{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import numpy.random as nr\n",
    "import matplotlib.pyplot as pl\n",
    "\n",
    "# Size matters in plots.\n",
    "pl.rcParams['figure.figsize'] = (12.0, 10.0)\n",
    "\n",
    "# Plotting with style! \n",
    "import seaborn as sb\n",
    "from matplotlib.pyplot import cm\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\LaTeX \\text{ commands here}\n",
    "\\newcommand{\\R}{\\mathbb{R}}\n",
    "\\newcommand{\\im}{\\text{im}\\,}\n",
    "\\newcommand{\\norm}[1]{||#1||}\n",
    "\\newcommand{\\inner}[1]{\\langle #1 \\rangle}\n",
    "\\newcommand{\\span}{\\mathrm{span}}\n",
    "\\newcommand{\\proj}{\\mathrm{proj}}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "0d550dc6-b222-4f90-8a5a-8fc373b860e9"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<hr style=\"border: 5px solid black\">\n",
    "\n",
    "**Georgia Tech, CS 4540**\n",
    "\n",
    "# L1:  Welcome and Introduction\n",
    "\n",
    "Jacob Abernethy\n",
    "\n",
    "*Tuesday, August 20, 2018*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "a69ec655-4bfe-4a3f-9d26-9965eceb71df"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Outline\n",
    "\n",
    "1. Welcome to the course!\n",
    "    * What this course is about\n",
    "    * What this course is NOT about\n",
    "    * The structure of the course, \"flipped classroom\"\n",
    "    * Quizzes\n",
    "    * Homeworks and Exams\n",
    "    * Using jupyter notebooks\n",
    "2. A taste of what's to come\n",
    "    * One of the simplest learning algorithms: perceptron\n",
    "    * Proof of perceptron's performance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## What is this course about?\n",
    "\n",
    "We are in a new world:\n",
    "- much of industry now views their main resource is **data**\n",
    "- In 2005 the question was: \"how do I efficiently store this data? How do I run queries more quickly?\"\n",
    "- In 2019 the question is: \"how do I leverage all this data for business decisions and customer value?\"\n",
    "\n",
    "This has driven the push for Machine Learning and Data Science.\n",
    "\n",
    "This core question of this course: **What are the algorithmic foundations of data science + ML?**\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## What is this course NOT about?\n",
    "\n",
    "- It's NOT about deep learning or Tensorflow (although we may learn a little about neural networks)\n",
    "- It's NOT about graph algorithms or matchings\n",
    "- It's NOT a coding course (although it may involve some *python* coding)\n",
    "\n",
    "Also: there will NOT be a fixed textbook -- although you may find some textbooks useful.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Structure of the course: FLIPPED classroom\n",
    "\n",
    "The *classical* way of teaching: lecture time reserved to describe content such as definitions and tools, and students solve challenge problems at home.\n",
    "\n",
    "The *flipped-classroom* style: students learn definitions and tools at home, lecture time is reserved for interactive problem solving in groups.\n",
    "* Each lecture will have an associated reading, posted a week before class, for students to go through. It shouldn't take much more than an hour!\n",
    "* Each lecture I will present 4-8 problems, and students will work on them in groups with the help of the instructor(s).\n",
    "\n",
    "**WHY FLIP?** Instruction time is precious. Why waste it just listening to a lecture? Only thing we care about, and that we evaluate you on, is problem solving!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The challenge with the flipped classroom:\n",
    "### We need to force students to actually do readings outside of class!\n",
    "\n",
    "**Solution**: We will *quiz* you at the beginning of each lecture. The quiz checks if you've done the reading or not, and penalizes you if you haven't.\n",
    "\n",
    "You need to bring a laptop, phone, or tablet, in order to take the quiz. Quizzes are given through Canvas, but you will be required to be in class to take the quiz.\n",
    "\n",
    "**Quiz scoring**: 2 points for correct answer, 1 point for any answer, 0 points for no-show. You get 5 quiz drops over the course of the semester!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Homeworks and Exams\n",
    "\n",
    "Aside from quizzes, course evaluation will be as follows:\n",
    "1. Homework 1 due\n",
    "1. Homework 2 due\n",
    "1. Homework 3 due\n",
    "1. *Midterm Exam* (in class)\n",
    "1. Homework 4 due\n",
    "1. Homework 5 due\n",
    "1. Homework 6 due\n",
    "1. *Final Exam* "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Course grade rubric\n",
