11-SVM/07-What-is-RBF-Kernel/07-What-is-RBF-Kernel.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 直观理解高斯核函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.arange(-4, 5, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4, -3, -2, -1,  0,  1,  2,  3,  4])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y = np.array((x >= -2) & (x <= 2), dtype='int')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 1, 1, 1, 1, 1, 0, 0])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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k2drtfgH4WeCZIcf+alVt6x57R8wpSRrRqIWxE3i8W34cuHvImNuAuao6WVWvAU9086iq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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ee24438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x[y==0], [0]*len(x[y==0]))\n",
    "plt.scatter(x[y==1], [0]*len(x[y==1]))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def gaussian(x, l):\n",
    "    gamma = 1.0\n",
    "    return np.exp(-gamma * (x-l)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "l1, l2 = -1, 1\n",
    "\n",
    "X_new = np.empty((len(x), 2))\n",
    "for i, data in enumerate(x):\n",
    "    X_new[i, 0] = gaussian(data, l1)\n",
    "    X_new[i, 1] = gaussian(data, l2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f150ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_new[y==0,0], X_new[y==0,1])\n",
    "plt.scatter(X_new[y==1,0], X_new[y==1,1])\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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}