box-figure.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 145,
   "id": "73d20f87",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 630x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import make_classification\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from mlxtend.plotting import plot_decision_regions\n",
    "\n",
    "def in_circle1(point):\n",
    "    x, y = point\n",
    "    return (x+3)**2 + y**2 <= 2**2\n",
    "\n",
    "def in_circle2(point):\n",
    "    x, y = point\n",
    "    return (x-1)**2 + y**2 <= 1**2\n",
    "\n",
    "np.random.seed(0)\n",
    "n = 200\n",
    "# Generate n random data points uniformly distributed in the box [-2, 2] x [-2, 2]\n",
    "data_points = np.column_stack((np.random.uniform(-5, 2, n), np.random.uniform(-2, 2, n)))\n",
    "labels = [1 if in_circle1(point) or in_circle2(point) else 0 for point in data_points]\n",
    "labels = np.array(labels)\n",
    "data = pd.DataFrame(data_points, columns=['x', 'y'])\n",
    "data['label'] = labels\n",
    "\n",
    "tree = DecisionTreeClassifier(max_depth=4)  # You can adjust the depth of the tree here\n",
    "tree.fit(data_points, labels)\n",
    "\n",
    "# 3. Visualize the tree on the 2D plane\n",
    "plt.figure(figsize=(6.3, 4))\n",
    "scatter_kwargs = {'s': 12, 'edgecolor': 'black',\\\n",
    "                  'alpha': 1, 'lw': 0.5}\n",
    "\n",
    "ax = plot_decision_regions(data_points, labels, clf=tree, \n",
    "                      scatter_kwargs=scatter_kwargs,zoom_factor = 0.6,\n",
    "                      legend=2, colors='mediumseagreen,orange')\n",
    "\n",
    "# Plot the eps\n",
    "trueCenter1 = -3\n",
    "trueCenter2 = 1\n",
    "trueR1 = 2\n",
    "trueR2 = 1\n",
    "t = np.linspace(0, 2*np.pi, 100)\n",
    "ax.plot(trueCenter1+trueR1*np.cos(t) , trueR1*np.sin(t),\\\n",
    "        label = 'True Boundaries', linestyle = 'dashed', color = 'royalblue')\n",
    "ax.plot(trueCenter2+trueR2*np.cos(t), trueR2*np.sin(t),\\\n",
    "     linestyle = 'dashed', color = 'royalblue')\n",
    "#plt.title('Decision Tree (CART) Decision Boundaries')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "ax.legend(handles, \n",
    "          ['class 0', 'class 1', 'True Boundaries'],framealpha=0.3, scatterpoints=1,loc='lower left')\n",
    "#plt.show()\n",
    "plt.savefig('CARTboundary.pdf')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "id": "10f9367e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x450 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeClassifier, plot_tree\n",
    "plt.figure(figsize=(7,4.5))\n",
    "tree_plot = plot_tree(tree, filled=True, feature_names=data.columns, class_names=['0','1'],\\\n",
    "impurity=False, fontsize=7)\n",
    "\n",
    "# Customize labels manually to show only the feature and threshold\n",
    "for node in tree_plot:\n",
    "    text = node.get_text()\n",
    "    if 'samples =' in text:  # Check if the node is not a leaf\n",
    "        # Find the line with the feature and threshold\n",
    "        lines = text.split('\\n')\n",
    "        for line in lines:\n",
    "            if '<=' in line or '>' in line:\n",
    "                node.set_text(line)  # Set text to only feature and threshold\n",
    "                break\n",
    "        text = node.get_text()\n",
    "        if 'class' in text:\n",
    "            node.set_text(lines[-1][-1])  # Display only the class name in leaf nodes\n",
    "\n",
    "plt.savefig('CARTstructure.pdf')\n",
    "#plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "f667b767",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\MSI-NB\\anaconda3\\lib\\site-packages\\sklearn\\base.py:432: UserWarning: X has feature names, but DecisionTreeClassifier was fitted without feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.89"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "n = 200\n",
    "# Generate n random data points uniformly distributed in the box [-2, 2] x [-2, 2]\n",
