{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Decision tree classifier\n",
    "\n",
    "In this notebook, we implement Decision tree classifier from scratch. \n",
    "Our formulation is based on Section 14.4 of the book PRML. However, we d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "import matplotlib as mpl\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "mpl.rc(\"savefig\",dpi=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 Setting\n",
    "\n",
    "Here we consider classification problems. \n",
    "\n",
    "* Let $N \\in \\mathbb{N}$ be the number of training data points, \n",
    "* $d \\in \\mathbb{N}$ be the dimension of input, \n",
    "* $\\mathcal{C} = \\left\\{ 0, 1, \\dots, C-1 \\right\\}$ be the set of class labels, \n",
    "* $x_0, x_1, \\dots , x_{N-1} \\in \\mathbb{R}^d$ be the training input data, $y_0, y_1, \\dots, y_{N-1} \\in \\mathcal{C}$ be the training labels, \n",
    "$y := {}^t (y_0, \\dots, y_{N-1}) \\in \\mathcal{C}^N$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 Theory\n",
    "\n",
    "### 2.1 Expressing a partitioning of the feature space with a decision tree\n",
    "\n",
    "In a decision tree classification, we parition the input space $\\mathbb{R}^d$ into disjoint hyperrectangles. \n",
    "In each hyperrectangle, the classifier predicts a single class. \n",
    "\n",
    "The partitioning is performed by selecting a hyperrectangle $A$ (for the first parition, $A = \\mathbb{R}^d$), the axis $i \\in \\{ 0,1, \\dots, d-1 \\}$, and the threshold $\\theta$, and partition $A$ into two parts \n",
    "$$\n",
    "\\begin{align}\n",
    "    A_1 &= \\left\\{ x \\ \\middle| \\ x \\in A, \\ x_i > \\theta \\right\\} \\\\\n",
    "    A_2 &= \\left\\{ x \\ \\middle| \\ x \\in A, \\ x_i \\leq \\theta \\right\\}\n",
    "\\end{align}\n",
    "$$\n",
    "Specific ways for choosing $i$ and $\\theta$ will be given later. \n",
    "\n",
    "We express a series of successive paritionings by a tree which we call a decision tree, where each node is \n",
    "* associated with one partitioning (splitting) operation if it is not a terminal (leaf) node, and \n",
    "* associated with one hyperrectangle and one class which is the prediction of the classifier on the hyperrectangle region. \n",
    "\n",
    "For the detail, see Figures 14.5 and 14.6 in the textbook.\n",
    "\n",
    "Our task here is to choose a good way of constructing a decision tree, namely, how to partition the feature space and how to choose the predicted class for each region. \n",
    "\n",
    "Although it is written in the textbook that it is customary to \n",
    "* first grow the tree using a given criterion, and \n",
    "* then prune the tree to make the model generalize better, \n",
    "we will not implement pruning here, and imposing regularization by limitting some properties of the tree (e.g. depth of the tree). \n",
