Code-Example-060.ipynb

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    "# Module 6: Classification\n",
    "\n",
    "The following tutorial contains Python examples for solving classification problems. You should refer to the Chapters 3 and 4 of the \"Introduction to Data Mining\" book to understand some of the concepts introduced in this tutorial. The notebook can be downloaded from http://www.cse.msu.edu/~ptan/dmbook/tutorials/tutorial6/tutorial6.ipynb.\n",
    "\n",
    "Classification is the task of predicting a nominal-valued attribute (known as class label) based on the values of other attributes (known as predictor variables). The goals for this tutorial are as follows:\n",
    "1. To provide examples of using different classification techniques from the scikit-learn library package.\n",
    "2. To demonstrate the problem of model overfitting.\n",
    "\n",
    "Read the step-by-step instructions below carefully. To execute the code, click on the corresponding cell and press the SHIFT-ENTER keys simultaneously.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.1 Vertebrate Dataset\n",
    "\n",
    "We use a variation of the vertebrate data described in Example 3.1 of Chapter 3. Each vertebrate is classified into one of 5 categories: mammals, reptiles, birds, fishes, and amphibians, based on a set of explanatory attributes (predictor variables). Except for \"name\", the rest of the attributes have been converted into a *one hot encoding* binary representation. To illustrate this, we will first load the data into a Pandas DataFrame object and display its content."
   ]
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  {
   "cell_type": "code",
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Name</th>\n",
       "      <th>Warm-blooded</th>\n",
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       "      <th>Aquatic Creature</th>\n",
       "      <th>Aerial Creature</th>\n",
       "      <th>Has Legs</th>\n",
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       "  </thead>\n",
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       "      <th>0</th>\n",
       "      <td>human</td>\n",
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       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>mammals</td>\n",
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       "      <th>2</th>\n",
       "      <td>salmon</td>\n",
       "      <td>0</td>\n",
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       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>fishes</td>\n",
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       "      <td>whale</td>\n",
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       "      <td>1</td>\n",
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       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>amphibians</td>\n",
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       "      <th>5</th>\n",
       "      <td>komodo</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>mammals</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>pigeon</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>birds</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>cat</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>mammals</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>leopard shark</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>fishes</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>turtle</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>reptiles</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>penguin</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>birds</td>\n",
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       "      <th>12</th>\n",
       "      <td>porcupine</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>mammals</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>eel</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>fishes</td>\n",
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       "      <td>salamander</td>\n",
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       "      <td>1</td>\n",
       "      <td>amphibians</td>\n",
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      "text/plain": [
       "             Name  Warm-blooded  Gives Birth  Aquatic Creature  \\\n",
       "0           human             1            1                 0   \n",
       "1          python             0            0                 0   \n",
       "2          salmon             0            0                 1   \n",
       "3           whale             1            1                 1   \n",
       "4            frog             0            0                 1   \n",
       "5          komodo             0            0                 0   \n",
       "6             bat             1            1                 0   \n",
       "7          pigeon             1            0                 0   \n",
       "8             cat             1            1                 0   \n",
       "9   leopard shark             0            1                 1   \n",
