier.html#sklearn.tree.DecisionTreeClassifier)를 이용해 학습시키는 코드이다.\n",
    "\n",
    "> Scikit-Learn은 **이진 트리**만 만드는 **CART** 알고리즘을 사용하기 때문에, 리프 노드를 제외한 모든 노드는 자식노드를 2개씩 가진다(조건에 대해, 'yes' or 'no'). 하지만, **ID3** 알고리즘을 이용해 2개 이상의 자식 노드를 가지는 결정트리를 만들 수 있다.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeClassifier(class_weight=None, criterion='gini', max_depth=2,\n",
       "            max_features=None, max_leaf_nodes=None,\n",
       "            min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "            min_samples_leaf=1, min_samples_split=2,\n",
       "            min_weight_fraction_leaf=0.0, presort=False, random_state=42,\n",
       "            splitter='best')"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "\n",
    "iris = load_iris()\n",
    "X = iris.data[:, 2:] # petal length and width\n",
    "y = iris.target\n",
    "\n",
    "tree_clf = DecisionTreeClassifier(max_depth=2, random_state=42)\n",
    "tree_clf.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.tree import export_graphviz\n",
    "\n",
    "export_graphviz(tree_clf, \n",
    "                out_file='./images/iris_tree.dot', \n",
    "                feature_names=[\"꽃잎 길이 (cm)\", \"꽃잎 너비 (cm)\"], \n",
    "                class_names=iris.target_names, \n",
    "                rounded=True, \n",
    "                filled=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# !conda install python-graphviz  # Windows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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       "<text text-anchor=\"middle\" x=\"138.5\" y=\"-290.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">꽃잎 길이 (cm) &lt;= 2.45</text>\r\n",
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       "<text text-anchor=\"middle\" x=\"217.5\" y=\"-171.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">꽃잎 너비 (cm) &lt;= 1.75</text>\r\n",
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     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import graphviz\n",
    "\n",
    "with open(\"./images/iris_tree.dot\", encoding='UTF8') as f:\n",
    "    dot_graph = f.read()\n",
    "dot = graphviz.Source(dot_graph)\n",
    "dot.format = 'png'\n",
    "dot.render(filename='iris_tree', directory='./images', cleanup=True)\n",
    "dot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "위의 그래프에서 노드의 각 속성에 대한 설명은 다음과 같다.\n",
    "\n",
    "- `sample` : 각 노드로 분류된 데이터의 개수를 말한다.\n",
    "- `value` : 각 노드에서 label(여기서는 `setosa, versicolor, virginica`)에 속하는 데이터의 개수를 말한다.\n",
    "    - 예를 들어, 왼쪽 주황색 노드는 `setosa`가 50개, `versicolor, virginica`는 0개를 의미한다.\n",
    "\n",
    "- `gini` : **불순도**(impurity)를 의미하며, 불순도를 측정하는 지표인 **지니(gini)** 계수를 이용한다.\n",
    "    - 예를 들어, level 2의 초록색 노드의 gini 계수는 $1-(\\frac{0}{54})^{2} - (\\frac{49}{54})^{2} - (\\frac{5}{54})^{2} \\approx 0.168$ 이다. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Gini 계수의 수식은 다음과 같다.\n",
    "\n",
    "$$\n",
    "G_i = 1 - \\sum_{k=1}^{n}{p_{i,k}^{2}}\n",
    "$$\n",
    "\n",
    "- $p_{i, k}$ 는 $i$번째 노드에 있는 데이터 중 클래스 $k$에 속한 샘플의 비율이다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.2 예측하기\n",
    "\n",
    "Decision Tree를 이용한 분류기가 어떻게 붓꽃의 종류를 예측하는지에 대해 위의 그래프(graphviz)를 통해 알아보자. \n",
    "\n",
    "1. 맨위의 노드인 **루트 노드**(root node)에서 꽃잎의 길이(petal length)가 `2.45cm`보다 짧은지 비교한다.\n",
    "2. `2.45cm`보다 짧다면 왼쪽 노드(주황색)인 **자식 노드**(child node)로 이동한다.\n",
    "    - 이 경우에는 더 이상의 자식 노드가 없으므로 **리프 노드**(leaf node)가 된다.\n",
    "    - 그리고, 꽃의 종류를 `setosa`라고 예측한다.\n",
    "3. 반대로, `2.45cm` 보다 긴 경우 오른쪽 자식 노드로 가며, 꽃잎 너비가 `1.75cm` 보다 짧은지 비교하게 된다. \n",
    "4. 꽃잎의 너비가 `1.75cm` 보다 짧으면 왼쪽 리프 노드(초록색)로 가게되며, `versicolor`라고 예측하며, `1.75cm` 보다 길면, 오른쪽 리프 노드(보라색)으로 가게되며, `virginica`로 예측한다. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Decision Tree 의 장점은 데이터 전처리가 거의 필요하지 않다는 것이며, 특히 특성(feature)의 스케일을 맞추거나 평균을 원점에 맞추는 작업(`StandardScaler`)이 필요하지 않다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "아래의 예제는 위의 결정 트리에 대한 결정 경계(decision boundary)를 보여준다. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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HTU34oTHmz3mdV2e91GD5MSccy4WTLm1a4BkuXGnY3BWhbweEu7cfqcQsHe6Np3v8mSTcg3yLm9DXrngCEZGm21u5l9ZtirjvmQcpKm4Tss35Ey6qe71/1wP419sf1Fv/zaq17N/1AMIZdc4pjDrnlITEm0mWvPchAIOGHNtgXbjSME916JFDt5fvCLk83UvM0j3+TBIy6Vtr/+Z0ICLSdF27d+OkX4zk+vG/j9jup8ceSecu+3PEMf158qG/sear1fQ8tBel20uZ/8Jr/PH/pjgUceaYetUNALzx30UN1gWWhsUzalu6l5ile/yZJGzJnjGmeSPbVltrYxomV0SSZ7/2bZn+/Axef+4VdpftZsxl5wE0eA+Qn5/PVVMmc/+N99C2Q1tKftjCmRecTbceB4btX5f34fY/fc2u3R4oLKVFn2VUfHk0bbr0o1leDpB6dffh4ol1v01pH2oq4Vil+7gEqShSnX4Fvvv6OdS/v1/7/q/AlckLTUSSqc8Rh/HQ839h25attNmvmOYFkb/n6/I+voQPFBy8AvI8FBz8Gb2O3/dnMNXq7sPFE+t+m9I+1LgEsVJdf+KFfXrfWptrrc2z1uYCT+MbQrf2/VmORSgiSZObm0uHzh0bTfgSoLCUnMLd5ORATuFuKNwJpF7dfbh4Yt1v09t7NfVtCoqlZM8b5rWIpICPP/yIiWMu58Wn5rJg7utMHHN5g/dL3/u3I7GccMowJk/7rSP7clrBwSuC3n8GpF7dfbh4Yt1vstsnux+pz9GpdUUkeY489qiEDKNb676Z0xPWV8YIOMsHyMmBD6fMBmZTOPC0ek1rz65D3dsPV7d+/MGDEnLvOvAsPzCeNVvXxbTfWONM1HEl+/PJZtEmfZ3ZS9YY0yf03avJU6+pG4Rl/pzXeHDa/WH7CHySe8Lo8axeuSpku5Fnn1w3ZvuqLyxXjbk8bJ8PPz+D3of5Jqx64OZ7ww792qtvbx554dG69yf1Cz+lhdvH9OS8Jzmge3cgPY6p4OAV7PpuByse+GeDNv+65lUADv/N8bQ+cD8AbvzdFNYt/jpkn6277cfh1xxf9/79q1/kfV5MyDHVnuV/ev/77F5fui9GXq173XlQd3qNPhyv18uct17iuT+GL9oKPCb73CecdXXoODv22J8+k47Ztz//ZxLquGI5puPuP63ubH/ezc/r3xPQrVs3li5dGrb/cCI9vb+Ifcm+D9DfGPNH//sONK2WXyRt7cndzY68bXWvI6ltB+AhdE02wN6cyrq2ZXk7I/ZZlrezru3enMqw7Tx46u0/ErePaYd3B4V5RXXbhZMqx5TborzuLD8alZ69Ydd5YziXivWYtpeXRmwTyOP18P2uTVG3jxT3Xs/eBvX44cRyTOCL85vS7/TvKU453uBhkvyMMeHH8PT51lr7ZdwRJMaPgLWlpd9RU5P5k3zEU++bjpw43ry8nfTpMwqA2bP/y67i7UndXzgFBflUVla5sm83uHG8e6p38f6G1xjc9VRaNmud1H09+cKXlFc0/JtU2KIZF43uk9R9uy2bfpfdONbC/GYM7XsQQA/gm2i3C3umb619I/6wRNKDx7NvFLv27SvZz7O/K3G0adGSnXv3uLJvN7hxvAtK/sHm8g38r+QzRh6Q3EKk8orPwyyvpluOO79jTsmm32U3jjU/lktOATThjohkjbKqnXxWugwvXj4rXc6u6vgvl4YzduxxfP7ydUnrX6QplPRFJGssLnmL2luaXm8NH2x5K2n72rZtM1UV0d9bF3GCZtkTkaxQe5Zf+9CUBw+flS7n5x2H07pZ6EmK4jFz5mLumtPwKX8RN0U7y94fgCeASENMaZY9EUlZgWf5tWrP9pNxb799+840L9wv4f2KxCOqWfaMMRcBL1hr1/jfHwhsstaGr0cREUkh68u/aVAa5cHD+vJvkrbP1i2as6ui4Z/J1i007LG4o6kj8t2Jb8KdDxprKCKSCkqWH0V5iARc0qI59GzY/s7n3w+bsK8bM7jR/T344BRaAtdNvg2ANm1asnPnnrq+b3iq4fME0fbttLKqnby04Rl+0e38pNwKEec09UG+EqBLIgMREUmmUAk8kcuDLVz4PAsXPp+Uvp22uOQtvitfm9QHH8UZ0Z7pvwGUBbzfDSR3VAsRkTQ2ceKtboeQEMFljsl68FGcEVXSt9beFrSoEshPfDgiIplh1Khfuh1CQoQqc0z2oEaSPE29vF+DZugTEclo4cockzmokSRXPEm/aWMAiohkgSVL3mHJknfcDiMukcocJT1FmmVvLeEH6CkGpiUlIhGRJIi1fC7ecrtp03xToC5Y0HDK1HQp5XOjzFGSK9Il+mGNbBtpoJ6QjDHHAfcAV1prPw1aNxq4F1jjX7TYWjsl1n2ISGaJt3SuVqQn5kOVz8Ui1PZtuvSre11WtZNZK2dw+v7n0bpZm7q4U70U7rKev3U7BEmwSLPs/S+ROzLGPA0UAeF+s9sBj1lrM+ORVxFJiFQrb4t2v72Ov7Lu9eKSt/imbDUf5NV/CC6wFE4Px4kTnJxw53Jr7Zn4avxDaRdhnYhIWgo3s5+TM/6J1HLsCXxrbWOTDbcALjPGXACsAqZYa7+NZR9FRS0g6P5TpiouLnQ7BEc5ebwtWxaQk9PSsf0Fa9PGvX27IZ7jdeuzimW/S3cuwut/PMpLDUtLF3Fmj3N5e+0rIZdnkmz6XXb6WJs1MXunTNmdtfYm4CZjTA4wDngROCqWPsrKKqipqU5GeCmluLiQ0tJyt8NwjNPHu2dPJR5PY99RkyNwqNZsEO/xuvVZRbPfT57zXd4vOvoXeLz+kjevh+Vb/k2/Vkfx0ZYPGyw/unhoSt7bb4ps+l1241jz83OA2E+GnLy8HxVrrdda+wzQ3RijAYBEJK2FKnl7acMslcKJK1Im6RtjOga8HgmssdZWuRiSiKSASCV1boh2v/1/+WeOuXVsyJK3HVVbVQonrnD18r4x5hJ8U/TOA242xgwAyoHtwBg3YxOR1JCoWeduv3B4QvqJre99y7PpcrekriYlfWPMIGvtkoD3k6y1D0WzrbV2SMDrJwJeT2hKLCKSmhJVXx+rSDX3oZJzuDhjkapT4oaT6uMDSPKETPrGmNOA+wg9It+1wAzqT637RyCqpC8i2SHV6uvDSUQ8ofqYOnU8ANOmPRp3/4mm8QGyV7gz/UXAKWHWbQRaGWMm+d/nANlTlyEiEoVlyxa5HUJImio3u4VM+tbaMsCG28gYkwf0Yt+kO3mJD01EJH1NnTrD7RBC0lS52S3iPX1jzI+Bc4C9wExr7Tf+VWXW2kkB7c5OWoQiImlo0KAT3Q6hgXBT5epsP3uELdkzxgwB5gPVQCvgA2PMIf7Vwff6w83GJyIiKUJT5UqkM/1bgTOttR8BGGOWAzfhGy0v1xhTiO/yfu1/IiJ10mX62HBxxtpHsPnznwNg1KhfxtV3ImmqXImU9LvUJny/hcBU/+uOwCb/66aNBSgiKSlRpXbh2t7w1FtxT2XbVLHsN94yvOnTbwRSK+lrqlyJlPQ9xpj8gFHxOgA7/K83W2sPqG1ojNmYrABFxFnpUmqXbPEe74gRGl9MUk+kpD8P+D9jzDVAc+Bu4CX/uo+D2uryvohIgMmTb3M7BJEGIo29fyPQDdiJb577UmA6gLU2uIa/Z1KiExERkYQJe6Zvrd0FnGOMaQl4rLWVEdpmzzyvIiJR2LrV99hT+/adXY5EZJ9Gx9631mqGCBGRGI0b9zMAFixY5XIkIvvENLWuMaZL461EJJ2l2lS2bon3eNu160S7dp0SFI1IYsQ6y94S4KDABcaY5tba7HqsVySDJWq2uFhnrwtXIhdrCWGiSg7vfP79kCV+0fYza9a/ot6XiFMijch3uDGmrzGmpzGmvX9xjn9d4GOpY4wxf0hmkCKSfmIteYu1VDBRyxMVj0g6iHR5fxkwE3gN+Nyf+GvHb7wkoN1wYGVywhMREZFEiXR5f7O1tn/gAmNM7cvaM/4ewEDgwqREJyKSpiZOPAOA6dNfdjkSkX0iJf1Ik+h4/WPvPwPcaK3VhDsiIgFWr/7C7RBEGoiU9GvP5k8HTq9daIwZDxQBK4CXrbVzkhqhpLwPP1zORx99yqRJl8W03euvv8nbb7/PAw/cnqTIRNzz0EMvNd5IxGGRkv5w//+/BWofQx0G1Phfe4Cq4I0ks/ztb7N44olZ9ZZ5vXDMMQO4775pAGzbtp01a75psO3cua/x7LP/YOvW7fTu3YNrrrmCvn1Ng3aSmWKdvS5SqWAss/Ulana/ePvp3btfTPsTcUKkpP+xMWYH8CXwHnAPMNVa+7gx5hbgJ8DrxphzdLafuS69dCyXXjq23rLbb7+f9u3bRdxu4cJ3mT37Re6++yZ69uzOm28u4uqrb2D27Ecb3TZa3367nv/7v4f5/PMvKS4uYuzYsxkz5oyE9O2kRJWYuSWe0rw2bVqyc2fk8b9i/QwS9Zmlw2cvEqtIT+9vB44F7gQKg4bhzfHX5l8E3GqMyUteiJJKtm7dzrvvLmbEiBMjtvvb32Zx9dW/pnfvnuTl5TFy5DCOP/5YZs36R0LiKC+vYOLE6xg48Ke88cbz3HLLH3n88ZksWrQ4If07Kd1LwxJVCpdpZs58iJkzH3I7DJF6IiV9r7V2nbX2HWvtDaEaWGs3Ah8ApyYlOkkp1dUepk27h5Ejh/GjHx0Ytt3WrdsoKdnKcccNrLd82LDj+fTTzxMSy/z5b9OxY3suuGAMLVq04Igj+nHuub9gzpxXE9K/SLxmzZrOrFnT3Q5DpJ5Il/ffjrDu0YDX76JZ9jLenj3lTJ16N1VVVUyc+KuIbTdt2kLHju3Jza3/nbJz50788MOWhMSzfPl/OOaYAfWWDRz4U5566jm8Xi85OZrtWdw1duxEt0MQaSDSLHsXh1ic4183NWDZPzQMb+aqqanh3XcX8/DDj9OvXx9uueWPFBREfpCpsLAF5eUNJ2UsLy+nZcsWCYlrw4bvGTz42HrL9t+/E5WVe9mxo5S2bfdLyH5EmmrcuEluhyDSQKxj7x8VvEAJP3Nt3PgDEyb8gWbNmjF58niGDv1ZVNsdcEBntm/fwfbtO+ol36+/XkOXLgdE3Pbjjz9jwoTQozofemhvnnzSd7m0vLycFi0K6q0vLPR9oaiqUlGJiEgoMSV9a+2mZAUiqadLl/25444bMKZXg0v1gU455f9xyin/r+59ixYtGDr0OJ577iWuuMJ3waiqqoo5c17hoot+GXGfRx55OEuWLKy3rLi4kNLS8nrL8vKaUV1dXW9ZZaUv2RcUJOZqglMSVWLmlkSV5mWaVav+C6h0T1JLrGf6kmX69DmEa6+dyrJln1BVVU1eXh65ub775V6vL5k3b55Pu3Ztefnlp+u2+/WvL+TXv/4t27eX0rt3T9588z06dGjHiScen5C4OnXqwKZN9Z8P2LRpM61bt6K4uCgh+3BKYGlYNCVsqUalbaFNmnQmAAsWrHI5EpF9HE36xpjj8NX7X2mt/TRo3YHA40AxUA1cFdxG3HHvvb5BeC699GouvvhcfvazowH48suvue662+ol+1rdunVh5sy/MH/+O2zc+ANnnXUKw4cPjnjFAKK/vH/44YexbNl/GDfunLr1y5f/h6OOOqJJx5gJQk0DW+v2C4c3WBZr+0ROWZuIKXdTXa9eh7kdgkgDjiV9Y8zT+IbvbROmyZ+B6dba140xRwLPAn2dik8Sr23b/Rg79qyYton28v5pp43g2WdfZO7c1zj11JP48suvmT37Re65Z1rccUtoyZ6yNlHtU4Um2pFUFPm0K7Eut9aeCZQErzDGtAX6WGtfB7DWfgzsNsYc6mB8kkY6derAffdN45VXFjBs2FncdddDXHfd1fTrp18ZEZFwHDvTt9ZGulF5EPBN0LJ1QFfgq2j3UVTUAt+UAJmvuLjQsX0NHHgylZV7qaqq4rrrbiUnx/dd0ev1UlVVxfHHnwbAyy8/QY8e4QftCdayZXOaNcuL6lhCtRkyZCBDhgwM0To+LVsWkJPTMuH9RqtNm8TvO9Y+k90+Vsnu3ymZchzRyqbjdfpYmzUxe6fKg3wF+O7jB/Kwb3KfqJSVVVBTE9xN5gl1uTvs3CaZAAAVKklEQVSZ3nprbtRtY4lr0KCjOfzwwxvdxunj3bOnEo/HnYfpkvUgX6x9Jrt9rNLt4UaAsWOPA2DWLN98Zen4kGY8sul43TjW/PwcIPaTv1RJ+uvxne0H6k7Ds3/JIC1bFtKypXNXLESctG3bZrdDEGnAyXv6YfnH8N9hjBkCYIzpD+y11q51NTARqRNpKttE9JOo9qli5szFzJyZfhNASWZz9UzfGHMJsMlaOw+4AHjMGHMHUAFEHuBdROoJVWaXyPbJmLI2ky8Bt2/f2e0QRBpwPOlba4cEvH4i4PVqYKjT8YiIiGSLlLi8LyKSaR58cAoPPjjF7TBE6lHSFxFJgoULn2fhwufdDkOknlR5el9EJKNMnHir2yGINKCkLyKSBKNGRZ5RUsQNurwvIiKSJZT0RUSSYMmSd1iy5B23wxCpR5f3RUSSYNq0ywFYsGCVy5GI7KOkLyKSBAMHatgRST1K+iIiSTBt2qNuhyDSgO7pi4iIZAklfRERkSyhpC8ikgQjR/Zm5MjebochUo+SvoiISJbQg3wiIkmgUj1JRTrTFxERyRJK+iIiIllCSV9EJAmmTh3P1Knj3Q5DpB7d0xcRSYJlyxa5HYJIA0r6IiJJMHXqDLdDEGlASV9EJAkGDTrR7RBEGlDSlyYrK/ma7RuWUL13F82at6Zt10EUdTjE7bAkC1RV7eXDD99k8OBTGm27Z88uvvtuNcYc4UBkIqlNSV+apKzka0rWvYe3phqA6r27KFn3HoASvyTMY4/dwdq1XwFQXV1Nbm4ud901k717K3n33ZfrJf01a77kb3+7C4/HQ+/e/bjoomvJy2vG9u1beOONOY4n/fnznwNg1KhfOrpfkUiU9KVJtm9YUpfwa3lrqtm+YYmSvsSlsrKCP/3pD/zmN3dx2WXX1y1fuvRdvvzyk5DbeDzVzJhxC7/73X107NiFZ599mDfeeIFRo86Lef9PP/0nVq/+nIqKck444QxGjBjDW2/9g7y8PE444Yyo+5k+/UZASV9Si0r2pEmq9+6KablItBYsmM2JJ55BQUFh3bLKynJefvnvnHxy6CT+9defc+ihR9CxYxcAzjzzYj788K0m7b9Pn59yyy1PcPvtT/Hmm3PZunUzw4efxeLFC6isLI+6nxEjxjBixJgmxSCSLEr60iTNmreOablItD755AOOPHJw3fuyslLuvfdaTj31/LqkHmzbtk107nxg3fvCwlZUV+9t0v4HDBgCQH5+c7p06U5Z2XYAjjlmOEuWvBN1P5Mn38bkybc1KQaRZNHlfWmStl0H1bunD5CT24y2XQe5GJWku23bNtOuXWdyc3OprCxn0aJX+ec/5zF69OUcccSxYbdr1aoNGzZ8U/fe6/WSm5sXsu3nny9j7txH6y3r1KkrEyZMq7ds06b1bN68gQMP7AVA375H8frrM6N6eFAkVSnpS5PU3rfX0/uSSFu3bqZ9+84AVFSUU11dxY03zqCwsGW9ds2bt+CUU8bVvT/44L7MnfsoZ589ntzcXD755AN69uwbch8//vFAfvzjgRHjWLnyY2bOfJCJE28jL8/35aF9+85s3bophmPZVLedSKpwLOkbY4YCdwPVwGbgEmvttoD1o4F7gTX+RYuttVOcik9iV9ThkJBJXqV80nRecnJyACgubseAAUO5/fYJfPvtag466GAgh507t1FTU0OPHofWXYovKtqP4447ibvumkyvXofx6acf8tvf3htyD42d6b/33qssW/Ye11//MK1bt6lr44vLG/WRjBv3M0Cz7UlqcSTpG2NaADOA4dbab40xvwHuAC4PaNYOeMxae6sTMUlyqJRP4tG2bUe2bdtS975z567cdtvfmTr1V9xwwyM0b17AokWvUlGxh5Ej6z8VP3LkufTvfzxbt/7A6adfWO9BwECRzvS3bdvMG2/M4bbb/k5eXrOgdZto27Zj1MfSrl2nqNuKOMWpM/2TgH9Za7/1v38csDRM+iUOxSNJolI+iUeHDvuzZctGvN59Z/yx6Ny5K507d23y/tetW0VJyQ/ccsu+P00jRozhmGOGs3LlJxx6aPS1/rNm/avJcYgki1NJ/0fsu2yPtbbMGNPMGJNvra3yL24BXGaMuQBYBUwJ+JIQlaKiFoAnQSGntuLi0GcxbotUyhdPzE4eb8uWBeTktGy8YZK0aePevt0QfLxHH308X3/9EQMGDOajjz7gmWem8+23q7nllvHk5ORQWuq7vP/hhwu5666/U1jYKmL/O3a0ID8/L6rPdfDg4QwePDzkumXL3uHGGx+iZcum/3yy/WebyZw+1mZNzN5OJf0CfPfyA1UTcIPMWnsTcJMxJgcYB7wIHBXLTsrKKqipCd5N5ikuLqS0NPp6YSc1a946ZOJv1rx1k2N2+nj37KnE49nj2P4CtWnTkp073dm3G0Id7/DhY3jwwRvo0eMnHHLIkdx665Nht6+qgqqqyJ/XfvsdwBVX3BLX57po0SsMGHAC1dW5Te5HP9vM5cax5ufnALGfDDlVp78eOKj2jTGmFVBhrW2Qoa21XmvtM0B3Y0y+Q/FJgrTtOoic3PrfJVXKJ7EoKCjk97+/n+bNC9wOpc7QoaczbNgvYtpm4sQzmDgx+hH8RJzgVNJfAIwwxtTWrowHng1sYIzpGPB6JLAm4NK/pImiDofQofuQukF6mjVvTYfuQ3Q/X7LO6tVfsHr1F26HIVKPI5f3rbXbjTETgdeMMTX47u9fZoy5BNhkrZ0H3GyMGQCUA9sBjV+ZJLGW1G348hUqd22oe1/Quitd+5yesNI8lfhJJnrooZfcDkGkAcfq9P2JfV7Q4icC1k9wKpZsFmtJXXDCB6jctYF1K56lpmpXg34qyr5n1zYbdf8q8ZNM1bt3P7dDEGlAY+9nmUgldaEEJ/xansodIfspK1kZU/+xxiMiIk2npJ9lkj87XugRy2Ldr2brk3Q3c+ZDzJz5kNthiNSjpJ9lkj87XugBVWLdr2brk3Q3a9Z0Zs2a7nYYIvUo6WeZWEvqClqHHt0sr2C/kP0UdegbU/8q8ZNMNXbsRMaOneh2GCL1aJa9LBPr7Hhd+5we89P7LYoOiLp/zdYnmWrcuEluhyDSgJJ+Fqoo+57qvbsBqN67m4qy7ynqcEjY5N6