    "\n",
    "Note that scikit-learn also employs this approach."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Criteria for partitioning\n",
    "\n",
    "Given a hyperrectangle to be splitted, we split the region according to a given criteria as follows\n",
    "(In terms of decision tree terminology, given a non-terminal node, we add two nodes to the given node.).\n",
    "\n",
    "First, as the criteria, we can use cross entropy: \n",
    "$$\n",
    "\\begin{align}\n",
    "    Q(R_{\\tau}) := -\\sum_{c=0}^{C-1} p_{\\tau}^{c} \\log p_{\\tau}^{c}\n",
    "\\end{align}\n",
    "$$\n",
    "or Gini index:\n",
    "$$\n",
    "\\begin{align}\n",
    "    Q(R_{\\tau}) := \\sum_{c=0}^{C-1} p_{\\tau}^{c} \\left( 1 - p_{\\tau}^{c} \\right)\n",
    "\\end{align}\n",
    "$$\n",
    "where\n",
    "$$\n",
    "\\begin{align}\n",
    "    p_{\\tau}^{c} &:= \\frac{N_{\\tau}^{c}}{N_{\\tau}} \\\\\n",
    "    N_{\\tau}^{c} &:= \\left| \\left\\{  i \\in [N] \\middle| x_i \\in R_{\\tau}, \\ y_i = c  \\right\\} \\right|, \\\\\n",
    "    N_{\\tau} &:= \\sum_{c=0}^{C-1} N_{\\tau}^{c}.\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Suppose split the region $R_{\\tau}$ into two disjoint regions $R_{\\rho}$ and $R_{\\sigma}$. \n",
    "Then, it can be shown easily from the properties of conditional entropy (for cross-entropy) or direct calculation (Gini index) that \n",
    "$$\n",
    "\\begin{align}\n",
    "    Q(R_{\\tau}) \\geq \\frac{N_\\sigma}{N_\\tau} Q(R_{\\sigma})  + \\frac{N_\\rho}{N_\\tau} Q(R_{\\rho}) \n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Our criteria here isto find the \"best\" splitting by which the quantity decrease the most, i.e., the splitting $\\sigma, \\rho$ with the smallest value of \n",
    "$$\n",
    "\\begin{align}\n",
    "    \\frac{N_\\sigma}{N_\\tau} Q(R_{\\sigma})  + \\frac{N_\\rho}{N_\\tau} Q(R_{\\rho}) \n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3 Stopping criteria\n",
    "\n",
    "We have shown how we split a node (a hyperrectangular region). Next problem is when to stop. \n",
    "\n",
    "Here we use a simple criteria: we stop growing tree when \n",
    "* there is only one class inside the region, or \n",
    "* the number of data associated with the node is smaller than a predefined minimum value, or \n",
    "* the depth of the tree has reached a predefined maximum depth.\n",
    "\n",
    "Having raeched a leaf node, we associate the node with a predicted class, which will be determined by the most frequently appearing class in the corresponding region. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 From math to code\n",
    "\n",
    "In this notebook, we employ the gini index as our splitting criteria.\n",
    "\n",
    "We define two classes, namely, Node and DecisionTreeClassifier.\n",
    "Here, the Node class contains all the attributes and methods required to construct a decision tree and to make prediction accordingly.\n",
