FYS-STK4155/doc/Programs/ANN/Ann1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <p style=\"text-align: right;\"> Nicolas Dronchi </p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Day 22 Pre-Class assignment: Introduction to Artificial Neural Networks\n",
    "\n",
    "This entire Artificial Neural Networks module is from Neural Networks Demystified by @stephencwelch.  We have streamlined the content to better fit the format of the class. However, if you have questions or are just curious I highly recommend downloading everything from the following git repository.  It is a great reference to have:\n",
    "\n",
    "    git clone https://github.com/stephencwelch/Neural-Networks-Demystified\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Goals for today's pre-class assignment \n",
    "\n",
    "</p>\n",
    "\n",
    "1. Think about the architecture of Artificial Neural Networks\n",
    "1. Model data flow by performing forward propagation\n",
    "1. Explore A Neural Network (through a visualization)\n",
    "\n",
    "## Assignment instructions\n",
    "\n",
    "**This assignment is due by 11:59 p.m. the day before class** and should be uploaded into the appropriate \"Pre-class assignments\" dropbox folder in the Desire2Learn website.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. The architecture of Artificial Neural Networks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Watch the following video:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"640\"\n",
       "            height=\"360\"\n",
       "            src=\"https://www.youtube.com/embed/bxe2T-V8XRs\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x21a31c34e48>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('bxe2T-V8XRs',width=640,height=360)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use the data from the video above:\n",
    "$$X = \\left[\\begin{matrix} 3 & 5 \\\\ 5 & 1 \\\\ 10 & 2 \\end{matrix}\\right] \\hspace{1cm} , \\hspace{1cm}y = \\left[ \\begin{matrix} 75 \\\\ 82 \\\\ 93 \\end{matrix}\\right] $$\n",
    "\n",
    "\n",
    "### &#9989; Step 1: Initialize your inputs\n",
    "Create two numpy arrays to store the values of the variables $X$ and $y$, as well as their normalized counterparts \n",
    "$X_{norm}$ and $y_{norm}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# your code here (Note include needed libraries):\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# input data (hours of sleep, hours of study)\n",
    "X = np.array([[3,5],[5,1],[10,2]])\n",
    "\n",
    "# normalized X\n",
    "X_norm = X/np.amax(X)\n",
    "\n",
    "# output data (test score)\n",
    "y = np.array([[75],[82],[93]])\n",
    "\n",
    "# normalized y\n",
    "y_norm = y/100\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Data flow: forward propagation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Data in a neural network flows via a process called **forward propagation**. Watch the following video:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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S0lRUufLE8QF0UT5S1sUbg7U4uqLuvbMknbewCsqqnC6SoBj7rmo6echzS2J0r4mSOYQM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\nEQEREH//2Q==\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"640\"\n",
       "            height=\"360\"\n",
       "            src=\"https://www.youtube.com/embed/UJwK6jAStmg?align=Center\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x21a350dba90>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('UJwK6jAStmg',width=640,height=360, align='Center')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 1:** How many input layers, hidden layers and output layers are there in the neural network shown in the video?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Put your answer here\n",
    "inputLayerSize = 2\n",
    "outputLayerSize = 1\n",
    "hiddenLayerSize = 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### &#9989; Step 2:  Initialize random weights\n",
    "Randomly initialize two numpy arrays W1 and W2, of the right dimensions, to store the weights (zero-one) in the synapses between input layer --> hidden layer, and hidden layer --> output layer  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# your code here:\n",
    "\n",
    "W1 = np.random.randn(inputLayerSize, hiddenLayerSize)\n",
    "\n",
    "\n",
    "W2 = np.random.randn(hiddenLayerSize, outputLayerSize)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### &#9989; Step 3: Multiply the normalized input matrix by $W^{(1)}$\n",
    "$$Z^{(2)} = X  W^{(1)} $$ \n",
    "Here is the code using the NumPy `dot` function. If you get an error you may have initilized the size of your variables incorrectly. Make sure the second dimension of ```X_norm``` matches the first dimension of ```W1```:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.85206517, -0.46315777,  0.47725383],\n",
       "       [-0.96041205, -1.14843537,  0.98384797],\n",
       "       [-1.92082411, -2.29687075,  1.96769593]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z2 = np.dot(X_norm, W1)\n",