    "\n",
    "|Content|Score|\n",
    "|------|------|\n",
    "|Homeworks|35%|\n",
    "|Attendance Quizzes|15%|\n",
    "|Midterm Exam|20%|\n",
    "|Final Exam|30%|\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Let's look at an implementation of the Perceptron Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate some points\n",
    "N = 100\n",
    "xn = nr.rand(N,2)\n",
    "\n",
    "x = np.linspace(0,1);\n",
    "\n",
    "# Pick a line \n",
    "a = nr.rand();\n",
    "b = nr.rand();\n",
    "f = lambda x : a*x + b;\n",
    "\n",
    "fig =pl.figure()\n",
    "figa = pl.gca();\n",
    "\n",
    "pl.plot(xn[:,0],xn[:,1],'bo');\n",
    "pl.plot(x,f(x),'r')\n",
    "\n",
    "# Linearly separate the points by the line\n",
    "yn = np.zeros([N,1]);\n",
    "\n",
    "for i in range(N):\n",
    "    if(f(xn[i,0])>xn[i,1]):\n",
    "        # Point is below line\n",
    "        yn[i] = 1;\n",
    "        pl.plot(xn[i,0],xn[i,1],'go')\n",
    "    else:\n",
    "        # Point is above line\n",
    "        yn[i] = -1;\n",
    "        \n",
    "        \n",
    "pl.legend(['Above','Separator','Below'],loc=0)\n",
    "pl.title('Selected points with their separating line.')\n",
    "figa.axes.get_xaxis().set_visible(False)\n",
    "figa.axes.get_yaxis().set_visible(False)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "def perceptron(xn,yn,MaxIter=100,w=np.zeros(3)):\n",
    "    '''\n",
    "        A very simple implementation of the perceptron algorithm for two dimensional data.\n",
    "        \n",
    "        Given points (x,y) with x in R^{2} and y in {0,1}, the perceptron learning algorithm searches for the best\n",
    "        line that separates the data points according to the difference classes defined in y. \n",
    "        \n",
    "        Input: \n",
    "            xn : Data points, an Nx2 vector. \n",
    "            yn : Classification of the previous data points, an Nx1 vector. \n",
    "            MaxIter : Maximum number of iterations (optional).\n",
    "            w  : Initial vector of parameters (optional).\n",
    "            \n",
    "        Output: \n",
    "            w : Parameters of the best line, y = ax+b, that linearly separates the data. \n",
    "        \n",
    "        Note:\n",
    "            Convergence will be slower than expected, since this implementation picks points\n",
    "            to update without a specific plan (randomly). This is enough for a demonstration, not \n",
    "            so good for actual work. \n",
    "'''\n",
    "    \n",
    "    N = xn.shape[0];\n",
    "    \n",
    "    # Separating curve\n",
    "    f = lambda x: np.sign(w[0]+w[1]*x[0]+w[2]*x[1]);\n",
    "    color=iter(cm.rainbow(np.linspace(0,1,10)))\n",
    "    for rndind in range(MaxIter):\n",
    "        i = nr.randint(N);\n",
    "        if rndind % 10 == 0:\n",
    "            bnew = -w[0]/w[2];\n",
    "            anew = -w[1]/w[2];\n",
    "            y = lambda x: anew * x + bnew\n",
    "            col = next(color)\n",
    "            pl.plot(x,y(x),'--',c=col,label='Line from perceptron round %d' % rndind)\n",
    "\n",
    "        if(yn[i] != f(xn[i,:])): # If not classified correctly, adjust the line to account for that point.\n",
    "             w[0] = w[0] + yn[i];\n",
    "             w[1] = w[1] + yn[i]*xn[i,0];\n",
    "             w[2] = w[2] + yn[i]*xn[i,1];\n",
    "            \n",
    "    return w;\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "//anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:31: RuntimeWarning: invalid value encountered in double_scalars\n",
      "//anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:32: RuntimeWarning: invalid value encountered in double_scalars\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figa = pl.gca()\n",
    "w= perceptron(xn,yn)\n",
    "\n",
    "# Using weights w to compute a,b for a line y=a*x+b\n",
    "bnew = -w[0]/w[2];\n",
    "anew = -w[1]/w[2];\n",
    "y = lambda x: anew * x + bnew;\n",
    "\n",
    "# Computing the colors for the points\n",
    "sep_color = (yn+1)/2.0;\n",
    "\n",
    "# pl.figure();\n",
    "\n",
    "\n",
    "pl.scatter(xn[:,0],xn[:,1],c=sep_color.flatten(), s=30)\n",
    "pl.plot(x,y(x),'b--',label='Line from perceptron implementation.')\n",
    "pl.plot(x,f(x),'r',label='Original line.')\n",
    "pl.legend()\n",
    "\n",
    "pl.title('Comparison between the linear separator and the perceptron approximation.')\n",
    "\n",
    "figa.axes.get_xaxis().set_visible(False)\n",
    "figa.axes.get_yaxis().set_visible(False)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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