    "\n",
    "Specifically, the split method of the node recursively split the training data, and thereby construct a decision tree classifier."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Node:\n",
    "    '''\n",
    "    the class representing a single node in a decision tree\n",
    "    '''\n",
    "    def __init__(self, depth, X=None, y=None):\n",
    "        '''\n",
    "        isleaf : a Boolean variable indicating whether the node is a leaf node or not.\n",
    "        depth : the depth of the node\n",
    "        X : the indices of data set associated with the nodes (to be splitted by the node)\n",
    "        y : label associated with the data\n",
    "        feature : the index of axis by which the node separate data\n",
    "        thresh : the threshold $\\theta$ of splitting applied to the feature.\n",
    "        label : the most frequent class in the points associated with the node.\n",
    "        left : the left child node of the node\n",
    "        right : the right child node of the node\n",
    "        '''\n",
    "        self.isleaf = None\n",
    "        self.depth = depth\n",
    "        self.X = X\n",
    "        self.y = y\n",
    "        self.n, self.m = np.shape(self.X)\n",
    "        self.feature = None\n",
    "        self.thresh = None\n",
    "        self.label = np.argmax(np.bincount(y))\n",
    "        self.left = None\n",
    "        self.right = None\n",
    "        \n",
    "        \n",
    "    def gini(self, y):\n",
    "        '''\n",
    "        The method calculates gini index for a given label array y.\n",
    "        '''\n",
    "        Ns = np.bincount(y)\n",
    "        N = len(y)\n",
    "        return np.sum(Ns/N * (1- Ns/N))\n",
    "        \n",
    "    def calc_gini_splitted(self, y_left, y_right):\n",
    "        '''\n",
    "        The method calculates 'gini index' after the splitting, where the values is given by weighted sum of gini indices of two regions.\n",
    "        '''\n",
    "        Nl = len(y_left)\n",
    "        Nr = len(y_right)\n",
    "        N =  Nl + Nr \n",
    "        return Nl/N*self.gini(y_left) + Nr/N*self.gini(y_right)\n",
    "        \n",
    "    \n",
    "    def find_best_split(self):\n",
    "        best_feature = None\n",
    "        best_thresh = None\n",
    "        val = float(\"inf\")\n",
    "        for feature in range(self.m):\n",
    "            sort_ind = np.argsort(self.X[:, feature])\n",
    "            X_sorted = self.X[sort_ind]\n",
    "            y_sorted = self.y[sort_ind]\n",
    "            for i in range(1, self.n):\n",
    "                y_left = y_sorted[:i]\n",
    "                y_right = y_sorted[i:]\n",
    "                tmp_val = self.calc_gini_splitted(y_left, y_right)\n",
    "                if tmp_val < val:\n",
    "                    val = tmp_val\n",
