{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- dom:TITLE: Data Analysis and Machine Learning: Support Vector Machines -->\n",
    "# Data Analysis and Machine Learning: Support Vector Machines\n",
    "<!-- dom:AUTHOR: Morten Hjorth-Jensen at Department of Physics, University of Oslo & Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University -->\n",
    "<!-- Author: -->  \n",
    "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
    "\n",
    "Date: **May 30, 2018**\n",
    "\n",
    "Copyright 1999-2018, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "## Support Vector Machines, overarching aims"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "from sklearn.svm import SVR\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Generate sample data\n",
    "X = np.sort(5*np.random.rand(40,1), axis=0)\n",
    "y = X**3\n",
    "y=y.ravel()\n",
    "\n",
    "# Add noise to targets\n",
    "X[::4] +=3*(0.5 - np.random.rand(1))\n",
    "y[::5] += 50 * (0.5 - np.random.rand(8))\n",
    "\n",
    "plt.plot(X,y, 'g^')\n",
    "\n",
    "#SVR Fit\n",
    "svr_poly = SVR(kernel='poly', C=1e3, degree=3)\n",
    "y_poly = svr_poly.fit(X, y).predict(X)\n",
    "\n",
    "# Plots\n",
    "z = np.arange(0, 5, 0.1)\n",
    "t = z**3\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "plt.plot(z,z**3, 'r--', label='Cubic Function with No Noise')\n",
    "lw = 2\n",
    "plt.scatter(X, y, color='darkorange', label='Gaussian Cubic Noise')\n",
    "plt.plot(X, y_poly, color='green', lw=lw, label='Polynomial model')\n",
    "plt.xlabel('data')\n",
    "plt.ylabel('target')\n",
    "plt.title('Cubic Gaussian Distribution')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {},
 "nbformat": 4,
 "nbformat_minor": 2
}