       "10         turtle             0            0                 1   \n",
       "11        penguin             1            0                 1   \n",
       "12      porcupine             1            1                 0   \n",
       "13            eel             0            0                 1   \n",
       "14     salamander             0            0                 1   \n",
       "\n",
       "    Aerial Creature  Has Legs  Hibernates       Class  \n",
       "0                 0         1           0     mammals  \n",
       "1                 0         0           1    reptiles  \n",
       "2                 0         0           0      fishes  \n",
       "3                 0         0           0     mammals  \n",
       "4                 0         1           1  amphibians  \n",
       "5                 0         1           0    reptiles  \n",
       "6                 1         1           1     mammals  \n",
       "7                 1         1           0       birds  \n",
       "8                 0         1           0     mammals  \n",
       "9                 0         0           0      fishes  \n",
       "10                0         1           0    reptiles  \n",
       "11                0         1           0       birds  \n",
       "12                0         1           1     mammals  \n",
       "13                0         0           0      fishes  \n",
       "14                0         1           1  amphibians  "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "data = pd.read_csv('datasets/vertebrate.csv',header='infer')\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given the limited number of training examples, suppose we convert the problem into a binary classification task (mammals versus non-mammals). We can do so by replacing the class labels of the instances to *non-mammals* except for those that belong to the *mammals* class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
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       "      <td>pigeon</td>\n",
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       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>non-mammals</td>\n",
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       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>cat</td>\n",
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       "    <tr>\n",
       "      <th>9</th>\n",
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       "      <td>turtle</td>\n",
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       "      <td>1</td>\n",
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       "      <th>11</th>\n",
       "      <td>penguin</td>\n",
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       "      <td>1</td>\n",
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       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>non-mammals</td>\n",
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       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>porcupine</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>mammals</td>\n",
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      "text/plain": [
       "             Name  Warm-blooded  Gives Birth  Aquatic Creature  \\\n",
       "0           human             1            1                 0   \n",
       "1          python             0            0                 0   \n",
       "2          salmon             0            0                 1   \n",
       "3           whale             1            1                 1   \n",
       "4            frog             0            0                 1   \n",
       "5          komodo             0            0                 0   \n",
       "6             bat             1            1                 0   \n",
       "7          pigeon             1            0                 0   \n",
       "8             cat             1            1                 0   \n",
       "9   leopard shark             0            1                 1   \n",
       "10         turtle             0            0                 1   \n",
       "11        penguin             1            0                 1   \n",
       "12      porcupine             1            1                 0   \n",
       "13            eel             0            0                 1   \n",
       "14     salamander             0            0                 1   \n",
       "\n",
       "    Aerial Creature  Has Legs  Hibernates        Class  \n",
       "0                 0         1           0      mammals  \n",
       "1                 0         0           1  non-mammals  \n",
       "2                 0         0           0  non-mammals  \n",
       "3                 0         0           0      mammals  \n",
       "4                 0         1           1  non-mammals  \n",
       "5                 0         1           0  non-mammals  \n",
       "6                 1         1           1      mammals  \n",
       "7                 1         1           0  non-mammals  \n",
       "8                 0         1           0      mammals  \n",