    "                    best_feature = feature\n",
    "                    best_thresh = (X_sorted[i-1, feature] + X_sorted[i, feature]) / 2\n",
    "        self.feature = best_feature\n",
    "        self.thresh = best_thresh\n",
    "    \n",
    "    def split(self, max_depth, min_samples_split):\n",
    "        '''\n",
    "        The method splits data points recursively, where the splitting is based on the feature and threshold given by the result of find_best_split\n",
    "        '''\n",
    "        if len(self.y) < min_samples_split:\n",
    "            self.isleaf = True\n",
    "            return\n",
    "        elif self.depth >= max_depth:\n",
    "            self.isleaf = True\n",
    "            return\n",
    "        elif len(np.unique(self.y)) <= 1:\n",
    "            self.isleaf = True\n",
    "            return\n",
    "        else:\n",
    "            self.isleaf = False\n",
    "            self.find_best_split()\n",
    "            left_ind = np.where(self.X[:, self.feature] < self.thresh)\n",
    "            right_ind = np.where(self.X[:, self.feature] >= self.thresh)\n",
    "            self.left = Node(depth=self.depth+1, X=self.X[left_ind], y=self.y[left_ind])\n",
    "            self.right = Node(depth=self.depth+1, X=self.X[right_ind], y=self.y[right_ind])\n",
    "            self.left.split(max_depth, min_samples_split)\n",
    "            self.right.split(max_depth, min_samples_split)\n",
    "            return\n",
    "            \n",
    "    def judge(self, x):\n",
    "        '''\n",
    "        The method makes prediction as to which class the input x falls into.\n",
    "        '''\n",
    "        if self.isleaf:\n",
    "            return self.label\n",
    "        else:\n",
    "            if x[self.feature] < self.thresh:\n",
    "                return self.left.judge(x)\n",
    "            else:\n",
    "                return self.right.judge(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class DecisionTreeClassifier:\n",
    "    def __init__(self, max_depth, min_samples_split):\n",
    "        self.max_depth = max_depth\n",
    "        self.min_samples_split = min_samples_split\n",
    "    \n",
    "    def fit(self, X, y):\n",
    "        self.root_node = Node(depth=0, X=X, y=y)\n",
    "        self.root_node.split(max_depth=self.max_depth, min_samples_split=self.min_samples_split)\n",
    "        return self\n",
    "        \n",
    "    def predict(self, X):\n",
    "        y = np.zeros(len(X), dtype='int')\n",
    "        for i in range(len(X)):\n",
    "            y[i] = self.root_node.judge(X[i])\n",
    "        return y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5 Experiment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "\n",
    "N = 100\n",
    "X, y = datasets.make_moons(n_samples = N, noise = 0.2)\n",
    "\n",