mYx+27y2tS8ptOvYBws+yF6tE9SMiIpEp6WeZLWvfp6wkcMAQL2UlX7Br+xq8nvpD3UYqzQOV4IlEsmrVfwGV7klq0T39LFNWsjLk8uCEXytcaZ5K8EQimzTpTCZNOtPtMETq0Zl+1gldUhcrleCJRNar12FuhyDSgJJ+1skhEYk/UqlduFn2RLLJ9Okvux2CSAO6vJ9lijr0Dbk8Jy/0FI3hSvNUgicikn6U9LNMxx6DKepwGPsG0cmhqMNh9Oh/cYOa/ILWXen+k/NimjVPs+yJiKQuXd7PQh17DKZjj8ENlnftc3rI9rGW1KkETwTGjj0OgFmz/uVyJCL7KOmnkVinoPWV563Edw8/h6IOfenYYzDrVjyLp3JHXbu8gv3o/pPzWLP8zw366DngStZ89Bh4q/YtzMmn51GXsfaTv9d76j8nr5Ae/S+OOU5NrSuZaNu2zW6HINKAkn6aiLX+PVw9ftnWr+sncHxleaESPhB6ubcq5HKvp5w1Hz1GTo5Xdf2S9WbOXOx2CCIN6J5+moi1/j1cPX5wwk84b5Xq+kWA9u070759Z7fDEKlHST9NxF7/nph6/ERRXb+IiPuU9NNE7FPQhp7i1i2aWleyzYMPTuHBB6e4HYZIPUr6aSLW+vdw9fjk5Cc6tAb9q65fBBYufJ6FC593OwyRepT000Ss9e/h6vF7HnUZeQX71WubV7AfPQdcGbKfngOubPhFISefngOubDCgT05eIT2Pukx1/SLAxIm3MnHirW6HIVKPnt5PI7X178XFhZSW7iuVC1fyFq4ev/tPzgvZf8cewxr0A5DXvFX9Er/mrQDo0f/iiHHGelwimWTUqF+6HYJIAzrTT3O1JW+1D77VlryVlXydkH7WfvL3egkffCV+61Y8m5gDEBERxyjpp7lElbyF6yfSlLsiEt6SJe+wZMk7bochUo8u76e5RJW8qUROJLGmTbscgAULVrkcicg+SvppLlFT2YbrR0SaZuDAoW6HINKAkn6aa9t1UL1hbKFpJW/h+iEnP+Ql/uAKABGpb9q0R90OQaQBJf00V/vUe7wT1kTqJ9wEPSIikl4cS/rGmKHA3UA1sBm4xFq7LWD9gcDjQLG/zVXW2k+dii+dJarkLVw/SvAiIpnBkaf3jTEtgBnA2dbaY4H3gTuCmv0ZmG6tHQRMBlQTJiJpa+TI3owc2dvtMETqcepM/yTgX9bab/3vHwcscDmAMaYt0Mda+zqAtfZjY8xuY8yh1tqvoug/DyAnJ4/crChCzCM3N5vuzDhzvN26dQMgPz+P3Fx35i5o1gzy81Nr3oRkyuTj3ff75Du+TD7WULLpeN041oD95cWynVOZ40fAmto31toyY0wzY0y+tbYKOAj4JmibdUBXIJqkfwBAmzZdEhJsOigudjsCZzlxvEuXLk3+TqJS2HiTjJKZxxv69ykzjzW8bDpe1471AOB/0TZ2KukX4LtPH6iaffO/hlrvAWqi7H858HPge/92IiIimSwPX8JfHstGTiX99cDPat8YY1oBFdba6oD1BwVt052GZ//hVAKL44xRREQknUR9hl/LqTvgC4ARxpjO/vfjCXhQz1q7EdhhjBkCYIzpD+y11q51KD4REZGMl+P1ehtvlQDGmJOBqfgu2a8BLgPGAJustfOMMb2Ax/Bd6q8ALrfWxjZrjIiIiITlWNIXERERd2VFgZuIiIgo6YuIiGQNJX0REZEsoaQvIiKSJZT0RUREskTaD+De2Ox9mcYYcxxwD3Blps9CaIyZhm9Qp0J8oy1eYq0tdTeq5DHGTAf6AG3wzU0x3lpb7m5UyWWMGQy8B7S11u5opHlaMsb8Gd/vce3fpYettXNdDCmpjDHN8f1NHgrsAuZaax9wN6rkMMacD1wasKglcLC1tr1LITUqrZN+wOx9w6213xpjfoNv9r7L3Y0sOYwxTwNF+JJCNvjKWjsVwBhzK3A98Ad3Q0qqKbVfavw/69HAU+6GlDzGmELgJmCr27EkWTtggrX2A7cDccidwB5r7REAxpiMnXXHWvsM8Ezte2PM7cBM9yJqXLpf3g81e99pLsaTbJdba88EStwOxAnW2tkBb5fjn1gpUwUk/Db4jvUzdyNKuunAvfjOBjNZO7Lk36wxph0wEt+XOQCstVkxGIwxpitwCvAXt2OJJN2T/o8Imr0PaGaMyXctoiSy1u5xOwY3+H+ek4AX3I4lmYwxJxhjluKbYfKNTL59Y4y5AdhorV3gdiwOyAMeN8b8yxhzp/8KR6b6Cb5bUw8bY943xrxsjDnE7aAccj3wgH/m2JSV7km/sdn7JM35h2d+C5hjrX3d7XiSyVr7rrX2aHyTTfU3xlztdkzJYIy5EOiHb1jujGetPdFaexxwIr5bc7e6HFIy7Q8cBdxnrR2M76x3jrshJZ8xphgYDsxyO5bGpHvSrzc7X4jZ+ySNGWNOw3dPe4K19q9ux+MUa+1OfH8sT3Q7liT5I/Bj4D/GmE+BLsAHxpi+7oaVXNbaCnzPIA10O5Yk+gH42Fq7GsBa+wawf6ZefQ1wAfCqtXav24E0Jt2TfsTZ+yR9+X+m9wCjrLVfuB1Pshlj2htj9ve/zgHOADLywS9rbR9rbT9r7RH+h702Aj+31q50O7ZkMMZ09P8/BxgL/NvdiJJqCdDbGNMNwBgzCFiX6pe8E+BsIC0qMtL66X1r7XZjzETgNWNM4Ox9kv5+CnQAXjHG1C7bZq39hXshJVVr4AVjjAfwAO8D97kbkiTIPGNMFZADfAz8zuV4ksZaW2GM+RUw2/+7XIHvi07GMsYUAEcAn7gdSzQ0y56IiEiWSPfL+yIiIhIlJX0REZEsoaQvIiKSJZT0RUREsoSSvoiISJZQ0heRqBhj2hhjTk9QX4c0ZcRBY8wIY8x7iYhBJBuldZ2+iDRkjHkSGIavLrwdcCTwZkCTTsDR1tr/BG1XhG+I2JPx/W3YiG/mv0X+Jl3wjR3wShQxvAgcG7Aox7/flv7pgg8Cfgk8ELRdR+AR4P8BlcBjwE3W2prG9ikijVPSF8kw1tqLAIwxPwL+7R/prlvtev/Qt6FGSPs7sAHoZ62tNMYMAF4yxpxsrY1pxr/gQZSMMScCt/kTfiTPAF/h+4LRBvgH8Ft8ozOKSJx0eV8kcx0MfGmM6W+MOSNgeXN8I6XV8c9bMQL4rbW2EsBauxzfmfY58QRhjGkN3A/c2Ei7wwHjj2GPtfYH4FfA74wxOkERSQAlfZHMNQx4D+iPbyz/Wu2A0qC2HnyX4IMnRikEmjyJiH8OhTeAZ6y1bzfS/HDgbWutp3aBtfZLYA9wYFNjEJF99O1ZJENZa68zxrQAxgWt6gdsDWpbYYyZBTxpjPk9UAKcBJwP/DzWffunGr0MmIDvuYBophzt5N9vsC3+dWtjjUNE6lPSF8kQ/ln6Poqwfn3Qe4BB1tra5ROAicBMYD/gc2CYtXZNjHH8HHgRmI3vgcHNIZp9DTwUtOx7INT0ugfge6hQROKkpC+SIfz3wLsFLzfGXAbkWWtnNLJ9Fb577/eHabIR30N1jcXxgTGmO3AosCJglsRgH1N/KuxlwN3GmPzaqViNMUcCXnwPGIpInDTLnkiGMcbcAowPWNTa//9dAcuesNZeH2LbefhK/Drhu6xe+weiCN99/z3AL6y1H8YZ4xDgLmvtoKDlM/37/D3QHngOeMha+6h//Qjgj9baIfHsXyRb6UxfJMNYa28CboK6ub5X4Pu3/hNr7e5Gtj3Zv90u4GBr7S7/+4eB1dbaByJtnwDjgTuAxcBuYEZtwheR+Cnpi2QoY0wX4CngJXxP5b9pjDk/1nv0cex/EPBPINQ9fYBPghdYa/cAV/v/E5EEU9IXySD+M/uzgBOA4/GNZvecf90YYIExZjm+EfpesNZWhO0sMVZaa49I8j5EJEq6py+SYYwx1wJrgNdqH4gLWJcHnAL0tdbeGbSupX87iHxP/65oLvP7z/Q/IKg8MMgga+03jfUV0Kfu6YvEQUlfRNKGf36Aztba1W7HIpKOlPRFRESyhIbhFRERyRJK+iIiIllCSV9ERCRLKOmLiIhkCSV9ERGRLKGkLyIikiX+P9u+flstSnK2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.colors import ListedColormap\n",
    "\n",
    "def plot_decision_boundary(clf, X, y, axes=[0, 7.5, 0, 3], iris=True, legend=False, plot_training=True):\n",
    "    x1s = np.linspace(axes[0], axes[1], 100)\n",
    "    x2s = np.linspace(axes[2], axes[3], 100)\n",
    "    x1, x2 = np.meshgrid(x1s, x2s)\n",
    "    X_new = np.c_[x1.ravel(), x2.ravel()]\n",
    "    y_pred = clf.predict(X_new).reshape(x1.shape)\n",
    "    custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
    "    plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)\n",
    "    if not iris:\n",
    "        custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])\n",
    "        plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)\n",
    "    if plot_training:\n",
    "        plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\", label=\"Iris-Setosa\")\n",
    "        plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\", label=\"Iris-Versicolor\")\n",
    "        plt.plot(X[:, 0][y==2], X[:, 1][y==2], \"g^\", label=\"Iris-Virginica\")\n",
    "        plt.axis(axes)\n",
    "    if iris:\n",
    "        plt.xlabel(\"꽃잎 길이\", fontsize=14)\n",
    "        plt.ylabel(\"꽃잎 너비\", fontsize=14)\n",
    "    else:\n",
    "        plt.xlabel(r\"$x_1$\", fontsize=18)\n",
    "        plt.ylabel(r\"$x_2$\", fontsize=18, rotation=0)\n",
    "    if legend:\n",
    "        plt.legend(loc=\"lower right\", fontsize=14)\n",
    "\n",
    "plt.figure(figsize=(8, 4))\n",
    "plot_decision_boundary(tree_clf, X, y)\n",
    "plt.plot([2.45, 2.45], [0, 3], \"k-\", linewidth=2)\n",
    "plt.plot([2.45, 7.5], [1.75, 1.75], \"k--\", linewidth=2)\n",
    "plt.plot([4.95, 4.95], [0, 1.75], \"k:\", linewidth=2)\n",
    "plt.plot([4.85, 4.85], [1.75, 3], \"k:\", linewidth=2)\n",
    "plt.text(1.40, 1.0, \"깊이=0\", fontsize=15)\n",
    "plt.text(3.2, 1.80, \"깊이=1\", fontsize=13)\n",
    "plt.text(4.05, 0.5, \"(깊이=2)\", fontsize=11)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 화이트박스 vs 블랙박스\n",
    "\n",
    "위에서 확인할 수 있듯이, 결정 트리 모델은 매우 직관적이며, 모델의 예측 즉, 결정 방식을 이해하기 쉽다. 이러한 모델을 **화이트박스**(white box) 모델이라고 한다. 반대로, 추후에 다룰 랜덤포레스트나 신경망은 이러한 결정 방식을 이해하기에는 어렵기 때문에 **블랙박스**(black box)모델이라 한다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.3 클래스 확률 추정\n",
    "\n",
    "결정 트리는 어떤 하나의 데이터(샘플)이 특정 클래스 $k$에 분류될 확률을 추정(계산)할 수 있다. 확률을 추정하는 방법은 각 리프 노드의 클래스 $k$의 비율을 계산하여 구할 수 있다.\n",
    "\n",
    "예를 들어, 꽃잎의 길이가 5cm이고, 너비가 1.5cm인 경우에는 위의 그래프에서 초록색 노드로 분류될 것이다. 이러한 확률을 계산하면, $\\text{setosa} = \\frac{0}{54} = 0$, $\\text{versicolor} = \\frac{49}{54} = 0.907$, $\\text{virginica} = \\frac{5}{53} = 0.093$ 이다.\n",