       "9                 0         0           0  non-mammals  \n",
       "10                0         1           0  non-mammals  \n",
       "11                0         1           0  non-mammals  \n",
       "12                0         1           1      mammals  \n",
       "13                0         0           0  non-mammals  \n",
       "14                0         1           1  non-mammals  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['Class'] = data['Class'].replace(['fishes','birds','amphibians','reptiles'],'non-mammals')\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can apply Pandas cross-tabulation to examine the relationship between the Warm-blooded and Gives Birth attributes with respect to the class. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Class                     mammals  non-mammals\n",
       "Warm-blooded Gives Birth                      \n",
       "0            0                  0            7\n",
       "             1                  0            1\n",
       "1            0                  0            2\n",
       "             1                  5            0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.crosstab([data['Warm-blooded'],data['Gives Birth']],data['Class'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results above show that it is possible to distinguish mammals from non-mammals using these two attributes alone since each combination of their attribute values would yield only instances that belong to the same class. For example, mammals can be identified as warm-blooded vertebrates that give birth to their young. Such a relationship can also be derived using a decision tree classifier, as shown by the example given in the next subsection."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2 Decision Tree Classifier\n",
    "\n",
    "In this section, we apply a decision tree classifier to the vertebrate dataset described in the previous subsection."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import tree\n",
    "\n",
    "Y = data['Class']\n",
    "X = data.drop(['Name','Class'],axis=1)\n",
    "\n",
    "clf = tree.DecisionTreeClassifier(criterion='entropy',max_depth=3)\n",
    "clf = clf.fit(X, Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The preceding commands will extract the predictor (X) and target class (Y) attributes from the vertebrate dataset and create a decision tree classifier object using entropy as its impurity measure for splitting criterion. The decision tree class in Python sklearn library also supports using 'gini' as impurity measure. The classifier above is also constrained to generate trees with a maximum depth equals to 3. Next, the classifier is trained on the labeled data using the fit() function. \n",
    "\n",
    "We can plot the resulting decision tree obtained after training the classifier. To do this, you must first install both graphviz (http://www.graphviz.org) and its Python interface called pydotplus (http://pydotplus.readthedocs.io/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pydotplus \n",
    "from IPython.display import Image\n",
    "\n",
    "dot_data = tree.export_graphviz(clf, feature_names=X.columns, class_names=['mammals','non-mammals'], filled=True, \n",
    "                                out_file=None) \n",
    "graph = pydotplus.graph_from_dot_data(dot_data) \n",
    "Image(graph.create_png())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, suppose we apply the decision tree to classify the following test examples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Name</th>\n",
       "      <th>Warm-blooded</th>\n",
       "      <th>Gives Birth</th>\n",
       "      <th>Aquatic Creature</th>\n",
       "      <th>Aerial Creature</th>\n",
       "      <th>Has Legs</th>\n",
       "      <th>Hibernates</th>\n",
       "      <th>Class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>gila monster</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>non-mammals</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>platypus</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>mammals</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>owl</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>non-mammals</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>dolphin</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>mammals</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Name  Warm-blooded  Gives Birth  Aquatic Creature  Aerial Creature  \\\n",
       "0  gila monster             0            0                 0                0   \n",
       "1      platypus             1            0                 0                0   \n",
       "2           owl             1            0                 0                1   \n",
       "3       dolphin             1            1                 1                0   \n",
       "\n",
       "   Has Legs  Hibernates        Class  \n",
       "0         1           1  non-mammals  \n",
       "1         1           1      mammals  \n",
       "2         1           0  non-mammals  \n",
