C2_W1_Lab_3_combine_features__M.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Combine Features\n",
    "\n",
    "In this lab, you will practice how to combine features in a pandas dataframe.  This will help you in the graded assignment at the end of the week.  \n",
    "\n",
    "In addition, you will explore why it makes more sense to multiply two features rather than add them in order to create interaction terms.\n",
    "\n",
    "First, you will generate some data to work with."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import pandas\n",
    "import pandas as pd\n",
    "\n",
    "# Import a pre-defined function that generates data\n",
    "from utils import load_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate features and labels\n",
    "X, y = load_data(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Age</th>\n",
       "      <th>Systolic_BP</th>\n",
       "      <th>Diastolic_BP</th>\n",
       "      <th>Cholesterol</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>77.196340</td>\n",
       "      <td>78.784208</td>\n",
       "      <td>87.026569</td>\n",
       "      <td>82.760275</td>\n",
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       "      <td>87.250583</td>\n",
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      "text/plain": [
       "         Age  Systolic_BP  Diastolic_BP  Cholesterol\n",
       "0  77.196340    78.784208     87.026569    82.760275\n",
       "1  63.529850   105.171676     83.396113    80.923284\n",
       "2  69.003986   117.582259     91.161966    92.915422\n",
       "3  82.638210    94.131208     69.470423    95.766098\n",
       "4  78.346286   105.385186     87.250583   120.868124"
      ]
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     "execution_count": 3,
     "metadata": {},
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    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Age', 'Systolic_BP', 'Diastolic_BP', 'Cholesterol'], dtype='object')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feature_names = X.columns\n",
    "feature_names"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Combine strings\n",
    "Even though you can visually see feature names and type the name of the combined feature, you can programmatically create interaction features so that you can apply this to any dataframe.\n",
    "\n",
    "Use f-strings to combine two strings.  There are other ways to do this, but Python's f-strings are quite useful."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "name1: Age\n",
      "name2: Systolic_BP\n"
     ]
    }
   ],
   "source": [
    "name1 = feature_names[0]\n",
    "name2 = feature_names[1]\n",
    "\n",
    "print(f\"name1: {name1}\")\n",
    "print(f\"name2: {name2}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Age_&_Systolic_BP'"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Combine the names of two features into a single string, separated by '_&_' for clarity\n",
    "combined_names = f\"{name1}_&_{name2}\"\n",
    "combined_names"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Add two columns\n",
    "- Add the values from two columns and put them into a new column.\n",
    "- You'll do something similar in this week's assignment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Age</th>\n",
       "      <th>Systolic_BP</th>\n",
       "      <th>Diastolic_BP</th>\n",
       "      <th>Cholesterol</th>\n",
       "      <th>Age_&amp;_Systolic_BP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "      <th>0</th>\n",
       "      <td>77.19634</td>\n",
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       "      <td>155.980548</td>\n",
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       "      <th>1</th>\n",
       "      <td>63.52985</td>\n",
       "      <td>105.171676</td>\n",
       "      <td>83.396113</td>\n",
       "      <td>80.923284</td>\n",
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      "text/plain": [
       "        Age  Systolic_BP  Diastolic_BP  Cholesterol  Age_&_Systolic_BP\n",
       "0  77.19634    78.784208     87.026569    82.760275         155.980548\n",
       "1  63.52985   105.171676     83.396113    80.923284         168.701526"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[combined_names] = X['Age'] + X['Systolic_BP']\n",
    "X.head(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Why we multiply two features instead of adding\n",
    "\n",
    "Why do you think it makes more sense to multiply two features together rather than adding them together?\n",
    "\n",
    "Please take a look at two features, and compare what you get when you add them, versus when you multiply them together."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>v1</th>\n",
       "      <th>v2</th>\n",
       "      <th>v1 + v2</th>\n",
       "      <th>v1 x v2</th>\n",
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       "      <th>0</th>\n",
       "      <td>1</td>\n",
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       "      <td>100</td>\n",
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       "      <td>600</td>\n",
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       "      <th>6</th>\n",
       "      <td>3</td>\n",
       "      <td>100</td>\n",
       "      <td>103</td>\n",
       "      <td>300</td>\n",
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       "      <th>7</th>\n",
       "      <td>3</td>\n",
       "      <td>200</td>\n",
       "      <td>203</td>\n",
       "      <td>600</td>\n",
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       "      <th>8</th>\n",
       "      <td>3</td>\n",