    "\n",
    "따라서, 결정 트리는 꽃잎의 길이가 5cm이고, 너비가 1.5cm인 꽃은 `Versicolor`로 예측할 것이다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        , 0.90740741, 0.09259259]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tree_clf.predict_proba([[5, 1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tree_clf.predict([[5, 1.5]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.4 CART 알고리즘\n",
    "\n",
    "Scikit-Learn은 결정 트리 알고리즘 중 **CART**(Classification And Regression Tree)알고리즘을 사용한다. \n",
    "\n",
    "CART 알고리즘은 먼저 학습 데이터셋(train set)을 하나의 특성(feature) $k$의 임계값 $t_k$를 사용해 두 개의 서브셋(child node)로 나눈다. \n",
    "\n",
    "예를 들어, 위의 그래프에서 루트 노드(root node)는 꽃잎의 길이(petal length)라는 특성을 임계값 2.45로 (**꽃잎의 길이 $\\le$ 2.45cm**)로 `True/False`로 나눴다. \n",
    "\n",
    "CART 알고리즘의 비용 함수(cost function)는 다음과 같다.\n",
    "\n",
    "$$\n",
    "J\\left(k, t_k \\right) = \\frac{m_{\\text{left}}}{m} G_{\\text{left}} + \\frac{m_{\\text{right}}}{m} G_{\\text{right}}\n",
    "$$\n",
    "\n",
    "- $G_{\\text{left/right}}$ : 왼쪽/오른쪽 자식노드의 불순도(지니계수)\n",
    "- $m_{\\text{left/right}}$ : 왼쪽/오른쪽 자식노드의 데이터(샘플) 수"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "이와 같은 방법으로 자식 노드(subset)로 나누는 과정을 결정 트리의 최대 깊이(sklearn에서는 `max_depth` 인자) 또는 불순도를 줄일 수 있는 분할을 찾을 수 없을 때까지 반복한다.\n",
    "\n",
    "이렇듯 CART 알고리즘은 각 단계 즉, 각 노드에서 그 다음 자식 노드로 분할할때 가장 좋은 최적의 분할만 찾아갈 뿐, 현재 단계의 분할이 몇 단계를 거쳐 가장 낮은 불순도가 될지는 고려하지 않는다. 이러한 알고리즘을 **탐욕적 알고리즘**(greedy algorithm)이라고 한다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "따라서, 최적의 결정 트리를 찾는 것은 **NP-완전**(NP-Complete)문제이며, $O(\\exp{(m)})$시간이 필요하다. 따라서, 교재의 표현처럼 *납득할만한 좋은 솔루션* 으로만 만족해야 한다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.5 계산 복잡도\n",
    "\n",
    "결정 트리에서 예측을 하기 위해서는 루트 노드에서 부터 리프 노드까지 탐색해야 한다. 일반적인 결정 트리는 대부분 좌/우 균형을 이루기 때문에 약 $O(\\log_{2}{(m)})$ 개의 노드를 탐색해야 한다.\n",
    "\n",
    "각 노드는 하나의 특성값만 확인하기 때문에 예측에 필요한 전체 시간 복잡도는 특성의 개수와 무관하게 $O(\\log_{2}{(m)})$이다. 따라서, 예측 속도는 매우 빠르다.\n",
    "\n",
    "반면, 학습 단계에서는 각 노드마다 모든 데이터를 모든 특성($n$)에 비교하므로, 학습 단계에서의 복잡도는 $O(n \\times m \\log{(m)})$이다. 따라서, 학습 단계에서의 속도는 데이터의 크기가 클 수록 느리다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.6 지니 불순도 또는 엔트로피?\n",
    "\n",
    "의사결정나무는 '6.4 - CART 알고리즘'에서 알아 보았듯이, 학습 데이터셋(train set)을 하나의 특성(feature)을 가지고 두 개의 서브셋(child node)로 나누는 알고리즘 이다. \n",
    "\n",
    "이렇게 하나의 특성에서 두 개의 서브셋으로 나누는 기준은 **불순도(impurity)**를 **최소**(또는, 순도, homogeneity를 최대)로 하는 것이다. 이렇게 불순도 즉, 불확실성이 감소하는 것을 정보이론에서는 **정보획득**(Information Gain)이라고 한다.\n",
    "\n",
    "Scikit-Learn의 [`DecisionTreeClassifier`](http://scikit-learn.org/stable/modules/generated/sklearn.tree.DecisionTreeClassifier.html#sklearn.tree.DecisionTreeClassifier)에서는 기본값(default)으로 지니 계수(`Gini`)가 사용되지만, `criterion` 인자를 `\"entropy\"`로 설정하면, **엔트로피** 지표를 사용할 수 있다. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import graphviz\n",
    "\n",
    "with open(\"./images/iris_tree.dot\", encoding='UTF8') as f:\n",
    "    dot_graph = f.read()\n",
    "dot = graphviz.Source(dot_graph)\n",
    "dot.format = 'png'\n",
    "dot.render(filename='iris_tree', directory='./images', cleanup=True)\n",
    "dot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "지니계수와 엔트로피 계수는 다음과 같다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 지니 계수\n",
    "\n",
    "$$\n",
    "G_i = 1 - \\sum_{k=1}^{n}{p_{i,k}^{2}}\n",
    "$$\n",
    "\n",
    "- $p_{i, k}$ 는 $i$번째 노드에 있는 데이터 중 클래스 $k$에 속한 샘플의 비율이다.\n",
    "- 예를 들어, level 2의 초록색 노드의 gini 계수는 $1 - (\\frac{49}{54})^{2} - (\\frac{5}{54})^{2} \\approx 0.168$ 이다. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 엔트로피 계수\n",
    "\n",
    "$$\n",
    "H_i = - \\sum_{\\underset{p_{i,k} \\neq 0}{k=1}}^{n}{p_{i,k} \\log_{2}{\\left( p_{i, k} \\right)}}\n",
    "$$\n",
    "\n",
    "- 예를 들어,  level 2의 초록색 노드의 엔트로피 계수는 $-\\frac{49}{54} \\log_{2}{\\left( \\frac{49}{54} \\right)} -\\frac{5}{54} \\log_{2}{\\left( \\frac{5}{54} \\right)} \\approx 0.445$ 이다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 둘 중 어느 계수를 사용할까?\n",
    "\n",
    "지니(Gini)나 엔트로피(Entropy) 계수 둘 다 비슷한 트리를 만든다. 지니 계수가 계산이 조금 더 빠르기 때문에 Scikit-Learn에서는 지니 계수를 기본값을 사용한다. \n",
    "\n",
    "하지만, 지니 계수는 가장 빈도가 높은 클래스를 한쪽 가지(branch)로 고립시키는 경향이 있다고 한다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.7 규제 매개변수\n",
    "\n",
    "의사결정나무는 학습(또는 훈련) 데이터에 대한 제약이 거의 없기 때문에 학습 데이터에 오버피팅(overfitting, 과대적합)되기 쉽다. 의사결정나무는 모델 파라미터가 없는 것이 아니라 학습 전에 파라미터 개수가 결정되지 않기 때문에, 이러한 모델을 **비파라미터 모델**(nonparametric model)이라 부르기도 한다. \n",
    "\n",
    "의사결정나무 모델이 학습 데이터에 과적합 되는 것을 방지하기 위해 몇 가지 규제(regularization)가 있는데, 일반적으로 결정 트리의 **깊이(depth)**를 조절한다. Scikit-Learn에서는 `max_depth` 인자로 트리의 깊이를 설정할 수 있다. \n",
    "\n",
    "[`DecisionTreeClassifier`](http://scikit-learn.org/stable/modules/generated/sklearn.tree.DecisionTreeClassifier.html#sklearn.tree.DecisionTreeClassifier)에서는 트리의 깊이(`max_depth`) 뿐만 아니라 규제를 하기위한 다른 인자들이 있다. 아래의 매개변수에서 `min_`으로 시작하는 매개변수를 증가 시키거나, `max_`로 시작하는 매개변수를 감소시키면 모델에 규제가 **커진다**.\n",
    "\n",
    "- `min_samples_split` : 분할되기 위해 노드가 가져야 하는 최소 샘플(데이터) 수\n",
    "- `min_samples_leaf` : 리프 노드가 가지고 있어야 하는 최소 샘플 수\n",
    "- `min_weight_fraction_leaf` : `min_samples_leaf`와 같지만 가중치가 부여된 전체 샘플 수에서의 비율\n",
    "- `max_leaf_nodes` : 리프 노드의 최대 개수\n",
    "- `max_features` : 각 노드에서 분할에 사용할 특성의 최대 수"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "아래의 예제는 sklearn의 `moons` 데이터셋에 위의 매개변수 중 `min_samples_leaf`(리프 노드의 최소 샘플 수) 매개변수를 다르게 하여 결정 트리를 학습시킨 것이다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 792x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_moons\n",
    "Xm, ym = make_moons(n_samples=100, noise=0.25, random_state=53)\n",
    "\n",
    "deep_tree_clf1 = DecisionTreeClassifier(random_state=42)\n",
    "deep_tree_clf2 = DecisionTreeClassifier(min_samples_leaf=4, random_state=42)\n",
    "deep_tree_clf1.fit(Xm, ym)\n",
    "deep_tree_clf2.fit(Xm, ym)\n",
    "\n",
    "plt.figure(figsize=(11, 4))\n",
    "plt.subplot(121)\n",
    "plot_decision_boundary(deep_tree_clf1, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)\n",
    "plt.title(\"규제 없음\", fontsize=16)\n",
    "plt.subplot(122)\n",
    "plot_decision_boundary(deep_tree_clf2, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)\n",
    "plt.title(\"min_samples_leaf = {}\".format(deep_tree_clf2.min_samples_leaf), fontsize=14)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 가지치기(pruning)\n",
    "\n",
    "**가지치기**(pruning)는 결정트리를 아무런 규제 없이 학습 시킨 뒤 불필요한 노드를 제거하는 방법을 말하며, 마치 나무에서 불필요한 가지를 자르는 것과 같기 때문에 가지치기라 한다.\n",
    "\n",