    "data_points = np.column_stack((np.random.uniform(-5, 2, n), np.random.uniform(-2, 2, n)))\n",
    "labels = [1 if in_circle1(point) or in_circle2(point) else 0 for point in data_points]\n",
    "labels = np.array(labels)\n",
    "df = pd.DataFrame(data_points, columns=['x', 'y'])\n",
    "df['label'] = labels\n",
    "tree.score(df[df.columns[:-1]], df[df.columns[-1]])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "58ef8c39",
   "metadata": {},
   "outputs": [],
   "source": [
    "data.insert(loc=0, column='x2', value=data['x']*data['x'])\n",
    "data.insert(loc=0, column='y2', value=data['y']*data['y'])\n",
    "data.insert(loc=0, column='xy', value=data['x']*data['y'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c0d5f00f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import gurobipy as gp\n",
    "from gurobipy import GRB, quicksum\n",
    "def complete_tree_edges(n):\n",
    "    edges = []\n",
    "    for i in range(n):\n",
    "        left_child = 2 * i + 1\n",
    "        right_child = 2 * i + 2\n",
    "        if left_child <= n:\n",
    "            edges.append((i, left_child))\n",
    "        if right_child <= n:\n",
    "            edges.append((i, right_child))\n",
    "    return edges\n",
    "def at(t):\n",
    "    if t % 2 == 1:\n",
    "        return int((t-1)/2)\n",
    "    else:\n",
    "        return int((t-2)/2)\n",
    "\n",
    "def lt(t):\n",
    "    return 2*t + 1\n",
    "def rt(t):\n",
    "    return 2*t + 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2da4b0c7",
   "metadata": {},
   "outputs": [],
   "source": [
    "K = set(data['label'].tolist())\n",
    "I = [i for i in range(len(data))]\n",
    "J = [j for j in range(len(data.columns)-1)]\n",
    "countDict = {}\n",
    "for k in K:\n",
    "    countDict[k] = 0\n",
    "for i in I:\n",
    "    countDict[data['label'][i]] += 1\n",
    "alpha = 0\n",
    "beta = 0\n",
    "sigma = 2\n",
    "Lhat = len(I)-max(countDict.values())\n",
    "mu = 1e-4\n",
    "N = [t for t in range(np.power(2, sigma)-1)]\n",
    "L = [l for l in range(len(N), len(N)+np.power(2, sigma))]\n",
    "s_node = -1\n",
    "w_node = L[-1]+1\n",
    "edges = complete_tree_edges(L[-1])\n",
    "edges = edges + [(-1, 0)]\n",
    "edges = edges + [(t, w_node) for t in N+L]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "deed31ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "C = 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "cb27b733",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Set parameter TimeLimit to value 100\n"
     ]
    }
   ],
   "source": [
    "OCTH = gp.Model()\n",
    "ahat = OCTH.addVars(J,N, vtype = GRB.CONTINUOUS, lb=0, ub =1)\n",
    "a = OCTH.addVars(J,N, vtype = GRB.CONTINUOUS, lb=-1, ub =1)\n",
    "b = OCTH.addVars(N, vtype = GRB.CONTINUOUS, lb = -GRB.INFINITY)\n",
    "d = OCTH.addVars(N, vtype = GRB.BINARY)\n",
    "s = OCTH.addVars(J, N, vtype = GRB.BINARY)\n",
    "g = OCTH.addVars(K, N+L, vtype = GRB.BINARY)\n",
    "u = {}\n",
    "for i in I:\n",
    "    for edge in edges:\n",
    "        u[i, edge] = OCTH.addVar(vtype=GRB.BINARY)\n",
    "\n",
    "\n",
    "OCTH.addConstrs(quicksum(ahat[j,t] for j in J) <= d[t] for t in N)\n",
    "OCTH.addConstrs(-ahat[j,t]<= a[j,t] for j in J for t in N)\n",
    "OCTH.addConstrs(a[j,t] <= ahat[j,t] for j in J for t in N)\n",
    "OCTH.addConstrs(-s[j,t]<= a[j,t] for j in J for t in N)\n",
    "OCTH.addConstrs(a[j,t] <= s[j,t] for j in J for t in N)\n",
    "OCTH.addConstrs(s[j,t] <= d[t] for j in J for t in N)\n",
    "OCTH.addConstrs(quicksum(s[j,t] for j in J) >= d[t] for t in N)\n",
    "OCTH.addConstrs(-d[t] <= b[t] for t in N)\n",
    "OCTH.addConstrs(b[t] <= d[t] for t in N)\n",
    "OCTH.addConstrs(quicksum(g[k,l] for k in K) ==1 for l in L)\n",
    "OCTH.addConstrs(u[i,(at(t), t)] == \n",
    "                u[i, (t, lt(t))] + u[i, (t, rt(t))] + u[i, (t, w_node)] for t in N[1:] for i in I)\n",
    "OCTH.addConstrs(u[i,(-1, 0)] == \n",