       "3         0           0      mammals  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "testData = [['gila monster',0,0,0,0,1,1,'non-mammals'],\n",
    "           ['platypus',1,0,0,0,1,1,'mammals'],\n",
    "           ['owl',1,0,0,1,1,0,'non-mammals'],\n",
    "           ['dolphin',1,1,1,0,0,0,'mammals']]\n",
    "testData = pd.DataFrame(testData, columns=data.columns)\n",
    "testData"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first extract the predictor and target class attributes from the test data and then apply the decision tree classifier to predict their classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Name</th>\n",
       "      <th>Predicted Class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>gila monster</td>\n",
       "      <td>non-mammals</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>platypus</td>\n",
       "      <td>non-mammals</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>owl</td>\n",
       "      <td>non-mammals</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>dolphin</td>\n",
       "      <td>mammals</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Name Predicted Class\n",
       "0  gila monster     non-mammals\n",
       "1      platypus     non-mammals\n",
       "2           owl     non-mammals\n",
       "3       dolphin         mammals"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "testY = testData['Class']\n",
    "testX = testData.drop(['Name','Class'],axis=1)\n",
    "\n",
    "predY = clf.predict(testX)\n",
    "predictions = pd.concat([testData['Name'],pd.Series(predY,name='Predicted Class')], axis=1)\n",
    "predictions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Except for platypus, which is an egg-laying mammal, the classifier correctly predicts the class label of the test examples. We can calculate the accuracy of the classifier on the test data as shown by the example given below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on test data is 0.75\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "print('Accuracy on test data is %.2f' % (accuracy_score(testY, predY)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.3 Model Overfitting\n",
    "\n",
    "To illustrate the problem of model overfitting, we consider a two-dimensional dataset containing 1500 labeled instances, each of which is assigned to one of two classes, 0 or 1. Instances from each class are generated as follows:\n",
    "1. Instances from class 1 are generated from a mixture of 3 Gaussian distributions, centered at [6,14], [10,6], and [14 14], respectively. \n",
    "2. Instances from class 0 are generated from a uniform distribution in a square region, whose sides have a length equals to 20.\n",
    "\n",
    "For simplicity, both classes have equal number of labeled instances. The code for generating and plotting the data is shown below. All instances from class 1 are shown in red while those from class 0 are shown in black."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f9923288670>,\n",
       " <matplotlib.lines.Line2D at 0x7f9923288760>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy.random import random\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "N = 1500\n",
    "\n",
    "mean1 = [6, 14]\n",
    "mean2 = [10, 6]\n",
    "mean3 = [14, 14]\n",
    "cov = [[3.5, 0], [0, 3.5]]  # diagonal covariance\n",
    "\n",
    "np.random.seed(50)\n",
    "X = np.random.multivariate_normal(mean1, cov, int(N/6))\n",
    "X = np.concatenate((X, np.random.multivariate_normal(mean2, cov, int(N/6))))\n",
    "X = np.concatenate((X, np.random.multivariate_normal(mean3, cov, int(N/6))))\n",
    "X = np.concatenate((X, 20*np.random.rand(int(N/2),2)))\n",
    "Y = np.concatenate((np.ones(int(N/2)),np.zeros(int(N/2))))\n",
    "\n",
    "plt.plot(X[:int(N/2),0],X[:int(N/2),1],'r+',X[int(N/2):,0],X[int(N/2):,1],'k.',ms=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, we reserve 80% of the labeled data for training and the remaining 20% for testing. We then fit decision trees of different maximum depths (from 2 to 50) to the training set and plot their respective accuracies when applied to the training and test sets. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Accuracy')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#########################################\n",
    "# Training and Test set creation\n",
    "#########################################\n",
    "\n",
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=0.8, random_state=1)\n",
    "\n",
    "from sklearn import tree\n",
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "#########################################\n",
    "# Model fitting and evaluation\n",
    "#########################################\n",
    "\n",
    "maxdepths = [2,3,4,5,6,7,8,9,10,15,20,25,30,35,40,45,50]\n",
    "\n",
    "trainAcc = np.zeros(len(maxdepths))\n",
    "testAcc = np.zeros(len(maxdepths))\n",
    "\n",
    "index = 0\n",
    "for depth in maxdepths:\n",
    "    clf = tree.DecisionTreeClassifier(max_depth=depth)\n",
    "    clf = clf.fit(X_train, Y_train)\n",