       "      <td>300</td>\n",
       "      <td>303</td>\n",
       "      <td>900</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "   v1   v2  v1 + v2  v1 x v2\n",
       "0   1  100      101      100\n",
       "1   1  200      201      200\n",
       "2   1  300      301      300\n",
       "3   2  100      102      200\n",
       "4   2  200      202      400\n",
       "5   2  300      302      600\n",
       "6   3  100      103      300\n",
       "7   3  200      203      600\n",
       "8   3  300      303      900"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Generate a small dataset with two features\n",
    "df = pd.DataFrame({'v1': [1,1,1,2,2,2,3,3,3],\n",
    "                   'v2': [100,200,300,100,200,300,100,200,300]\n",
    "                  })\n",
    "\n",
    "# add the two features together\n",
    "df['v1 + v2'] = df['v1'] + df['v2']\n",
    "\n",
    "# multiply the two features together\n",
    "df['v1 x v2'] = df['v1'] * df['v2']\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It may not be immediately apparent how adding or multiplying makes a difference; either way you get unique values for each of these operations.\n",
    "\n",
    "To view the data in a more helpful way, rearrange the data (pivot it) so that:\n",
    "- feature 1 is the row index \n",
    "- feature 2 is the column name.  \n",
    "- Then set the sum of the two features as the value. \n",
    "\n",
    "Display the resulting data in a heatmap."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import seaborn in order to use a heatmap plot\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v1 + v2\n",
      "\n"
     ]
    },
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       "      <td>101</td>\n",
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       "      <td>301</td>\n",
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       "      <th>2</th>\n",
       "      <td>102</td>\n",
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       "      <td>302</td>\n",
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       "      <th>3</th>\n",
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      "text/plain": [
       "v2  100  200  300\n",
       "v1               \n",
       "1   101  201  301\n",
       "2   102  202  302\n",
       "3   103  203  303"
      ]
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      "\n"
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     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Pivot the data so that v1 + v2 is the value\n",
    "\n",
    "df_add = df.pivot(index='v1',\n",
    "                  columns='v2',\n",
    "                  values='v1 + v2'\n",
    "                 )\n",
    "print(\"v1 + v2\\n\")\n",
    "display(df_add)\n",
    "print()\n",
    "sns.heatmap(df_add);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that it doesn't seem like you can easily distinguish clearly when you vary feature 1 (which ranges from 1 to 3), since feature 2 is so much larger in magnitude (100 to 300).  This is because you added the two features together."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### View the 'multiply' interaction\n",
    "\n",
    "Now pivot the data so that:\n",
    "- feature 1 is the row index \n",
    "- feature 2 is the column name.  \n",
    "- The values are 'v1 x v2' \n",
    "\n",
    "Use a heatmap to visualize the table."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v1 x v2\n"
     ]
    },
    {
     "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>v2</th>\n",
       "      <th>100</th>\n",
       "      <th>200</th>\n",
       "      <th>300</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v1</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>100</td>\n",
       "      <td>200</td>\n",
       "      <td>300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>200</td>\n",
       "      <td>400</td>\n",
       "      <td>600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>300</td>\n",
       "      <td>600</td>\n",
       "      <td>900</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "v2  100  200  300\n",
       "v1               \n",
       "1   100  200  300\n",
       "2   200  400  600\n",
       "3   300  600  900"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_mult = df.pivot(index='v1',\n",
    "                  columns='v2',\n",
    "                  values='v1 x v2'\n",
    "                 )\n",
    "print('v1 x v2')\n",
    "display(df_mult)\n",
    "print()\n",
    "sns.heatmap(df_mult);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how when you multiply the features, the heatmap looks more like a 'grid' shape instead of three vertical bars.  \n",
    "\n",
    "This means that you are more clearly able to make a distinction as feature 1 varies from 1 to 2 to 3."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discussion\n",
    "\n",
    "When you find the interaction between two features, you ideally hope to see how varying one feature makes an impact on the interaction term.  This is better achieved by multiplying the two features together rather than adding them together.  \n",
    "\n",
    "Another way to think of this is that you want to separate the feature space into a \"grid\", which you can do by multiplying the features together.\n",
    "\n",
    "In this week's assignment, you will create interaction terms!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### This is the end of this practice section.\n",
    "\n",
    "Please continue on with the lecture videos!\n",
    "\n",
    "---"
   ]
  }
 ],
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