    "                u[i, (0, lt(0))] + u[i, (0, rt(0))] + u[i, (0, w_node)] for i in I)\n",
    "OCTH.addConstrs(u[i, (at(l),l)] == u[i, (l, w_node)] for l in L for i in I)\n",
    "OCTH.addConstrs(u[i, (t, w_node)] <= g[data['label'][i], t] for i in I for t in N+L)\n",
    "OCTH.addConstrs(d[t] + quicksum(g[k,t] for k in K) == 1 for t in N)\n",
    "OCTH.addConstrs(quicksum(a[j,t]*data[data.columns[j]][i] for j in J) + mu <= \n",
    "               b[t] + (2+mu)*(1-u[i, (t, lt(t))]) for t in N for i in I)\n",
    "OCTH.addConstrs(quicksum(a[j,t]*data[data.columns[j]][i] for j in J) >= \n",
    "               b[t] - 2*(1-u[i,(t, rt(t))]) for t in N for i in I)\n",
    "OCTH.addConstrs(u[i, (t, lt(t))] <= d[t] for i in I for t in N)\n",
    "OCTH.addConstrs(u[i, (t, rt(t))] <= d[t] for i in I for t in N)\n",
    "OCTH.addConstr(quicksum(s[j,t] for j in J for t in N)<=C)\n",
    "\n",
    "OCTH.setObjective(1/Lhat *(len(I) - quicksum(u[i, (s_node, 0)] for i in I)) + \n",
    "                  alpha * quicksum(s[j,t] for j in J for t in N), GRB.MINIMIZE)\n",
    "OCTH.Params.TimeLimit = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a6166122",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gurobi Optimizer version 11.0.2 build v11.0.2rc0 (win64 - Windows 10.0 (19045.2))\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i7-10750H CPU @ 2.60GHz, instruction set [SSE2|AVX|AVX2]\n",
      "Thread count: 6 physical cores, 12 logical processors, using up to 12 threads\n",
      "\n",
      "Optimize a model with 5295 rows, 2865 columns and 17830 nonzeros\n",
      "Model fingerprint: 0xf6c648f5\n",
      "Variable types: 33 continuous, 2832 integer (2832 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e-07, 2e+01]\n",
      "  Objective range  [1e-02, 1e-02]\n",
      "  Bounds range     [1e+00, 1e+00]\n",
      "  RHS range        [1e+00, 6e+00]\n",
      "Found heuristic solution: objective 2.1052632\n",
      "Presolve removed 804 rows and 1004 columns\n",
      "Presolve time: 0.03s\n",
      "Presolved: 4491 rows, 1861 columns, 16016 nonzeros\n",
      "Variable types: 33 continuous, 1828 integer (1828 binary)\n",
      "Found heuristic solution: objective 1.0000000\n",
      "\n",
      "Root relaxation: objective -8.881784e-16, 1292 iterations, 0.05 seconds (0.09 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0   -0.00000    0  386    1.00000   -0.00000   100%     -    0s\n",
      "     0     0   -0.00000    0  552    1.00000   -0.00000   100%     -    0s\n",
      "H    0     0                       0.7157895   -0.00000   100%     -    0s\n",
      "     0     0   -0.00000    0  577    0.71579   -0.00000   100%     -    0s\n",
      "H    0     0                       0.1894737   -0.00000   100%     -    0s\n",
      "     0     0   -0.00000    0  590    0.18947   -0.00000   100%     -    1s\n",
      "     0     0   -0.00000    0  537    0.18947   -0.00000   100%     -    1s\n",
      "H    0     0                       0.1684211   -0.00000   100%     -    1s\n",
      "     0     2   -0.00000    0  537    0.16842   -0.00000   100%     -    2s\n",
      "H 1198   986                       0.0736842   -0.00000   100%  37.6    4s\n",
      "  2158  1540    0.02131  128  537    0.07368   -0.00000   100%  36.3    5s\n",
      "H 2159  1463                       0.0631579   -0.00000   100%  36.3    6s\n",
      "H 2162  1392                       0.0421053   -0.00000   100%  36.2    6s\n",
      "H 2166  1324                       0.0000000   -0.00000  0.00%  36.1    7s\n",
      "\n",
      "Cutting planes:\n",
      "  Flow cover: 1\n",
      "\n",
      "Explored 2166 nodes (103641 simplex iterations) in 7.71 seconds (8.60 work units)\n",
      "Thread count was 12 (of 12 available processors)\n",
      "\n",
      "Solution count 9: 1.33227e-15 0.0421053 0.0631579 ... 2.10526\n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 1.332267629550e-15, best bound 1.332267629550e-15, gap 0.0000%\n"
     ]
    }
   ],
   "source": [
    "OCTH.optimize()\n",
