ex1-linear regression/ex1-normal-equation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 线性回归（单变量）\n",
    "预测food truck的收益值。\n",
    "ex1data1.txt：数据集，第一列表示城市人数，第二列该城市的food truck收益"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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>Population</th>\n",
       "      <th>Profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.1101</td>\n",
       "      <td>17.5920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.5277</td>\n",
       "      <td>9.1302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.5186</td>\n",
       "      <td>13.6620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.0032</td>\n",
       "      <td>11.8540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.8598</td>\n",
       "      <td>6.8233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Population   Profit\n",
       "0      6.1101  17.5920\n",
       "1      5.5277   9.1302\n",
       "2      8.5186  13.6620\n",
       "3      7.0032  11.8540\n",
       "4      5.8598   6.8233"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path = 'ex1data1.txt'\n",
    "data = pd.read_csv(path, header=None, names=['Population', 'Profit'])\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>Population</th>\n",
       "      <th>Profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>97.000000</td>\n",
       "      <td>97.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>8.159800</td>\n",
       "      <td>5.839135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>3.869884</td>\n",
       "      <td>5.510262</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>5.026900</td>\n",
       "      <td>-2.680700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>5.707700</td>\n",
       "      <td>1.986900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>6.589400</td>\n",
       "      <td>4.562300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>8.578100</td>\n",
       "      <td>7.046700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>22.203000</td>\n",
       "      <td>24.147000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Population     Profit\n",
       "count   97.000000  97.000000\n",
       "mean     8.159800   5.839135\n",
       "std      3.869884   5.510262\n",
       "min      5.026900  -2.680700\n",
       "25%      5.707700   1.986900\n",
       "50%      6.589400   4.562300\n",
       "75%      8.578100   7.046700\n",
       "max     22.203000  24.147000"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.plot(kind='scatter', x='Population', y='Profit', figsize=(12,8))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>Ones</th>\n",
       "      <th>Population</th>\n",
       "      <th>Profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>6.1101</td>\n",
       "      <td>17.5920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>5.5277</td>\n",
       "      <td>9.1302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>8.5186</td>\n",
       "      <td>13.6620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>7.0032</td>\n",
       "      <td>11.8540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>5.8598</td>\n",
       "      <td>6.8233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Ones  Population   Profit\n",
       "0     1      6.1101  17.5920\n",
       "1     1      5.5277   9.1302\n",
       "2     1      8.5186  13.6620\n",
       "3     1      7.0032  11.8540\n",
       "4     1      5.8598   6.8233"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 新增一例，x0\n",
    "data.insert(0, 'Ones', 1)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "cols = data.shape[1]\n",
    "X = data.iloc[:, 0:cols-1]\n",
    "Y = data.iloc[:, cols-1:cols]\n",
    "\n",
    "X = np.matrix(X.values)\n",
    "Y = np.matrix(Y.values)\n",
    "theta = np.matrix(np.array([0, 0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 代价函数\n",
    "def computeCost(X, Y, theta):\n",
    "    inner = np.power((X * theta.T) - Y, 2)\n",
    "    return np.sum(inner) / (2 * len(X))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 正则方程\n",
    "\n",
    "![](img/regularization.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def normalEqn(X, Y):\n",
    "    theta = np.linalg.inv(X.T@X)@X.T@Y\n",
    "    return theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[-3.89578088],\n",
       "        [ 1.19303364]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta = normalEqn(X, Y)\n",
    "# 梯度下降的theta为 matrix([[-3.24140214,  1.1272942 ]])\n",
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.476971375975179"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 梯度下降的cost为 4.515955503078912\n",
    "computeCost(X, Y, theta.reshape(1, -1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 画出拟合图像\n",
    "x = np.linspace(data.Population.min(), data.Population.max(), 100)\n",
    "f = theta[0,0] + theta[1,0] * x\n",
    "\n",
    "plt.figure(figsize=(12, 8))\n",
    "plt.xlabel('Population')\n",
    "plt.ylabel('Profit')\n",
    "l1 = plt.plot(x, f, label='Prediction', color='red')\n",
    "l2 = plt.scatter(data.Population, data.Profit, label='Traing Data', )\n",
    "plt.legend(loc='best')\n",
    "plt.title('Predicted Profit vs Population Size')\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}