    "Z2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### &#9989; **Do This:** Implement and test the sigmoid function \n",
    "\n",
    "$$a(z) = \\frac{1}{1 + e^{-z}} $$ \n",
    "\n",
    "The implemented  sigmoid function should take as input a numpy array and return a numpy array of the same dimension, with the function $f$ applied to each entry."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# your code here:\n",
    "def sigmoid(z):\n",
    "    # apply sigmoid activation function\n",
    "    return 1/(1+np.exp(-z))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test your sigmoid function using the following testing code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vCHLobsh3kF/nOTtzYGvbFCo7tyXvuNM56bzrOFq7LorIPqjcm0C1v4o1xfPZ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\npHIXEUlA/w9Y/WjLrGBbcQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x21a2f8a4908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "testInput = np.arange(-6,6,0.01)\n",
    "plt.plot(testInput, sigmoid(testInput), linewidth= 2)\n",
    "plt.grid(1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### &#9989; Step 4: Apply the sigmoid function to  $Z^{(2)}$\n",
    "$$a^{(2)} = f({Z^{(2)}})$$ \n",
    "Here is the code to apply the sigmoid function to $Z^{(2)}$ and display the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.29899982, 0.38623698, 0.6170992 ],\n",
       "       [0.2767957 , 0.24077498, 0.72787107],\n",
       "       [0.1277697 , 0.09138246, 0.87736342]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2 = sigmoid(Z2)\n",
    "a2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### &#9989; Step 5:  multiply $A^{(2)}$ by $W^{(2)}$ to get $Z^{(3)}$\n",
    "$$Z^{(3)} = A^{(2)}  W^{(2)} $$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.72574334],\n",
       "       [1.70159205],\n",
       "       [1.58224372]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z3 = np.dot(a2, W2)\n",
    "Z3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### &#9989; Step 6: Apply the sigmoid function again to $Z^{(3)}$ to produce $\\hat{y}$\n",
    "$$\\hat{y} = f({Z^{(3)}})$$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# your code here:\n",
    "yHat = sigmoid(Z3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Final Comparison\n",
    "Now compare the estimation output ($\\hat{y}$) to the actual output ```y_norm```.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.75],\n",
       "       [0.82],\n",
       "       [0.93]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.84886714],\n",
       "       [0.84574255],\n",
       "       [0.82952205]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yHat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course the results from forward propagation are terrible; no surprises here! The weights have not been properly chosen. That's what training a network does:  the goal is to find a combination of weights so that the result of forward propagation fits the intended output data as best as possible. \n",
    "\n",
    "We will be covering this topic in class."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Exploring A Neural Network\n",
    "\n",
    "Please go to the following website : http://playground.tensorflow.org/\n",
    "\n",
    "There, you'll have the opportunity to play with an actual neural network (e.g., choosing its architecture and the type of activation function) for classification purpose. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "# Assignment wrap-up\n",
    "\n",
    "Please fill out the form that appears when you run the code below.  **You must completely fill this out in order to receive credit for the assignment!**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<iframe \n",
       "\tsrc=\"https://goo.gl/forms/XqTdYAtXYDSc1R7V2\" \n",
       "\twidth=\"80%\" \n",
       "\theight=\"1200px\" \n",
       "\tframeborder=\"0\" \n",
       "\tmarginheight=\"0\" \n",
       "\tmarginwidth=\"0\">\n",
       "\tLoading...\n",
       "</iframe>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import HTML\n",
    "HTML(\n",
    "\"\"\"\n",
    "<iframe \n",
    "\tsrc=\"https://goo.gl/forms/XqTdYAtXYDSc1R7V2\" \n",
    "\twidth=\"80%\" \n",
    "\theight=\"1200px\" \n",
    "\tframeborder=\"0\" \n",
    "\tmarginheight=\"0\" \n",
    "\tmarginwidth=\"0\">\n",
    "\tLoading...\n",
    "</iframe>\n",
    "\"\"\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---------\n",
    "### Congratulations, you're done with your pre-class assignment!\n",
    "\n",
    "Now, you just need to submit this assignment by uploading it to the course <a href=\"https://d2l.msu.edu/\">Desire2Learn</a> web page for today's dropbox (Don't forget to add your name in the first cell)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "&#169; Copyright 2017,  Michigan State University Board of Trustees"
   ]
  }
 ],
 "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": "3.6.0"
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 },
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