    "OCTH.update()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a7dfdb67",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<gurobi.LinExpr: 6.0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quicksum(s[j,t].x for j in J for t in N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "711809f3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 0.0\n",
      "0 0.08367405121538495\n",
      "0 0.08291744420475307\n",
      "0 0.4952793527924158\n",
      "0 0.0\n",
      "-0.40185103096781705\n",
      "2 0.0\n",
      "2 -0.041831337033335456\n",
      "2 -0.05350244897285808\n",
      "2 0.1073918439004798\n",
      "2 0.0\n",
      "0.004398322508579459\n"
     ]
    }
   ],
   "source": [
    "lines = []\n",
    "for t in N:\n",
    "    if d[t].x>0.5:\n",
    "        line = []\n",
    "        for j in J:\n",
    "            print(t, a[j,t].x)\n",
    "            line.append(a[j,t].x)\n",
    "        print(b[t].x)\n",
    "        line.append(b[t].x)\n",
    "        lines.append(line)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1fec91fd",
   "metadata": {},
   "outputs": [],
   "source": [
    "b1 = (0.4952793527924158)/(2*np.sqrt(0.08291744420475307))\n",
    "center1 = - (b1)/np.sqrt(0.08367405121538495)\n",
    "r1_temp = -0.4 + b1**2\n",
    "r1a = np.sqrt(r1_temp/0.08291744420475307)\n",
    "r1b = np.sqrt(r1_temp/0.08367405121538495)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "bb2a88bb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.973047691745581"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "center1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "6077bc79",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.023756812855084"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r1a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "7a8e2e3c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0145863132772908"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r1b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0861aba8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['xy', 'y2', 'x2', 'x', 'y', 'label'], dtype='object')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "9acfd0b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "b2 = (-0.1073918439004798)/(2*np.sqrt(0.05350244897285808))\n",
    "center2 = -(b2)/np.sqrt(0.041831337033335456)\n",
    "r2_temp = -0.004398322508579459 + b2**2\n",
    "r2a = np.sqrt(r2_temp/0.05350244897285808)\n",
    "r2b = np.sqrt(r2_temp/0.041831337033335456)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "b53efcc8",
   "metadata": {},
   "outputs": [],
   "source": [
    "center2=center2-0.11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "8918c899",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.025020223739891"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "center2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "b8727f92",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9617887021426037"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "4fbe2c50",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0877162807054768"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "be19e8b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 630x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.patches import Ellipse\n",
    "import matplotlib.colors as mcolors\n",
    "\n",
    "backalpha1 = 0.5\n",
    "backalpha2 = 0.5\n",
    "# Plotting\n",
    "fig, ax = plt.subplots(figsize=(6.3,4))\n",
    "color_rgba = mcolors.to_rgba('mediumseagreen', alpha=backalpha1)  # Set alpha to 0.5\n",
    "\n",
    "ax.set_facecolor(color_rgba)\n",
    "ellipse11 = Ellipse((center1, 0), width=2*r1a, height=2*r1b, \n",
    "                  angle=0, color='white', alpha=1)\n",
    "ax.add_patch(ellipse11)\n",
    "ellipse22 = Ellipse((center2, 0), width=2*r2a, height=2*r2b, \n",
    "                  angle=0, color='white', alpha=1)\n",
    "ax.add_patch(ellipse22)\n",
    "\n",
    "ellipse1 = Ellipse((center1, 0), width=2*r1a, height=2*r1b, \n",