    "xx1 = np.linspace(np.min(X[:,0]),np.max(X[:,0]),101)\n",
    "xx2 = np.linspace(np.min(X[:,1]),np.max(X[:,1]),100)\n",
    "Xtest = np.array([[x1,x2] for x1 in xx1  for x2 in xx2])\n",
    "xxx1, xxx2 = np.meshgrid(xx1, xx2)\n",
    "\n",
    "def plot_result(clf):\n",
    "    plt.plot(X[:,0][y==1], X[:,1][y==1],\"o\",label=\"1\")\n",
    "    plt.plot(X[:,0][y==0], X[:,1][y==0],\"o\",label=\"0\")\n",
    "    plt.legend()\n",
    "    pred_val = clf.predict(Xtest)\n",
    "    pred_val_2D = np.reshape(pred_val,(len(xx1),len(xx2))).T\n",
    "    plt.pcolormesh(xxx1, xxx2, pred_val_2D)\n",
    "    plt.colorbar()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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1juary2jBgNRtqHxchOe1UtKCoap7gVG5fRF5Fvh8FF4rRsYpFrUXVjRfrcfP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\n5IZhGCnHFLlhGEbK+f/lt4eEB3rkdgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dtc = DecisionTreeClassifier(max_depth=40, min_samples_split=2)\n",
    "dtc.fit(X, y)\n",
    "plot_result(dtc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that decreasing the max_depth or increasing min_sample_split makes the decision tree (or its decision boundary) more regular. \n",
    "Thus, we can regularize the model by tweaking these parameters.\n",
    "\n",
    "decreasing max_depth ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KJ0WMceS1PBgl46dGmdMtcgcY7XMFMWzdEPpef/Toibxnzj3MmLgFYcyYuIUr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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dtc2 = DecisionTreeClassifier(max_depth=4, min_samples_split=2)\n",
    "dtc2.fit(X, y)\n",
    "plot_result(dtc2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DLJfoO/mgnM+1wL7BMax9ei4/W/Lplt2/46oFm6QTS+WTQnj3Qych6k1Nq+Vb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\nx3GcjOOK3HEcJ+P8fy7MaowE3WeiAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dtc3 = DecisionTreeClassifier(max_depth=2, min_samples_split=2)\n",
    "dtc3.fit(X, y)\n",
    "plot_result(dtc3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "increasing min_samples_split ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KJ0WMceS1PBgl46dGmdMtcgcY7XMFMWzdEPpef/Toibxnzj3MmLgFYcyYuIUr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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dtc4 = DecisionTreeClassifier(max_depth=40, min_samples_split=10)\n",
    "dtc4.fit(X, y)\n",
    "plot_result(dtc4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DLJfoO/mgnM+1wL7BMax9ei4/W/Lplt2/46oFm6QTS+WTQnj3Qych6k1Nq+Vb\ndd9r+vCHX/twRZ5iFsztz2Vv8kbysiv5XIuPO07HknJF3rE+8gVz+7niHRuZOnk/owRTJ+/ninds\nZMHc7BeWNpKXXc7nWsB9r07Hk3Ifeccq8iULN49Y8g2gZ8wwSxZuTkii+GgkNa044AhGl4bAA4+O\nc6j7YRzph62iY10rR08q34um0niWaDQ1LVM+1037UAsWU/ayd6cs7lpJJ8/v7KlrPEvkPjVt0z70\n011oz3CQUbBnGP10F2za19S0XvbuVCLGEv2W0LGKfPmaWew/OPLX339wFMvXzEpIovhoR172ysdP\n4fTlV/HKL17P6cuvaquy07170GDJ2GAw3gze88WphLtWUkohOyWPWSvQWjdJ4t0K91QwfSqNRyTv\nZe/uNmqQhAOZUehYRQ6BMs+L4m4niTdsGj+qvNIe39wXzDyXvSf+8M06KVfkHetacRonacvVThuP\nlZgg1h2MN0OeYwvuNmqcQmWnu1acXJG45Tp7XGAgxZy1EqXsPavuiaQfvllHw+k2yV2RO3WTim6F\ns8dhMaQbllIttpBl90TiD98skwEfubtWnLqpNysmyQyXOMmyeyLPbqN24K4VJ5dEzYrJshVbSpbd\nE94tsUlSbpG7IndaSuIZLjGSdfdEpip3U0baux825VqR1CvpDkmbwp+HmSaSTpb0C0kbJD0s6fyi\nY9+U9LSkB8Pt5GbkcdJHlq3YUrLinsiLKytVpLxpVrMW+VJgjZldK2lpuP/RknP2Ah8ws02SpgP3\nS1ptZjvC41ea2feblMNJKVm3YovJgnsiiisrq5k3iWHJlt9HoVlFvhg4M3z9LeAuShS5mf2q6HW/\npOeAo4EdOLknFRkuMZJ290QtV1aeYhbtIgsrBDWbtTLVzLYAhD+PqXaypFOBMcCTRcOfCV0uX5A0\ntsq1l0paL2n9AAeaFNtpF74eZ3up5crKcuZNophF2xKipkUu6SfAy8sc+kQ9N5I0Dfgn4CIzK3xR\n+RjwnwTKfRmBNX91uevNbFl4DhPVm/Lno1NM2q3YPFHLlZWnmEU7ybxFbmZnmdmry2wrga2hgi4o\n6ufKzSFpInAr8Ndmdk/R3Fss4ADwDeDUOH4px+lUagVkJ439bdnrKo07RA90ZjjYuQq4CLg2/Lmy\n9ARJY4B/Bb5tZt8rOTbNzLZIEnAe8GiT8jhO6qgVXIwz+FgrICuVv67SuBOQ92DntcB3JS0BngHe\nAyBpHvBBM7sEeC9wBnCUpIvD6y42sweB70g6miCe8CDwwSblcZxUUSu42IrgYzVX1o79R9Q17gTk\nWpGb2YvAwjLj64FLwtcrgBXS3cUlAAANF0lEQVQVrn9zM/d3nLRTK4uk3QVTeUoHbRtGooHMKHiv\nFcdpIbWCi+0OPmalqCltpL3Xiityx2khlSzdwnit462gp/sghejc5LF7PB00CikPdroid5wWUssC\nbqeFXPDHb98/nrDMhQNDY2pd1vFkYWEJV+SO00JqFUS1s2DKi4EaxAwNR9uSwrsfOk6LqVUQ1a6C\nKS8GaoJ0xzpdkTtOM2SpAZVnrDRO5is7HccpT8Hn3L+7F0OHcsDT2jbWM1YaxIBhi7YlhCtyx2mQ\nrPmcvYFZE6Q8a8VdK47TIFn0OXsDs8aI07UiaRHwJaAL+LqZXVty/AqCgspB4HngT83s19XmdEXu\nOA2ShM85Sz75PBFXRoqkLuArwNlAH3CfpFVmtrHotH8H5pnZXkkfAj4LnH/4bC/hrhXHaZB2+5yz\n5pPPDfF2PzwV2GxmT5nZQeAmggV6Xrqd2Voz2xvu3gPMrDWpK3LHaZB2+5yz5pPPC0FBkEXagCmF\nBXDC7dKS6WYAvyna7wvHKrEE+FEtGd214jhN0E6fcxZ98rkhevfDF8xsXpXj5RoGl7XlJb0fmAe8\nqdZN3SJ3nIyQRF8WJ6AOi7wWfcCxRfszgf7D7iedRbAK27nhwjtVcUXu5I6Vj5/C6cuv4pVfvJ7T\nl1+VGx+y54EnRLw+8vuA2ZKODxfduYBggZ5DSHot8DUCJV521bVS3LXi5Io8rxJfa/Ufp1XE10fF\nzAYlXQasJkg/vMHMNki6GlhvZquAzwHjge8Fi6fxjJmdW21eV+ROrmj3Qg3tTgf0PPCEiHFhCTO7\nDbitZOyTRa/PqndOV+ROW2iXwmtnQDDP1r9ThOV8qTfHiUIrFd5Vd76Lmx55I0M2ii4NM677AHsH\new47rxUBwXZb/06C5HmpN0m9ku6QtCn8WdbskTQk6cFwW1U0fryke8Prbw6d/07OaFX+81V3vovv\nPHw6Q9YFiCHrYu/gWEYxNOK8VgUEs5gOmNdAcMtJea+VZrNWlgJrzGw2sCbcL8c+Mzs53Iqd9tcB\nXwiv306Q/O7kjFYpvJseeSOHp+UKQ20p0slaOqBXhjaOhocjbUnRrGtlMXBm+PpbwF3AR6NcqCAc\n+2bgfUXXfwr4apMyOSmjFT1JVj5+CkNW3g4xxM+WfLrsNY366ctde+X8W0e4jCDd6YDuCmoQo56C\noERo1iKfamZbAMKfx1Q4rycsV71H0nnh2FHADjMbDPerlqpKurRQ9jpAzfx4J0XEnf9csCzLF8lB\nV5nIVDPWaKVrgUy1hc2iKygNiGjFQBELglpCTYtc0k+Al5c59Ik67nOcmfVLOgG4U9IjwK4y51V8\nJ8xsGbAMYKJ60x15cEYQd/5zOcvyJYwLXvPzSNdEtUarXfuzJZ9OreIuxVcIaoKUBztrKvJqOY2S\ntkqaZmZbJE0DylYhmVl/+PMpSXcBrwX+BZgsqTu0ysuWqjr5IM7858oWpPFff+9nfPrNP4h8TRRr\nNC+WbNZcQaki64q8BquAi4Brw58rS08IM1n2mtkBSVOA+cBnzcwkrQXeTdDKsez1Tvap5Jtu1Gdd\nybKcPmF7WSVe7ZrJPb9t+H5Zs2S9MrRBMuAjb1aRXwt8V9IS4BngPQCS5gEfNLNLgJOAr0kaJvDJ\nX1vURP2jwE2S/o6gmfryJuVxUkalHPL1/a/gBxtPayi3vBHL8sr5t/JXt1/IwPDIj/yeAz2sfPyU\nqvfMkyXrlaGNkWRGShSaUuRm9iKwsMz4eoKlijCznwOvqXD9UwSN1p2cUsm/HBTxdB02HsVn3Yhl\nufjEB/jbte9kx4HxI8YHrLvmPd2S7XQs964Vx6lKJT9ypdTBqH7nRizLnQeOaPiebsl2MIYrcqez\nqeRf7tLwYRZ54fwCcfdnyYuv20mAdHtWvB+501oq5ZBf8JqfV80tb0UVovfzdhol83nkjtMM1fzL\n86b/R0WLuxVViO7rdhrGXStOp1PJv1zN79yq3G33dTt1YwZD6fatuGvFSSVZa0jl5ByzaFtCuCJ3\nUon7s51UkXJF7q4VJ5W4P9tJDQbEtGZnq3BF7qQW92c76cDA0u0jd0XuOI5TDSP1wU5X5I7jOLXw\n9EPHcZyM44rccRwny3jTLMdxnGxjQJ7b2DqO43QEbpE7juNkmfSX6LsidxzHqYaBeR654zhOxvHK\nTsdxnIyTch95U02zJPVKukPSpvDnYT1GJS2Q9GDRtl/SeeGxb0p6uujYyc3I4ziOEztmQdZKlC0h\nmu1+uBRYY2azgTXh/gjMbK2ZnWxmJwNvBvYCtxedcmXhuJk92KQ8juM48ZPz7oeLgTPD198C7gI+\nWuX8dwM/MrO9Td7XcWIh7nVBnTxi2NBQ0kJUpVmLfKqZbQEIfx5T4/wLgBtLxj4j6WFJX5A0ttKF\nki6VtF7S+gEONCe149CadUGdHFJoYxtlS4iailzSTyQ9WmZbXM+NJE0DXgOsLhr+GHAi8AdAL1Ws\neTNbZmbzzGzeaCrqe8eJTLV1QR1nBDYcbUuImq4VMzur0jFJWyVNM7MtoaJ+rspU7wX+1cwGiube\nEr48IOkbwEciyu04TRPnuqDuoskvBliM1rakRcCXgC7g62Z2bcnxscC3gdcBLwLnm9l/VJuzWdfK\nKuCi8PVFwMoq515IiVslVP5IEnAe8GiT8jhOZOJaF9RdNDnHLDaLXFIX8BXgbcAc4EJJc0pOWwJs\nN7NZwBeA62rN26wivxY4W9Im4OxwH0nzJH29SPhXAMcCPy25/juSHgEeAaYAf9ekPI4TmbjWBXUX\nTf6xoaFIWwROBTab2VNmdhC4iSBppJjFBMkjAN8HFobGbkVkKU90L4ek54Ff13HJFOCFFonTCGmS\nJ02yQJvlGTVuYm/X+N4Z6uoeY0ODB4f2bHt2eN+ubfXIM+bls15X6djB/9x8f1yyRpGlzWRFnt8x\ns6MbnVTSj8O5o9AD7C/aX2Zmy4rmejewyMwuCff/GDjNzC4rOufR8Jy+cP/J8JyK73UmKzvr/aNI\nWm9m81olT72kSZ40yQIuTzXSJAt0jjxmtijG6cpZ1qXWdJRzRtCsa8VxHMeJTh+Bm7nATKC/0jmS\nuoFJwDaq4IrccRynfdwHzJZ0vKQxBLU1q0rOKU4ieTdwp9XwgWfStdIAy2qf0lbSJE+aZAGXpxpp\nkgVcnroxs0FJlxHU03QBN5jZBklXA+vNbBWwHPgnSZsJLPELas2byWCn4ziO8xLuWnEcx8k4rsgd\nx3EyTi4VuaT3SNogaVhSxXQkSYskPSFps6TDWvDGKE/Nvu3heUNFvdlLAyDNylD1d5U0VtLN4fF7\nwyKulhFBnoslPV/0flzSQllukPRcmL9b7rgkfTmU9WFJLS3ZjCDPmZJ2Fr03n2yhLMdKWivpsfD/\n1F+UOadt709Eedr2/qQGM8vdBpwE/C5BW915Fc7pAp4ETgDGAA8Bc1okz2eBpeHrpcB1Fc7b06L7\n1/xdgf8G/EP4+gLg5hb+faLIczHw9236vJwBnAI8WuH4OcCPCPJ7Xw/cm7A8ZwL/1qb3ZhpwSvh6\nAvCrMn+rtr0/EeVp2/uTli2XFrmZPWZmT9Q4LUqpbFwUl9x+i6CvTDtpSVlwi+VpG2a2jup5uouB\nb1vAPcDkQp+ghORpG2a2xcweCF/vBh4DZpSc1rb3J6I8HUcuFXlEZgC/Kdrvo3UfiKh923sU9Fy/\nR+FyeDER5Xc9dI6ZDQI7gaNilKFeeQD+KPyq/n1Jx5Y53i7a+VmJyhskPSTpR5LmtuOGobvttcC9\nJYcSeX+qyAMJvD9Jktk8ckk/AV5e5tAnzKxaF8ZDU5QZazgXs5o8dUxznJn1SzoBuFPSI2b2ZKMy\nFYtXZqzpsuAmiHKvW4AbzeyApA8SfFt4c4vkqUU735soPEDQP2SPpHOAHwKzW3lDSeOBfwH+0sx2\nlR4uc0lL358a8rT9/UmazCpyq9InPSJRSmVjkUcR+7abWX/48ylJdxFYG3Eo8nrKgvuilgW3Uh4z\ne7Fo9x+J0MqzhcT6WWmWYsVlZrdJ+r+SpliVpkrNIGk0gdL8jpn9oMwpbX1/asnT7vcnDXSyayVK\nqWxc1OzbLulIhUvdSZoCzAc2xnT/lpQFt1KeEh/ruQS+0KRYBXwgzM54PbDTXloUpe1IenkhfiHp\nVIL/xy9Wv6rhe4mg0vAxM7u+wmlte3+iyNPO9yc1JB1tbcUGvJPASjgAbAVWh+PTgduKzjuHIOr9\nJIFLplXyHAWsATaFP3vD8XkEK4QAvJGgL/tD4c8lMctw2O8KXA2cG77uAb4HbAZ+CZzQ4r9RLXn+\nF7AhfD/WAie2UJYbgS3AQPi5WQJ8EPhgeFwEiwE8Gf5tymZCtVGey4rem3uAN7ZQltMJ3CQPAw+G\n2zlJvT8R5Wnb+5OWzUv0HcdxMk4nu1Ycx3FygStyx3GcjOOK3HEcJ+O4Inccx8k4rsgdx3Eyjity\nx3GcjOOK3HEcJ+P8fy7MaowE3WeiAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dtc5 = DecisionTreeClassifier(max_depth=40, min_samples_split=20)\n",
    "dtc5.fit(X, y)\n",
    "plot_result(dtc5)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}