    "불순도를 최소화하는 것이 **통계적으로** 효과가 없다면 리프 노드는 필요없는 노드라 할 수 있다. 이렇게 판단하는 기준은 **$\\chi^{2}$ 검정**(chi-squared, 카이 제곱검정)을 사용하며, **$p$-value** 값이 $0.05$보다 높으면 해당 노드는 불필요한 노드로 추정하여 해당 노드의 자식 노드를 가지치기 한다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.8 회귀(Regression)\n",
    "\n",
    "의사결정나무는 회귀(regression)문제에도 사용할 수 있다. Scikit-Learn에서는 `DecisionTreeRegressor`를 이용해 회귀 트리를 모델링할 수 있다.\n",
    "\n",
    "아래의 예제는 아래의 식\n",
    "\n",
    "$$\n",
    "y = 4 \\left( x - 0.5 \\right)^{2} + \\text{noise}\n",
    "$$\n",
    "\n",
    "헝태의 임의의 데이터셋을 만들어 `max_depth=2`로 설정하여 회귀트리를 만든 것이다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 2차식으로 만든 데이터셋 + 잡음\n",
    "np.random.seed(42)\n",
    "m = 200\n",
    "X = np.random.rand(m, 1)\n",
    "y = 4 * (X - 0.5) ** 2\n",
    "y = y + np.random.randn(m, 1) / 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeRegressor(criterion='mse', max_depth=2, max_features=None,\n",
       "           max_leaf_nodes=None, min_impurity_decrease=0.0,\n",
       "           min_impurity_split=None, min_samples_leaf=1,\n",
       "           min_samples_split=2, min_weight_fraction_leaf=0.0,\n",
       "           presort=False, random_state=42, splitter='best')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "tree_reg = DecisionTreeRegressor(max_depth=2, random_state=42)\n",
    "tree_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "다음은 `max_depth=2`와 `max_depth=3`을 비교한 것이다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 792x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tree_reg1 = DecisionTreeRegressor(random_state=42, max_depth=2)\n",
    "tree_reg2 = DecisionTreeRegressor(random_state=42, max_depth=3)\n",
    "tree_reg1.fit(X, y)\n",
    "tree_reg2.fit(X, y)\n",
    "\n",
    "def plot_regression_predictions(tree_reg, X, y, axes=[0, 1, -0.2, 1], ylabel=\"$y$\"):\n",
    "    x1 = np.linspace(axes[0], axes[1], 500).reshape(-1, 1)\n",
    "    y_pred = tree_reg.predict(x1)\n",
    "    plt.axis(axes)\n",
    "    plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "    if ylabel:\n",
    "        plt.ylabel(ylabel, fontsize=18, rotation=0)\n",
    "    plt.plot(X, y, \"b.\")\n",
    "    plt.plot(x1, y_pred, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
    "\n",
    "plt.figure(figsize=(11, 4))\n",
    "plt.subplot(121)\n",
    "plot_regression_predictions(tree_reg1, X, y)\n",
    "for split, style in ((0.1973, \"k-\"), (0.0917, \"k--\"), (0.7718, \"k--\")):\n",
    "    plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
    "plt.text(0.21, 0.65, \"깊이=0\", fontsize=15)\n",
    "plt.text(0.01, 0.2, \"깊이=1\", fontsize=13)\n",
    "plt.text(0.65, 0.8, \"깊이=1\", fontsize=13)\n",
    "plt.legend(loc=\"upper center\", fontsize=18)\n",
    "plt.title(\"max_depth=2\", fontsize=14)\n",
    "\n",
    "plt.subplot(122)\n",
    "plot_regression_predictions(tree_reg2, X, y, ylabel=None)\n",
    "for split, style in ((0.1973, \"k-\"), (0.0917, \"k--\"), (0.7718, \"k--\")):\n",
    "    plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
    "for split in (0.0458, 0.1298, 0.2873, 0.9040):\n",
    "    plt.plot([split, split], [-0.2, 1], \"k:\", linewidth=1)\n",
    "plt.text(0.3, 0.5, \"깊이=2\", fontsize=13)\n",
    "plt.title(\"max_depth=3\", fontsize=14)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "export_graphviz(\n",
    "        tree_reg1,\n",
    "        out_file=\"./images/regression_tree.dot\",\n",
    "        feature_names=[\"x1\"],\n",
    "        rounded=True,\n",
    "        filled=True\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<text text-anchor=\"middle\" x=\"234.5\" y=\"-245.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">x1 &lt;= 0.197</text>\r\n",
       "<text text-anchor=\"middle\" x=\"234.5\" y=\"-230.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">mse = 0.098</text>\r\n",
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       "<text text-anchor=\"middle\" x=\"297.5\" y=\"-126.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">mse = 0.074</text>\r\n",
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      ],
      "text/plain": [
       "<graphviz.files.Source at 0x21c2d18cef0>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import graphviz\n",
    "with open(\"./images/regression_tree.dot\") as f:\n",
    "    dot_graph = f.read()\n",
    "dot = graphviz.Source(dot_graph)\n",
    "dot.format = 'png'\n",
    "dot.render(filename='regression_tree', directory='./images/decision_trees', cleanup=True)\n",
    "dot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "위의 회귀 트리 그래프에서 확인할 수 있듯이, 분류 트리와 비슷한 모양인 것을 알 수 있다. 다만, 회귀 트리는 각 노드에서 클래스를 예측하는 것이 아니라 특정 **값**을 예측한다.\n",
    "\n",
    "예를들어 $x_1=0.6$인 데이터의 값을 예측한다고 했을 때, 위의 그래프를 따라 가다보면, $\\text{value} = 0.111$이 되며, 해당 노드의 110개의 샘플의 평균값이 예측값이 된다. 그리고 이 110개의 샘플에 대한 MSE값이 0.015이다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CART 알고리즘은 학습 데이터셋을 평균제곱오차(MSE)를 최소화하도록 트리를 분할한다.\n",
    "\n",
    "$$\n",
    "J\\left(k, t_k \\right) = \\frac{m_{\\text{left}}}{m} \\text{MSE}_{\\text{left}} + \\frac{m_{\\text{right}}}{m} \\text{MSE}_{\\text{right}}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{cases} \\text{MSE}_{\\text{node}} = \\sum_{i \\in \\text{node}}{\\left( \\hat{y}_\\text{node} - y_i \\right)^{2}} \\\\ \\hat{y}_\\text{node} = \\frac{1}{m_\\text{node}}\\sum_{i \\in \\text{node}}{y_i} \\end{cases}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "회귀 트리 또한 분류 트리처럼 과적합되기 쉽다. 아래의 예제는 규제가 없는 경우와 `min_sample_leaf=10`을 지정한 경우에 대한 차이를 나타낸 것이다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 792x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tree_reg1 = DecisionTreeRegressor(random_state=42)\n",
    "tree_reg2 = DecisionTreeRegressor(random_state=42, min_samples_leaf=10)\n",
    "tree_reg1.fit(X, y)\n",
    "tree_reg2.fit(X, y)\n",
    "\n",
    "x1 = np.linspace(0, 1, 500).reshape(-1, 1)\n",
    "y_pred1 = tree_reg1.predict(x1)\n",
    "y_pred2 = tree_reg2.predict(x1)\n",
    "\n",
    "plt.figure(figsize=(11, 4))\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(x1, y_pred1, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
    "plt.axis([0, 1, -0.2, 1.1])\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", fontsize=18, rotation=0)\n",
    "plt.legend(loc=\"upper center\", fontsize=18)\n",
    "plt.title(\"규제 없음\", fontsize=14)\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(x1, y_pred2, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
    "plt.axis([0, 1, -0.2, 1.1])\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.title(\"min_samples_leaf={}\".format(tree_reg2.min_samples_leaf), fontsize=14)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.9 불안정성\n",
    "\n",