    "                  angle=0, facecolor='orange', alpha=backalpha2, edgecolor='black', linewidth=1)\n",
    "ax.add_patch(ellipse1)\n",
    "ellipse2 = Ellipse((center2, 0), width=2*r2a, height=2*r2b, \n",
    "                  angle=0, facecolor='orange', alpha=backalpha2, edgecolor='black', linewidth=1)\n",
    "ax.add_patch(ellipse2)\n",
    "\n",
    "# Differentiating point types by label\n",
    "for label, group in data.groupby('label'):\n",
    "    if label == 1:\n",
    "        ax.scatter(group['x'], group['y'], marker='^',\\\n",
    "                   lw = 0.5, s=12, color = 'orange', edgecolors='black', label='Class 1')\n",
    "    else:\n",
    "        ax.scatter(group['x'], group['y'], marker='s',\\\n",
    "                   lw = 0.5, s=12, color = 'mediumseagreen',edgecolors='black', label= 'Class 0')\n",
    "\n",
    "\n",
    "#ax.scatter(group['x'], group['y'], label=f'Inside Circle ({label})' if label == 1 else f'Outside Circle ({label})',\n",
    "#               color='orange' if label == 1 else 'mediumseagreen')\n",
    "# Plot the eps\n",
    "trueCenter1 = -3\n",
    "trueCenter2 = 1\n",
    "trueR1 = 2\n",
    "trueR2 = 1\n",
    "t = np.linspace(0, 2*np.pi, 100)\n",
    "ax.plot(trueCenter1+trueR1*np.cos(t) , trueR1*np.sin(t),\\\n",
    "        label = 'True Boundaries', linestyle = 'dashed', color = 'royalblue')\n",
    "ax.plot(trueCenter2+trueR2*np.cos(t), trueR2*np.sin(t),\\\n",
    "     linestyle = 'dashed', color = 'royalblue')\n",
    "\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.set_xlim(-6.7, 3.9999)\n",
    "ax.set_ylim(-3.7, 3.5)\n",
    "ax = plt.gca()  # 获取当前的Axes对象\n",
    "ax.spines['top'].set_visible(False)    # 关闭上边框\n",
    "ax.spines['right'].set_visible(False)  # 关闭右边框\n",
    "ax.spines['left'].set_visible(False)   # 关闭左边框\n",
    "ax.spines['bottom'].set_visible(False) # 关闭下边框\n",
    "# Add labels, legend, and title\n",
    "#plt.title('Nonlinear Decision Tree Decision Boundaries')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.legend(framealpha=0.3, scatterpoints=1, loc = 'lower left')\n",
    "\n",
    "# Show plot\n",
    "#plt.show()\n",
    "plt.savefig('OCTNHboundary.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "4a98ead3",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(1)\n",
    "n = 200\n",
    "# Generate n random data points uniformly distributed in the box [-2, 2] x [-2, 2]\n",
    "data_points = np.column_stack((np.random.uniform(-5, 2, n), np.random.uniform(-2, 2, n)))\n",
    "labels = [1 if in_circle1(point) or in_circle2(point) else 0 for point in data_points]\n",
    "labels = np.array(labels)\n",
    "df = pd.DataFrame(data_points, columns=['x', 'y'])\n",
    "df['label'] = labels\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "6a36bf89",
   "metadata": {},
   "outputs": [],
   "source": [
    "df.insert(loc=0, column='x2', value=df['x']*df['x'])\n",
    "df.insert(loc=0, column='y2', value=df['y']*df['y'])\n",
    "df.insert(loc=0, column='xy', value=df['x']*df['y'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "56255fe6",
   "metadata": {},
   "outputs": [],
   "source": [
    "class temp:\n",
    "    pass\n",
    "OCTHmodel = temp()\n",
    "OCTHmodel.N = N\n",
    "OCTHmodel.K = K\n",
    "OCTHmodel.J = J\n",
    "OCTHmodel.I = I\n",
    "OCTHmodel.L = L\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "52b767c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import sys\n",
    "src_path = os.path.abspath('src')\n",
    "sys.path.append(src_path)\n",
    "from Trees import CustomDecisionTreeClassifier\n",
    "\n",
    "clf = CustomDecisionTreeClassifier(a, b, d, g, OCTHmodel)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "52b878b0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf.score(df[df.columns[:-1]],df[df.columns[-1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3953e4e3",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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