    "    Y_predTrain = clf.predict(X_train)\n",
    "    Y_predTest = clf.predict(X_test)\n",
    "    trainAcc[index] = accuracy_score(Y_train, Y_predTrain)\n",
    "    testAcc[index] = accuracy_score(Y_test, Y_predTest)\n",
    "    index += 1\n",
    "    \n",
    "#########################################\n",
    "# Plot of training and test accuracies\n",
    "#########################################\n",
    "    \n",
    "plt.plot(maxdepths,trainAcc,'ro-',maxdepths,testAcc,'bv--')\n",
    "plt.legend(['Training Accuracy','Test Accuracy'])\n",
    "plt.xlabel('Max depth')\n",
    "plt.ylabel('Accuracy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot above shows that training accuracy will continue to improve as the maximum depth of the tree increases (i.e., as the model becomes more complex). However, the test accuracy initially improves up to a maximum depth of 5, before it gradually decreases due to model overfitting."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.4 Alternative Classification Techniques\n",
    "\n",
    "Besides decision tree classifier, the Python sklearn library also supports other classification techniques. In this section, we provide examples to illustrate how to apply the k-nearest neighbor classifier, linear classifiers (logistic regression and support vector machine), as well as ensemble methods (boosting, bagging, and random forest) to the 2-dimensional data given in the previous section."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4.1 K-Nearest neighbor classifier\n",
    "\n",
    "In this approach, the class label of a test instance is predicted based on the majority class of its *k* closest training instances. The number of nearest neighbors, *k*, is a hyperparameter that must be provided by the user, along with the distance metric. By default, we can use Euclidean distance (which is equivalent to Minkowski distance with an exponent factor equals to p=2):\n",
    "\n",
    "\\begin{equation*}\n",
    "\\textrm{Minkowski distance}(x,y) = \\bigg[\\sum_{i=1}^N |x_i-y_i|^p \\bigg]^{\\frac{1}{p}}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Accuracy')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "numNeighbors = [1, 5, 10, 15, 20, 25, 30]\n",
    "trainAcc = []\n",
    "testAcc = []\n",
    "\n",
    "for k in numNeighbors:\n",
    "    clf = KNeighborsClassifier(n_neighbors=k, metric='minkowski', p=2)\n",
    "    clf.fit(X_train, Y_train)\n",
    "    Y_predTrain = clf.predict(X_train)\n",
    "    Y_predTest = clf.predict(X_test)\n",
    "    trainAcc.append(accuracy_score(Y_train, Y_predTrain))\n",
    "    testAcc.append(accuracy_score(Y_test, Y_predTest))\n",
    "\n",
    "plt.plot(numNeighbors, trainAcc, 'ro-', numNeighbors, testAcc,'bv--')\n",
    "plt.legend(['Training Accuracy','Test Accuracy'])\n",
    "plt.xlabel('Number of neighbors')\n",
    "plt.ylabel('Accuracy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4.2 Linear Classifiers\n",
    "\n",
    "Linear classifiers such as logistic regression and support vector machine (SVM) constructs a linear separating hyperplane to distinguish instances from different classes. \n",
    "\n",
    "For logistic regression, the model can be described by the following equation:\n",
    "\\begin{equation*}\n",
    "P(y=1|x) = \\frac{1}{1 + \\exp^{-w^Tx - b}} = \\sigma(w^Tx + b)\n",
    "\\end{equation*}\n",
    "The model parameters (w,b) are estimated by optimizing the following regularized negative log-likelihood function:\n",
    "\\begin{equation*}\n",
    "(w^*,b^*) = \\arg\\min_{w,b} - \\sum_{i=1}^N y_i \\log\\bigg[\\sigma(w^Tx_i + b)\\bigg] + (1-y_i) \\log\\bigg[\\sigma(-w^Tx_i - b)\\bigg] + \\frac{1}{C} \\Omega([w,b])\n",
    "\\end{equation*}\n",
    "where $C$ is a hyperparameter that controls the inverse of model complexity (smaller values imply stronger regularization) while $\\Omega(\\cdot)$ is the regularization term, which by default, is assumed to be an $l_2$-norm in sklearn.\n",
    "\n",
    "For support vector machine, the model parameters $(w^*,b^*)$ are estimated by solving the following constrained optimization problem:\n",
    "\\begin{eqnarray*}\n",
    "&&\\min_{w^*,b^*,\\{\\xi_i\\}} \\frac{\\|w\\|^2}{2} + \\frac{1}{C} \\sum_i \\xi_i \\\\\n",
    "\\textrm{s.t.} && \\forall i: y_i\\bigg[w^T \\phi(x_i) + b\\bigg] \\ge 1 - \\xi_i, \\ \\ \\xi_i \\ge 0  \n",
    "\\end{eqnarray*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Accuracy')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn import linear_model\n",
    "from sklearn.svm import SVC\n",
    "\n",
    "C = [0.01, 0.1, 0.2, 0.5, 0.8, 1, 5, 10, 20, 50]\n",
    "LRtrainAcc = []\n",
    "LRtestAcc = []\n",
    "SVMtrainAcc = []\n",
    "SVMtestAcc = []\n",
    "\n",
    "for param in C:\n",
    "    clf = linear_model.LogisticRegression(C=param)\n",
    "    clf.fit(X_train, Y_train)\n",
    "    Y_predTrain = clf.predict(X_train)\n",
    "    Y_predTest = clf.predict(X_test)\n",
    "    LRtrainAcc.append(accuracy_score(Y_train, Y_predTrain))\n",
    "    LRtestAcc.append(accuracy_score(Y_test, Y_predTest))\n",
    "\n",