    "의사결정나무 모델은 이해하고 해석하기 쉽고, 분류 및 회귀에 사용할 수 있을 뿐만아니라 성능도 좋다. 하지만, 위의 예제코드의 그래프에서 보았듯이, 결정 트리는 계단 모양의 결정 경계(decision boundary)를 만든다. 따라서, 학습 데이터셋의 회전(rotation)에 민감하다. 아래의 예제에서 오른쪽 그래프는 데이터셋을 45°도 회전시킨 후 결정 트리 모델링을 한 것이다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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odbrsQLv4RVpzYUd9EPsb9P3S3KkzY9y1/V6132tChakjwlon5GcHACUgqaVd/CLeuLCj3u9R27h0mInS/bs368K9BU3lp4xf65rCnALSGqj4qLeLX0TmGhxezfCK9TMjpD19Cz0dQ+onv/c3uLJu1lX5iTG27d81c+Gu5U71acQ0Zfy6Qg6rxZWuwONDu/hF2hP1jnq/R227/X7JH9/Diy8u8NKbexidWMG248k67vrhvVtnTrJS+73GNGKaMn5dIYe1cF9X4PGhXfwi8eL3qG033y+VQYh5vZDJZDivv5drLlzA1PFfdBSLa2Yu3IuzL9w1ajqXRkxTxq8r5LAW7ruwc1W8idvhASLi76htN98v9QYherMZCoe30zP8Ql/ii1LcTv2LkgrTlGnWAaCdzUxhLdxvVABncvN8fR/pXpwODxAR/7XbYab6O6ehhAxCtHPhnp8Y495d303tzn0VpilU7wq53bWcnba4ancn/+Jl6zi27/vA7EvNUnGS/PE9bRfUaZX2RCci4fA6Ajv35KsGEnLQTOXC3cuRn2lvuafCVIDONjO1OwXUyUamweHV/MeBzRQL47PvKBVn1plqc1RraU90IuKWet85tSaLJfqXXRZSRG5Qyz1tfpJpYazl7HQj05yitCq2NG+O8nrCUm2i02J7EYlao++WUqm89vKZ8UkePHI6EetL26GWeypMnRNVz06/+9nV02nx2yw2VzZHRXEMZ/UoaKvHpT3RiYhbGuX1s1PwP/9+is9vf5JfnJoMOapoNWq5l7bBBBWmDum0ab0fxeziZevIZGev7PB7M1OnxW+z2MIoqL3wWiT6xesoqBKdiLioXl4nkyWbgY/f3MMHL1vBCxf1RhNcRNRyryz0NabGmGuAzwBTwNPALdbaE1X3/xfgg5SL5h7gNmvtrrDjjEIn6zzrrds8tv8HHD/wCKXChOfNQJ1uZmpHpzv5W8UW9bF+UawJqjcKWm/tqEstSrQBq3PKm8lVb/Pm0NBa52Lye81+bV7P5vopFibo7QGo9DHtYer4L1Izna+We2WhFqbGmH7gi8CrrbUHjDEfAT4F3Fr1sAxwvbX2rDHmWuBvgMvDjDMqnUxL111AXipSKkzMPNfrZqCgTyHppvhtFFsYBXUrXotEv7RzwpJLiU4bsDqjvNlY3Dpy1MY7f9EKxk7YOZs3Bwb6yA2MNH1u9Z/Vz88hzNP2qvP6gZ13z9lPkKQ+pl500nIviRf8YY+Yvgb4obX2wPTPXwIsVQnWWntv1eO3A0vDCy9anTSt97KWMoijQjsVRPEb5bF+URzD2c4oqCu9RbXTtCvKm3XE7bjievHmj/98zuNKxSmO7H2Eiy8Zafrcyp8V/O1MEtZx07UafpclpI9pUJJ4wR/2GtMR4InKD9baPNBjjGm0kOT3gK+HEJcTOlnn6XUtZTkJhrORKk2iWBPk1yhomBu2tAGrKyMob84Rt44cXtojVUyO51s+t/Jn9ftziGpDacPvsoT0MQ1CUjuuhD1iOo/yGqlqU9R0TzfGDAJ/DhSA97fzBoOD/dNP88fQ0HzfXqv1e61lYKCPI3sfYXI8T2//IBeuvJolS9c0fM6yVS/nwGP3eUp4lSmiZq/ntzA/P6+y2czM/+ey2a5iPDr2y7pF4pGxX8553VNnxvjKln/ibVe8iUX93pJtvdg+ev17Oo632gM7HuLgySNsOfRj3nzp9R29hpfP7tSZMXYe2T1rVHnn0d3c8KvrPX8OQcXmRY6cL6/ThcDzJsQvdzYroLy8d9i5qZ3Crrd/cFZ8nRSLXj+Heu9dWxjXi8nvz6/ed9lkscSSVVcyv4P3cvG7p8Kv2B7Y8dBMEihR6iqXV4s6d4ZdmB4Crqr8YIxZAIxba6eqblsF/D3wKWvtP7f7Bvn8OEWPV6WteDmhwW+5gZFZUzhAwxiGhuaTGxhheMX6OQvIa09KgvJV9OHHH56zdqkd7axliuLz86JYPPfZFIpFTzE2Wsfz7l9/S8Pn1L7uxt2b2Hf8IBt/usnTlEuQn19+Yoxt+3dSosS2fbtYd9FL255a9xrfxt2bKNUMKxeLJc+fQyf8/Ox6sz0w5MtLdSrwvAnxy53Nlj61eu8oclOz9nbVMtkeLlx59az4Wi3z6vRzqOe8pZfX3VB63tLLZ14viM+v8l12aM8D9PWUGJ2YYtvxCd5w+XLOtvlern73gH+xVXJ4oTh9wV8sdJzLg4gPOs+dYU/lfw+43hjz3Omf3wt8teYx/wh8oNPkmkaDw6tZvnYDL7jsNkYuvYXnPL/xl3030zGdtrNKgm7bQbk25RLm1LpLG7BiKpV5s1UbvDBa3PmpUbyDw/9ppsDs6VvI8Ir1c2a1mv1Z/f4cBodXM7xi/ZyYwli3Ozi8ml0Hc6ntY9qOJLeWCnXE1Fp70hjzIeDbxpgi5XVT7zHG3AL8EvgB8BLgT40x1U/dULXwX1oYHF49M6pZq5v+nlEtio+aHxt3wt6530zYG7bed8XNidw5GpY05k0vG5tc6MjRjm67krR6rp+fQ5QbSsWbJF/wh97H1Fq7EdhYc/OXq/4/9JiSqNOeoc24cspS2LotKqPYud9MFL1Nk7hzNExpy5teL4LjVkB1E2+z58btc5DuudJxJQg6+SmhaqdjMrl5ZDI9HNv3QMenQ7lyylKY/Dg5ybUpl7CvtF1bxiDuS+tFsIgk7CrbdWE3g65cRVemxYpd9rkLYhTWdX6MLro25RL2lbZLyxgkHjrp6SwiyaDCNCStGiQHWbD6tTY0bmu6/OBHUZnkKZdWXFvGIPGQxotgiT+tpfeHCtOQNCoO/+PAZkqlqUBPL/FzWiyua5mqR6t/fVUfJyb6+JmHP36ai0o/RLGeVeIvjRfBEn9aS+8PFaYhaVQE1p4NDP7vdHdpWiyKs61rR6v7+zK87sULKT1+hl8WA33r1HNtGYPER1wvgiWdwj52OcmjsypMQ+K1uXKFn4v8XZkWi+ps63qj1X09Ga55/mLu2ftsYO8bJ0ElOY04i0gahL2WPsmjs9qVH5J6TZCb8XM0M8qGydWiOtu6UZE/NE/XZRXdHiAgIs21OjBA4suP7i2dvF9SO53omzkklSLw2L7vU++40GpBjGa6MC0WVQuYRqPVoxP+HL8Yd2FPQYnEhV9Lj6KaLXJJFMu4whL2WvqkdzrRiGmIyr+EzYvSdkYzTxx9LFZX4FH1Qa03Wn12qsSD+04G+r5xEebxpCL1uDia6OcRzFHNFrki6cdZh7mWPuzR2ShoxDRkzTYiLV+7wfPrxPEKPKq1rrU7fMfPlviXn43x87HTDJ8/z7f3ieNidLVzkqi5msv8PII57QcGJP046zDX0qeh04lGTENWb/Suk+IsjlfgUa51HRxezfK1G3jBZbex7fGz7D5ydua+/MQYd23/etdXnHFcp+naqVSSPq7mMj+LyTSemlctysLcr/zuijR0OvE0YmqMmQ88DhSBVdbaiar7vgS8E3irtfaeQKJMEK/9+Vqtx4nrFbgLa11r+bG7Ma7rNNOQ5KKk3Nmaq7nMzzZ7rnRGiYqfn2W7M1NJ272ehk4nngpTa+0ZY8wngS8BtwGfBTDGfBp4F/CBNCfWdrUqzrxMbbnUmzTOill8KSjjuhg9DUkuSsqdrbmay/wsJtN+YICfn2U7hWZcBwzSrp2p/LuAnwP/rzFmoTHmduAO4JPW2i8EEVxaeZnaatR+aursmDObB+JgYmGm640/SVyMnrTpr4jdRcJyp5+blfxa3uQ3v5ceVS8nWr52Q2qKUvDvs2y3TZI2dnYm6vzvuTC11hYoJ9PnAN8E/gz4S2vtHwYUW2p5mdoaHF7N8jXX1R1VSNqOx8D0ZDm7INN1QZnEdZpxXC/rqqTlTr93WLvSZ7meNBeTfvPjs2yn0EzigEFYos7/be3Kt9Z+xxjzE+Ba4B7gw9X3G2PmAZ+fvv8C4CjwV9baz/kTbvx56eXmdWprydI15AZGOLDz7jmPD2PHY9z70mUvGJhzWyfT8Elbp6npL/8lKXcGscPaxbXncffUU4f413/9LhMB9GvOZrMUi8Gc53zk6Dil806RmX6finY7iKRh93oQTp2JPv+3VZgaY24CXjL9Y95aW9uUswd4CrgOeAJ4MfCvxpij1tqvdRts3Hlti9LuepwoNg+42uKlHZmBHshkZt3WSUEZ5DrNKFpQxXW9rMuSlDtd3awk5+zY8X+5+54tnJr/DOSCKSDb0puhZ1U/U4+Pw2TzXt70TZKZd5ZcTw+vXnf9zM3tFppJGzAIy/27N0ee/z0XpsaY64CvAP8ETAK3GGM+a619rPIYa+1p4L9XPe1RY8xG4ErAqeQaBa8jDe0ulI9i80AS+tIVfvEMi89fwoff8XtRh9JQ2DtK1dfUf0nLna5uVpKyn/70R3z573bw7EVHyPQU5lx8RyH7vEEyi3Lknp+l+FS+5eMXDCzkXTe+j+ecf8HMbe0WmtrY2b78xBjb9u+KPP97bRd1OfB/gB8CbwUuAt4MfBp4Y5Pn9QBXAf+r60gToJ2RhnamtqJoRaJRk+BFMaWi6S9/JTF3pr31keuOHDnAeBEyuSL98/t5/TVvxO/SdGBgHs8+O9H6gcB4YYL7Dm+lSJHe4YVc9+Jr6c81Ptgkl+th1Yihr7dv1u0qNIP38N6tlGpOp4wi/7csTI0xa4CNwB7gjdN9+PYaY+4EbjXGXGmt/WGDp/8FMArc7VfAcRbUSEMYrUhq15Nmc/0UC+NzHqdRE/9EMaWi6S//JDV3pr31UZzkcjnWvuhXfX/doaH5jI6e8fTYjbu/TyaTgRJkyHA8c5rXvSjci5g4nsoXhUOjRykUo8//TQtTY8xy4D7KCfK11tpTVXf/IfB2ylf0V9Z57v+mfMX/Smvt2dr70yjIkYYgNw/UW08KGchkoXRu/ZJGTfwT1ZSKRiX8kfTcqc1KZXHfABo0V5YGJa3JflDed8XNbV10BKVpYWqtPQBc3OC+o8Dcbc2AMeZzlHeXvtJae7zbIJMiriMN9daTQolMto9crjdWf5a4cGVKRTqj3Jl8SdgAGjQXlgapy0hjro4kt7Ur3wtjzF8ArwSusdYeq3P/NcBngCngaeAWa+2JqvsvpnxKytD0Yz5orX3U7zijEseRhkbrRkuFCZZf+q6Qo0kHV6ZUJDzNcmfa86aLkrABNGguLA1Sl5HGXB1J9rUwNcasAD4ETAD7jDGVux6x1r7WGNMPfBF4tbX2gDHmI8CngFurXuYLlJtPf8cY82vAV4Ff8TNOaY924YbP65SKq1e80p5muRN4E8qbztEG0NaiXhrkylICF7k8kuxrYWqtfRKabgB8DfDD6WkuKF/hW6YTrDFmMbDGWvud6dfbYYw5bYx5kbX23/2MVWZrtlZKu3Dd5eoVr7SnWe40xvwGypvO0QV78Lq98HZhKYGrXB5J9nwkqU9GKDePBsBamwd6jDG90zctB/bXPOdJYFkYwaVVqyMGXT4ysGO9kHv+EMWwfwN81O650RJbIyhvOmfxsnVksrPHdpJ8wR7F+endHo0Z5FKCqM+T74brx7X6vsa0hXmU1z9Vm4KZXR717i8Ano+uGBzsn36KP4aG5vv2WkHwI76D/7a17lqpZ45u5aKVa6ffZ+3M/4cdn9+y2QyZi3NkFuQ4m/E/xlNnxvjKln/ibVe8iUX93Y2eNIvtgR0PzfzilCix5dCPefOl1zd8fBBc/Put8Cu2HDlfXqcLgedNUO5s//lrGRjo48jeR5gcz9PbP8iFK69mydI1kcbX13fu32smk/Ht7+GBHQ9x8OSRcp654PrA/37LfZx3UwJ2Ht3NDb+6vq18OjQ0n49e/57A4pv1ebSZd6P+3aj+7qiY+Q7x8e+209wZdmF6iHIbFACMMQuAcWvtVNX9y2ues4K5owEN5fPjFOfsIO+MC20Tmuk2vurp+3omx/Ndvb6rn984RTIX5MhkMkwMlDj89HFf19Zs3L2JfccPsvGnm7qaGmn2+ZXbSe2c2SBVKBbYtm8X6y56aWjrhFz9+wV/Y+vN9pS3FEUn8LwJyp2dyA2McPElI7Nu8+N1u4nv7NlzFxelUsmXeCr5pkSJbft28epfuYrSRLAXbBt3b6I0PddcLJbDQfgYAAAf4klEQVTayqdB//ur/Tzaybsu/G7sPXZw7ubaYoG9Tx8E/Pk3DJ3nzrAnMr8HXG+Mee70z++lvEgfAGvtEeAZY8x6AGPMpcBZa+2+kONMvNrp+3qSulbq0MLCrNV8nU4T1RPW9HqztVOSOMqbEqna9Yj3794c6Pu5PtVcb31m2LpZSvC+K27m96/7yJz/ot6sVhFqYWqtPUl55+m3jTFbgMuATxtjbjHG3DD9sA3AJ40xPwL+FHh3mDGmRf3epOckda3U6MQYTy8okclOV6aZjK8JL6yE5UIbFgmH8qZEqV6RuH3/rkCLRJcvvF0pmrtdf+uysKfysdZupHxMX7UvV93/C+CaUINKoVYjpUltlv+dvT+ac5tfOxLDbE3iypWthEN5U6JSr0gsBryL2+UL73Z3+gfR0s/lVk9+CL0wFTc0a3WyfO2GCCIKxxOjRyjVNOXxK+GpNYmIRKWyZ+BFzxnjA2/O8uDBhewfb2v/W111i8RisEWiyxfe7RbNQbT0c7nVkx9UmKZUWnuT/vcr3sFdd32WzfvGKC46xfD5S/jwO37Pl9d2+SpfRJKr+njUTAbOW5jhhtXP4YGDo12/dr0i0YUNPFFpp2iuN7I5RHc73tNwaIAK05SqTNM3aqov7XP5Kl9EkqvenoG+XJarLhyMKCKB+iObv3XB6317zYqkjZqqME2xweHVKkRFRGKu0Z6Bwd7Ie/CmVqORzRvG10MXvZHTMDOnwlSkis6eF2lf7ZHGy1a9nNzASMfP1+xNexrtGchPFuhv87WUA/3RaGTz/t2bedXKV3T8ummYmYvxgYwi/ktyC45qcT5OT9xS70jjA4/dN3OkcSfPrz4Sud1YDuy8mye2f4EDO+/m2L6HZv3cyWvGQb3jUc8Wimw+km/7tdKSA4PWaGRz/38cjiii+NCIqci0pLfgqBbETlGNtKRTvfWNpeIUJw9v8TTq2e3zK6o3AEG5wM0f//nM/ZWCF8rHiSZJ9Z6ByYkxRk+XePDgsbZ35acpBwat0chmmjeOeaURU2lL7YhEkkYgXDjNwy/NRkSDOp1KIy3p1Gh9Y7NeyX4+v6LVoSFwruBNosHh1Sxfu4F/P7aEv7q3yM+Ptff5QXA5MC0zNGn5cwZNhal45ueUm2tcOc3DL82KxCC+fMI6ilXc0+joYq9HGnf7/IpuC+G0CzIHpuWiNco/Z5KKYhWm4lmzKbe4c/kIvHY1KxKD+vJJ0miztKfe+sZ2eiJ3+/yKbgvhtAsqB6blojXqP2eSin8VpuKZX1NuLkpSC45mRWIQXz5JG22W9gwOr2Z4xfqZgq+nbyHL11zneX1ovecPr1jf9q78egVuLT8PEYnDsqZSLuN5FC2oHBjkRatLo4RRXpxHXRT7TZufxLNmx5i6oJuWM0lpwdHqVJAgvnzS0PBZmqvtidzuBg8/eirXOzRk/qIVnDn1pO9tqOpttKpsrHKpzVVhqK/lJsfKpsW3Xvom3zc6BX1KURCbODsR9WlMSTuiVIWpeObyMaZBfFHEcZd5qyIxiAI8SaPNEm9hHRrSqpNA0H1ZPb1+T5biwl6g+Q77IIu7IC9aXeogEOXFedRFcRBUmIpnLh9j6lfLmWquXI23I4oiMSmjzSJeNVvWFPRoqtfXz16wADLl/29UJAVd3AWZj1waJYzy4jyJM1YqTKUtrh5j6vf6V5euxtvhepEYx1FokVrNljUFcZFczdPrzyuRXTwfMuXKtNEoWtDFXVD5yLVRwijzbhJnrFSYSiL4vf7VpavxuGlWfMZxFFqi4+pRpc2WNR3b90Dd5/i1SdTLRXh29eSc+2vzmGvFXTuSOErYKdcHIzqhXfmSCJ22nClmmbOrU7vMu9OobUnSdo6Kv+odJ+pq3+RmnQT86svaiJfXzywpkslmZt1fO4oW5xZ5SRwllHM0YiqJ0On614mFmTkjeLoa71yzJRAahZZGWh0nWuHnlHi3Gi1rCnqTqJfXLzzUT+n5+1kwOMAd7/39uq8T5+IuylFCLUcKngrTFHN1mqxTba9/7clydkF5VCHolkpJUZ2Uh5g/5/5GxWecpw0leF6OE62oncp2LY8FvUnUr9dP4hRwGLQcKXgqTFMqLn34gpS9YGDm/4NuqZQU1Un5ty54/az7mhWfGoWWZtpZf1k9Ze1qHgt6k6irm1DDFvboZVw3xcaN1pg6IIoTRJJ8vKgnvZBd3D9n16rWPTZWm5RPjc8uJpoVnxqFlma8rr+snbJOfR5LubCP4dTRy+HQiGnEorriT/Lxol5kLs7NuU0jeM3VJuX7d2/mVStfMXN/s+JTo9DSTKN1kwuXmKYnN6U9j6VZ2KOXLixHSsv61lALU2PMTcAdwDiwB7jVWjte85hbgZumY5sAbrHWHgwzzjAF3fOuEb/aK7m2vquR6jh/fVUfPzlxlokWu1blnHpJefv+Xay76KUzCVLFZ3CSnjs7XTfp+jHJEpywN1O6sBwpLetbQ5vKN8YsBf4AeKW19mXAKHB7nYeeBK611r4cuAf407BijEJUV/ydtleqVhntdbGdS7XaOPv7Mtw2vJDVTz3L0JECv3/dR2b+U3FVX72kXNRUVijSkjsHh1ezfO0GXnDZbSxfu8HTBa4feUziJ4qWflEvR0pTu70wR0xvAu6x1j4z/fNfA3cCf1z9IGvt16p+3A68PZzwohHVFb8fOzujGu1tV704+3oyXPP8xdyz99mIooqXukm5qBHmkCh3NhDmMclxmR1KgyhGL6MetEhTu70wC9MRYEfVz08Cy1o853eBrwcVkAuC7nnXTLc7O+OyvqtRPEPzkrXEOsj1R/WS8tDQfEZHz/j6PlLXCMqdDTXLY34Vk67u/k+rsEYvo9j1X+/9XFjfGqbAvpmNMc+jPJ1U8QRQPWxVAIoNnvtc4G+AR621n2/nfQcH+6df2h9DQ3N7NfppaGgtAwN9HNn7CJPjeXr7B7lw5dUsWbrGifia6e0fZHI8X/f2SlxRxlfRKM7RiSly2awTMTbSTmwP7HiIgyePsOXQj3nzpde3fPypM2N8Zcs/8bYr3sSi/s5G6JPy2TWTY+5GuSApd/rjxNHH6haTAwN9MLSmrfgO/tvWurNDzxzdykUr1/oad0Wnn19f37l/r5lMJrC/hyj/fj96/XtaPsaP+NrNqV41iq3R+z2w4yFqBogpUfI9rlbxtavT3BlYYWqtfQpYX/nZGPMxYHnVQ1YA+2ufZ4xZB/wF8DvW2s3tvm8+P07RY6PmVsIaEcoNjHDxJSOzbvPyvlGPWJ239PK6o73nLb2c0dEzkcdXUS/Os1MlHtx3kkJxXqQxNrsib+fzy0+MsW3/TkqU2LZv9qakRjbu3sS+4wfZ+NNNHU0JufL3W4+fsfVme2DIl5fyRLnTH4cff7huMXn48YdZsnRNW/HVu7Ct3B7En7Obz+/s2XMXF6VSybn4wuBHfJ3k1G5ia/Z+e48dpFCcu5Rq79MHff97cCF3hjmXeS/wDWPMX1lrTwPvB75S/QBjTC/wD8A11toDIcYmHQhzfVc3auMcP1viX342xs/HTjN8/rxIY/Nrl2W764/UKDpWlDs74OdSI+3+T58od/3Xvl/U61vDFlphaq21xpjPAZuMMUXKi/P/FsAYcwfwfSAPPA+42xhT/fTrrLVnw4o1LElYTB+XE0iq47zrrs+y+8hZWBRtTH4Vh52sP0rTQvq4U+7sjJ/FZL29AJChWJjiie1fiG3+lvrCXtOZtjWkrYS6+8Naeyfl3aS1t1fvLk3F34IW04tfxWG7O1SVBONHubN9fm4srZ11yeTmUSpOUiyUW8kqfydL2Lv+XeiR6hIdSRoRHaWXbn724Wt3h2qzJOi3/MQYd23/eqJ77ombBodXM7xi/cwIaU/fQoZXrO+4cKzus5rL9UJp9v4z5e/kCLtnadQ9Ul2TrH45MRKXVksSDD+vkNtdfxRmEkzLSSXipqCWGil/J1vYazrTtoa0FRWmEdFi+nSL8go5rCSoDVaSVMrfwUrLmfBSnwrTiETZWF+il4YrZG2wipdjx44wOTnhy2vl8/M4fdqf1wpCt/FlFq6Ck7ug+uIykyOzcBVPPXUw0vhOn85TmtP1Ml4005JuKkwjEpdWSyKd0Aar+Pnz/+9fOX78RNRhxMaLVmS4+iU5Fi2AU6fhkUcn+PcntwHbIo3rbKZAaflRMpkSixa110TShZFKzbSICtMIxaXVkguS0ForTbTLNH4mlh5mfP6xqMOIjUeL8OhPam68OJJQapTIZODCZRfxjt94d1vPdGGk0stMiwsFtARHhak4T6214ke7TONnYMEACwr+fMlnMsy5MHFJkuPLZDJcuualXHvldWQz3hvvuDBS6XWmxYUCWoKjwlSc0GxEtFlrLRWmbkrDGtqkef9bPsRkgo4kbUbxzeXCmnAvMy0uFNASLPUxdVD++B4O7LybJ7Z/gQM77yZ/fE/UIQWqMiJa2eVaGRGt/LnVmkVEJDh+9lXuhpeZlnoFtCSLRkwdk8Zp61YjomrNIiISHFfWhLeaadGmynTQiKlj0ngiVKsR0cXL1pHJzr6GUmst/+h0JpFouPK7F5c14WGeWifR0YipY9I4bd1qRFSttYKljQQi0XDldy8ua8LjUkBLd1SYOiaN09ZeDhtQa61gaCOBSDT0u9e+uBTQ0h1N5TsmjdPWg8OrGV6xfqb47ulbyPCK9SpEQ6CNBCLRSOLvnitLEyTeVJg6Jq1F2uDwapav3cALLruN5Ws3JP7P64JWO3H1JSMSDFd2wfutemmCSKdUmDpIRZqEodVGAn3JiAQjiZt4apcmxL3IluioMJWOpK3XahI120igLxmR4CRxE08SlyZINLT5SdqWxl6rSdRsI8HG3d+P/BQYkaRK2iYe9RcVP2nEVDyrjJIe2/dA6nqtpklS17+JSDDisDRBa+bjQ4WpeFJ7bGg9Se61miZx+JIREXfEYWmC1szHh6byxZN6J1LVCqvXav74HjXbD1AcvmRExB2uL01Qz9h4UWEqnrQaDQ2r12qr9a1BFq35iTHu3fVdbnzxDYlOaq5/yYhI/ESZP+ttzNKaeXdpKl88aTYaGmav1Xojt5X1rbXLDSpFq18dAzQVJCLSGT/yZyfrRLVmPn5CHTE1xtwE3AGMA3uAW6214w0euwr4GXC5tfbR8KIMVlynoRsdGxp28/9GI7dTZ8eaFq3dxqipIImScmf8pWXGpR6/8md1cet1xLPZmnmNmroptBFTY8xS4A+AV1prXwaMArc3eGwW+DPgcFjxhSHoEb0guXIiVaOR256+hU2L1m6pR59ERbkzGdI84+JH/uy0t7LWzMdPmCOmNwH3WGufmf75r4E7gT+u89iPAxuBwZBiC0WQI3phGBxeHXmcjUZuFy9bNzMSXavbTVlR9uhL8yiLzEh97oy7NM+4+JU/va4TzU+M8fcPfoM3/qfXsnDeAq2Zj6EwC9MRYEfVz08Cy2ofZIy5GVhprf0fxpj/p903GRzsBwotH+fV0NB8316r2Yhep+/jZ3xB8Du+oaG1DAz0cWTvI0yO5+ntH+TClVezZOkaBgb6OPDYfXOK1mWrXj4rjmw2M/P/uWy2ZYwP7HiImpkgSpTYcujHvPnS6335czWy9eAODp48Esp7dcLlf39+xZYj58vrdGGEkHJnwdHcGYQw46vOIV5zR1I+Pz/y56kzY+w8sntWcbvz6G5u+NX1LOqfPfDwwI6H2Hf8kLM5E5Lzd9tKp7kzsMLUGPM84J6qm54AqocLC0Cx5jmvAt4JvK7T983nxym2aGvk1dDQfEZHz/jyWtB4urmnb2FH7+N3fH4LKr7cwAgXXzIy67bR0TPkBkYYXrF+zhre3MDIrDiKxXNpslAstoxx77GDFIo1U0HFAnufPhjo55/pK7Bt/05KlNi2bxfrLnqpU6MsLv/78zO23mwPDPnyUp5EmTsnHc2dfgszvvzEGNv275zJIYVioeXvc5I+Pz/y58bdmyjVLBQtFkts/OmmWaOmlc/a1ZwJyfq7baXT3BlYYWqtfQpYX/nZGPMxYHnVQ1YA+2ue9lHgQmCrMQbghcDXjDEfsNY+EFSsYWk2DR2muG7A8iKI5QZRTQXdv3tzIlqcaDlCe5Q7kyXtm2/8yJ9e14k2m+5XHoqPMKfy7wW+YYz5K2vtaeD9wFeqH2Ctva76Z2PMJuD2pOwsrRRMURaFQZ9zX1309vYPct7SyxNT9IapfOW/KxFnT3eyk1ZmSX3ujLOgNt+kqdDyUty2WsuqPBQfoRWm1lprjPkcsMkYUwS2A38LYIy5A/i+tXZ7WPFEJeoNRIG2VKopeifH874WvWny8N6tlGpWZsVxlCXNmz78otwZb0HNuKjQmq3ZyPTVKy9XHoqRUPuYWmvvpLybtPb2ertLsdauDzqmtAmypVInRW+SlxV049Do0bnrsmLY4kQnrvhDuVOq6YJvrmYj08pD8aIjSVOm2QasVloVke0WvUEvKwibn1Nr77vi5kAXyYcxDRhlmy2RJFOhNVf1yHR17sxPjPGXj3xZeShGdCRpyixeto5Mdvb1iJcNWF4OB2jW/L6eZiOscRSnBtphxNpsak1EOuPKEZudHA8aBeWh+FFhmjKdnuDkpYhst+gNcllB2Do9lSQKYcWqE1dE/OdKoRWXC3HlofjRVH4KtbsBK398j6cisrbrQKtd+d0sK3BNnKbWwopVJ66I+M+FQqvc8D4ea1yVh+JHhWlCBLWJqDKF30htEVld9LZaI+lKX9duxWktZZxiFZG5XCi0ktJjWdykqfwE8LL+s1P1pvArui0iO11W4BpXpta8iFOsIuKeRj2WXV6+JPGiEdMECLI3abP1nn4UkVH3dfWDC1NrXsUpVhFxT9g9ltN0kICUqTBNgCA3ETVbBxr3gtIvLkyteRWnWEXEPWH3WNZBAumjqfwEaLdNUzs6bS8lIiLJ874rbuaTr/9terI5AHqyPfzOK94byEVvnLqdiH9UmCZAkMVjUtaBioiIP+ptfgpCvQ4iknyayk+A2jZNfh/tmYR1oCIi0r1Gm5/87uyhDiLppcI0IVQ8iohI0MLa/NSsg4jWmiabpvJFRETEk7A2P6mDSHppxFREREQ8ed8VN7c8PMWv95F00oipiIhIQuUnxrhr+9e1o11iQ4WpiIhIQlX3ARWJAxWmIiIiCaQ+oBJHKkxFREQSSH1AJY5UmIqIiCRMoz6gGjUV16kwFRERSZhmfUBFXKbCVEREJGHUB1TiSn1MRUREEkZ9QCWuQi1MjTE3AXcA48Ae4FZr7Xidx30CuBHIAz+y1v63MOMUEXGJcqeIpEVoU/nGmKXAHwCvtNa+DBgFbq/zuA8Bq4Bfs9ZeTTkZi4ikknKniKRJmGtMbwLusdY+M/3zXwNvrH6AMSYHfBD4sLW2AGCtrVm+LSKSKsqdIpIaYU7ljwA7qn5+ElhW85iLgZPAR40xVwJngN+31m7z+iaDg/1AoeXjvBoamu/bawVB8bUvm83M/H8um3UyxgqXYwO34/Mrthw5X16nCyOElDsLyp3OUHzdcTk+l2OD6HNnYIWpMeZ5wD1VNz0BTFX9XACKNU97HvAi4LettR8zxqwFvmWMWW2tnfDyvvn8OMXiVOsHejA0NJ/R0TO+vFYQFF9nisVzA0mFYtHJGMHdz6/C5fj8jK032wNDvryUJ1HmzknlTicovu64HJ/LsYEbuTOwwtRa+xSwvvKzMeZjwPKqh6wA9tc87Slgf+Uq31q70xjzNHARsDeoWEVEXKHcKXGRnxjj3l3f5cYX38DCeQuiDkcSIsw1pvcCbzPGVP71vh/4SvUDrLX7gYnpq32MMSsp19sHQoxTRMQlyp3ipIf3buXgycNq2i++Cq0wtdZa4HPAJmPMViAH/C2AMeYOY8xl0w99O/C/jTGbgC8Bb7XWToYVp4iIS5Q7xUWVI09LoKNOxVeh9jG11t4J3Fnn9j+u+v9/B14VZlwiIi5T7hTXVB95Wjnq9HW/cm20QUki6EhSERER8ezUmfJoaeXI00KpoFFT8Y0KUxEREfHs/t2bZ0ZLKyqjpiLdUmEqIiIinu0/cXhmtLSiUCpwcPRoRBFJkoS6xlRERETi7Xdf/S6ne3FKvGnEVEREREScoMJURERERJygwlREREREnKDCVERERESckKTNTzmATCZH1rdyO0c26/JHpPg6sWjREp6zZB7FhfNYsug8eh2MESBHztnYwO34/IytJzPzOjlfXtA9OZj+c/qUO13+twGKr1uKr3MuxwZu5M5MqbYZWXxdBTwSdRAiklhXA5ujDiIAyp0iEqS2cmeSCtN5wGXAUaDQ4rEiIl7lgKXAdmAi4liCoNwpIkHoKHcmqTAVERERkRjT5icRERERcYIKUxERERFxggpTEREREXGCClMRERERcYIKUxERERFxggpTEREREXGCClMRERERcYIKUxERERFxgrsHtkbAGHMTcAcwDuwBbrXWjtd53CeAG4E88CNr7X9zKb7px64CfgZcbq191JX4jDG3AjdR/rc3AdxirT0YYEzXAJ8BpoCnp9/vRNX9FwNfAoamH/PBsD4vj/H9F+CDlC8ie4DbrLW7XImv6nFLKP+dv9ta+02X4jPGvAe4DRgD9llrN4QVX1q4nDuVNzuOS7kzwPiqHqfcWUMjptOMMUuBPwBeaa19GTAK3F7ncR8CVgG/Zq29mnJCcSa+6cdmgT8DDocRW5vxnQSutda+HLgH+NMAY+oHvgjcOB3TQ8Cnah72BeAvrbXrgA8DXw0qng7jywDXW2vXA58E/sax+Cr+hHJyC42X+IwxbwB+E7hy+vf17WHGmAYu507lzY7jUu4MPr4K5c4aKkzPuQm4x1r7zPTPfw28sfoBxpgc5SuwD1trCwDW2rDOdG0ZX5WPAxuBA2EENs1TfNbar1V9Ztspn6MblNcAP7TWVj6HLwH/uXKnMWYxsMZa+53p2HYAp40xLwowJs/xTcd0r7X27PSPQX9ebccHYIx5G3AM2BZibOAtvo8DH7DWPguh/r6micu5U3mzM8qdAccHyp2NqDA9ZwR4ournJ4FlNY+5mPKV60eNMQ8ZY/7FGPPrDsWHMeZmYKW19oshxVUxgof4avwu8PWgAqImJmttHugxxvRO37Qc2F/zHC9x+2WE5vHV+j2C/bxqjdAivunpoLcAnwgxrooRmsRnjOkBLgReb4x50BjzA2PMayOIM+lGcDd3eolNeXOuEZQ7uzGCcmfHUrvG1BjzPMpTIhVPUF5rUVEAijVPex7wIuC3rbUfM8asBb5ljFltrZ2IOj5jzKuAdwKv8zMWv+Kreu5zKU+rPGqt/XxgQcK8mpiY/rnU5P6GcQegVXwAGGMGgT+nHNv7wwkNaBGfMeYS4NPAa621U8aYEEMDWn9+w8AFwF5r7TXTa+IeMca8zFp7JMQ4E8Xl3Km86Rvlzu4od3YhtYWptfYpYH3lZ2PMxyhfBVasYO4V4VPAfmvttunX2GmMeRq4CNjrQHwfpXyVs3X6H/oLga8ZYz5grX3AgfgwxqwD/gL4HWvtZj9jquMQcFXVey8Axq21U1X3L695Tt24A9IqvspmjL8HPmWt/eeQ4vIa3+3AEuDB6X9vy4FXGGMWWWvvdiC+48CYtfZbANbag8aY7cAaQIVph1zOncqbvlHuDDY+5c4mNJV/zr3A26b/gqB8dfWV6gdYa/cDE9NX+xhjVlLekRjGmiQv8V1nrV1jrX2JtfYlwI+B/+p3cu00vulpgn+gvOA6jOT6PeD66ZEGgPdStUB/+srvGWPM+un4LgXOWmv3hRBby/im/SPldT5hJ1Zo/fm9y1q7uurf27eAj4SUWL3ENwVsNsa8DsAYcz5wCfBvIcWXFi7nTuXNzih3dke5swuZUkl7ASqMMe8CbqU8HbGd6YX6xpg7gO9ba7dPL+7+POXR5hLwUWvtdlfiq3n8JuB2G17bk6bxUW4Rs2P6vmrXVS1S9zumGyjvyCxSnjZ7D/BfgV9aazcaY15IeXpsHuV2Lbdaa/cEEUu78QE/oPyZ1X4ZbahatB5ZfNbajTWPvQv4pg235Umrv9+llDeUDFL+nf0ja+2/hBVfWricO5U3O45LuTOg+JQ7m1NhKiIiIiJO0FS+iIiIiDhBhamIiIiIOEGFqYiIiIg4QYWpiIiIiDhBhamIiIiIOEGFqYiIiIg4QYWpiIiIiDhBhamIiIiIOEGFqYiIiIg4oSfqAESCYoyZDzxO+ci1Vdbaiar7vgS8E3irtfaeiEIUEXGOcqdESSOmkljW2jOUzwK+GLitcrsx5tPAu4APKbGKiMym3ClRypRKpahjEAmMMSYH7AQuAF4AvBv4LPBJa+0fRhmbiIirlDslKipMJfGMMa8Hvg18H3gl8Hlr7W9HG5WIiNuUOyUKKkwlFYwxO4BLgXuAt1hrSzX3fwB4O/BiYIu1dn3oQYqIOEa5U8KmzU+SeMaYm4CXTP+Yr02s044CfwxcBlwRVmwiIq5S7pQoaMRUEs0Ycx3lqahvA5PAbwKXWGsfa/D424E36qpfRNJMuVOiol35kljGmMuB/wP8EHgr8AnK7U8+HWVcIiIuU+6UKKkwlUQyxqwBNgJ7KF/FT1hr9wJ3Ar9hjLky0gBFRByk3ClRU2EqiWOMWQ7cB4wCr7XWnqq6+w+BM8D/iiI2ERFXKXeKC7T5SRLHWnuAcmPoevcdBQbCjUhExH3KneICFaYigDGmh/LvQw+QNcb0A0Vr7dloIxMRcZdyp/hNhalI2ScoH8FXcQZ4CFgfSTQiIvGg3Cm+UrsoEREREXGCNj+JiIiIiBNUmIqIiIiIE1SYioiIiIgTVJiKiIiIiBNUmIqIiIiIE1SYioiIiIgTVJiKiIiIiBNUmIqIiIiIE/5/BNad/IYOBkkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 792x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(6)\n",
    "Xs = np.random.rand(100, 2) - 0.5\n",
    "ys = (Xs[:, 0] > 0).astype(np.float32) * 2\n",
    "\n",
    "angle = np.pi / 4\n",
    "rotation_matrix = np.array([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]])\n",
    "Xsr = Xs.dot(rotation_matrix)\n",
    "\n",
    "tree_clf_s = DecisionTreeClassifier(random_state=42)\n",
    "tree_clf_s.fit(Xs, ys)\n",
    "tree_clf_sr = DecisionTreeClassifier(random_state=42)\n",
    "tree_clf_sr.fit(Xsr, ys)\n",
    "\n",
    "plt.figure(figsize=(11, 4))\n",
    "plt.subplot(121)\n",
    "plot_decision_boundary(tree_clf_s, Xs, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)\n",
    "plt.subplot(122)\n",
    "plot_decision_boundary(tree_clf_sr, Xsr, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 학습 데이터 셋에 민감함\n",
    "\n",
    "결정 트리의 주된 문제는 학습 데이터셋의 변화에 민감하다는 것이다. 아래의 예제는 붓꽃(iris) 데이터 셋에서 `Versicolor` 종류 중에서 `sepal width`가 가장 큰 데이터들을 지우고 결정 트리 모델링을 한 결과이다. 그림에서 볼 수 있듯이, 6.2의 결과와는 다른것을 알 수 있다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.8, 1.8]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris = load_iris()\n",
    "X = iris.data[:, 2:] # petal length and width\n",
    "y = iris.target\n",
    "\n",
    "tree_clf = DecisionTreeClassifier(max_depth=2, random_state=42)\n",
    "tree_clf.fit(X, y)\n",
    "X[(X[:, 1]==X[:, 1][y==1].max()) & (y==1)] # 가장 너비가 큰 Iris-Versicolor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeClassifier(class_weight=None, criterion='gini', max_depth=2,\n",
       "            max_features=None, max_leaf_nodes=None,\n",
       "            min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "            min_samples_leaf=1, min_samples_split=2,\n",
       "            min_weight_fraction_leaf=0.0, presort=False, random_state=40,\n",
       "            splitter='best')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "not_widest_versicolor = (X[:, 1]!=1.8) | (y==2)\n",
    "X_tweaked = X[not_widest_versicolor]\n",
    "y_tweaked = y[not_widest_versicolor]\n",
    "\n",
    "tree_clf_tweaked = DecisionTreeClassifier(max_depth=2, random_state=40)\n",
    "tree_clf_tweaked.fit(X_tweaked, y_tweaked)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 4))\n",
    "plot_decision_boundary(tree_clf_tweaked, X_tweaked, y_tweaked, legend=False)\n",
    "plt.plot([0, 7.5], [0.8, 0.8], \"k-\", linewidth=2)\n",
    "plt.plot([0, 7.5], [1.75, 1.75], \"k--\", linewidth=2)\n",
    "plt.text(1.0, 0.9, \"깊이=0\", fontsize=15)\n",
    "plt.text(1.0, 1.80, \"깊이=1\", fontsize=13)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "tensorflow",
   "language": "python",
   "name": "tensorflow"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}