11-SVM/05-Polynomial-Features-in-SVM-and-Kernel-Function/05-Polynomial-Features-in-SVM-and-Kernel-Function.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SVM中的使用多项式特征"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "\n",
    "X, y = datasets.make_moons()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 2)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100,)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BGyLiwsU+2wHAzGw4ZY8DuADYHRHPdVe+DdgAvBEAIuKv+pZ/ECilocuDXxLmK4FKuE4k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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110859c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[y==0,0], X[y==0,1])\n",
    "plt.scatter(X[y==1,0], X[y==1,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Mrh5/h+pnaloM3T7o7uu0adatq+fc3zih56NsK7VrC3z6jXDN8sbvXVuqLtHEmZrA4L5O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\nWQsHBjMza/H/AUTAjc/C5ZbKAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11084f940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, y = datasets.make_moons(noise=0.15, random_state=666)\n",
    "\n",
    "plt.scatter(X[y==0,0], X[y==0,1])\n",
    "plt.scatter(X[y==1,0], X[y==1,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 使用多项式特征的SVM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures, StandardScaler\n",
    "from sklearn.svm import LinearSVC\n",
    "from sklearn.pipeline import Pipeline\n",
    "\n",
    "def PolynomialSVC(degree, C=1.0):\n",
    "    return Pipeline([\n",
    "        (\"poly\", PolynomialFeatures(degree=degree)),\n",
    "        (\"std_scaler\", StandardScaler()),\n",
    "        (\"linearSVC\", LinearSVC(C=C))\n",
    "    ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(steps=[('poly', PolynomialFeatures(degree=3, include_bias=True, interaction_only=False)), ('std_scaler', StandardScaler(copy=True, with_mean=True, with_std=True)), ('linearSVC', LinearSVC(C=1.0, class_weight=None, dual=True, fit_intercept=True,\n",
       "     intercept_scaling=1, loss='squared_hinge', max_iter=1000,\n",
       "     multi_class='ovr', penalty='l2', random_state=None, tol=0.0001,\n",
       "     verbose=0))])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly_svc = PolynomialSVC(degree=3)\n",
    "poly_svc.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_decision_boundary(model, axis):\n",
    "    \n",
    "    x0, x1 = np.meshgrid(\n",
    "        np.linspace(axis[0], axis[1], int((axis[1]-axis[0])*100)).reshape(-1, 1),\n",
    "        np.linspace(axis[2], axis[3], int((axis[3]-axis[2])*100)).reshape(-1, 1),\n",
    "    )\n",
    "    X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "\n",
    "    y_predict = model.predict(X_new)\n",
    "    zz = y_predict.reshape(x0.shape)\n",
    "\n",
    "    from matplotlib.colors import ListedColormap\n",
    "    custom_cmap = ListedColormap(['#EF9A9A','#FFF59D','#90CAF9'])\n",
    "    \n",
    "    plt.contourf(x0, x1, zz, linewidth=5, cmap=custom_cmap)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+rKrDKQ+xpZP2WVKENgJsp2lsp1lspzltt1FU1WRDiIiooLhSmYiIADAgEBFR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\nVZnx8wuOI+sAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1143bdf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_decision_boundary(poly_svc, axis=[-1.5, 2.5, -1.0, 1.5])\n",
    "plt.scatter(X[y==0,0], X[y==0,1])\n",
    "plt.scatter(X[y==1,0], X[y==1,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 使用多项式核函数的SVM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.svm import SVC\n",
    "\n",
    "def PolynomialKernelSVC(degree, C=1.0):\n",
    "    return Pipeline([\n",
    "        (\"std_scaler\", StandardScaler()),\n",
    "        (\"kernelSVC\", SVC(kernel=\"poly\", degree=degree, C=C))\n",
    "    ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(steps=[('std_scaler', StandardScaler(copy=True, with_mean=True, with_std=True)), ('kernelSVC', SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,\n",
       "  decision_function_shape=None, degree=3, gamma='auto', kernel='poly',\n",
       "  max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
       "  tol=0.001, verbose=False))])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly_kernel_svc = PolynomialKernelSVC(degree=3)\n",
    "poly_kernel_svc.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PZzQjBHff5+4vVd2OUTK2c7lch7u/C3TLdZTpOuD+5Ov7gX9e8vGHyXJ+rgMe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\nICIiCQUEEREBFBBERCTx/wHzEckqkRk1mQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1143e0208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_decision_boundary(poly_kernel_svc, axis=[-1.5, 2.5, -1.0, 1.5])\n",
    "plt.scatter(X[y==0,0], X[y==0,1])\n",
    "plt.scatter(X[y==1,0], X[y==1,1])\n",
    "plt.show()"
   ]
  }
 ],
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