    "    clf = SVC(C=param,kernel='linear')\n",
    "    clf.fit(X_train, Y_train)\n",
    "    Y_predTrain = clf.predict(X_train)\n",
    "    Y_predTest = clf.predict(X_test)\n",
    "    SVMtrainAcc.append(accuracy_score(Y_train, Y_predTrain))\n",
    "    SVMtestAcc.append(accuracy_score(Y_test, Y_predTest))\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12,6))\n",
    "ax1.plot(C, LRtrainAcc, 'ro-', C, LRtestAcc,'bv--')\n",
    "ax1.legend(['Training Accuracy','Test Accuracy'])\n",
    "ax1.set_xlabel('C')\n",
    "ax1.set_xscale('log')\n",
    "ax1.set_ylabel('Accuracy')\n",
    "\n",
    "ax2.plot(C, SVMtrainAcc, 'ro-', C, SVMtestAcc,'bv--')\n",
    "ax2.legend(['Training Accuracy','Test Accuracy'])\n",
    "ax2.set_xlabel('C')\n",
    "ax2.set_xscale('log')\n",
    "ax2.set_ylabel('Accuracy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that linear classifiers perform poorly on the data since the true decision boundaries between classes are nonlinear for the given 2-dimensional dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4.3 Nonlinear Support Vector Machine\n",
    "\n",
    "The code below shows an example of using nonlinear support vector machine with a Gaussian radial basis function kernel to fit the 2-dimensional dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Accuracy')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.svm import SVC\n",
    "\n",
    "C = [0.01, 0.1, 0.2, 0.5, 0.8, 1, 5, 10, 20, 50]\n",
    "SVMtrainAcc = []\n",
    "SVMtestAcc = []\n",
    "\n",
    "for param in C:\n",
    "    clf = SVC(C=param,kernel='rbf',gamma='auto')\n",
    "    clf.fit(X_train, Y_train)\n",
    "    Y_predTrain = clf.predict(X_train)\n",
    "    Y_predTest = clf.predict(X_test)\n",
    "    SVMtrainAcc.append(accuracy_score(Y_train, Y_predTrain))\n",
    "    SVMtestAcc.append(accuracy_score(Y_test, Y_predTest))\n",
    "\n",
    "plt.plot(C, SVMtrainAcc, 'ro-', C, SVMtestAcc,'bv--')\n",
    "plt.legend(['Training Accuracy','Test Accuracy'])\n",
    "plt.xlabel('C')\n",
    "plt.xscale('log')\n",
    "plt.ylabel('Accuracy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observe that the nonlinear SVM can achieve a higher test accuracy compared to linear SVM."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4.4 Ensemble Methods\n",
    "\n",
    "An ensemble classifier constructs a set of base classifiers from the training data and performs classification by taking a vote on the predictions made by each base classifier. We consider 3 types of ensemble classifiers in this example: bagging, boosting, and random forest. Detailed explanation about these classifiers can be found in Section 4.10 of the book.\n",
    "\n",
    "In the example below, we fit 500 base classifiers to the 2-dimensional dataset using each ensemble method. The base classifier corresponds to a decision tree with maximum depth equals to 10."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0, 0, 'Random Forest'), Text(0, 0, 'Bagging'), Text(0, 0, 'AdaBoost')]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn import ensemble\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "\n",
    "numBaseClassifiers = 500\n",
    "maxdepth = 10\n",
    "trainAcc = []\n",
    "testAcc = []\n",
    "\n",
    "clf = ensemble.RandomForestClassifier(n_estimators=numBaseClassifiers)\n",
    "clf.fit(X_train, Y_train)\n",
    "Y_predTrain = clf.predict(X_train)\n",
    "Y_predTest = clf.predict(X_test)\n",
    "trainAcc.append(accuracy_score(Y_train, Y_predTrain))\n",
    "testAcc.append(accuracy_score(Y_test, Y_predTest))\n",
    "\n",
    "clf = ensemble.BaggingClassifier(DecisionTreeClassifier(max_depth=maxdepth),n_estimators=numBaseClassifiers)\n",
    "clf.fit(X_train, Y_train)\n",
    "Y_predTrain = clf.predict(X_train)\n",
    "Y_predTest = clf.predict(X_test)\n",
    "trainAcc.append(accuracy_score(Y_train, Y_predTrain))\n",
    "testAcc.append(accuracy_score(Y_test, Y_predTest))\n",
    "\n",
    "clf = ensemble.AdaBoostClassifier(DecisionTreeClassifier(max_depth=maxdepth),n_estimators=numBaseClassifiers)\n",
    "clf.fit(X_train, Y_train)\n",
    "Y_predTrain = clf.predict(X_train)\n",
    "Y_predTest = clf.predict(X_test)\n",
    "trainAcc.append(accuracy_score(Y_train, Y_predTrain))\n",
    "testAcc.append(accuracy_score(Y_test, Y_predTest))\n",
    "\n",
    "methods = ['Random Forest', 'Bagging', 'AdaBoost']\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12,6))\n",
    "ax1.bar([1.5,2.5,3.5], trainAcc)\n",
    "ax1.set_xticks([1.5,2.5,3.5])\n",
    "ax1.set_xticklabels(methods)\n",
    "ax2.bar([1.5,2.5,3.5], testAcc)\n",
    "ax2.set_xticks([1.5,2.5,3.5])\n",
    "ax2.set_xticklabels(methods)"
   ]
  },
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   "source": [
    "## 3.5 Summary\n",
    "\n",
    "This section provides several examples of using Python sklearn library to build classification models from a given input data. We also illustrate the problem of model overfitting and show how to apply different classification methods to the given dataset."
   ]
  }
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