01-Neural-Network-Basics/Manual Neural Network.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Manual Neural Network\n",
    "\n",
    "In this notebook we will manually build out a neural network that mimics the TensorFlow API. This will greatly help your understanding when working with the real TensorFlow!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "____\n",
    "### Quick Note on Super() and OOP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class SimpleClass():\n",
    "    \n",
    "    def __init__(self,str_input):\n",
    "        print(\"SIMPLE\"+str_input)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class ExtendedClass(SimpleClass):\n",
    "    \n",
    "    def __init__(self):\n",
    "        print('EXTENDED')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "EXTENDED\n"
     ]
    }
   ],
   "source": [
    "s = ExtendedClass()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class ExtendedClass(SimpleClass):\n",
    "    \n",
    "    def __init__(self):\n",
    "        \n",
    "        super().__init__(\" My String\")\n",
    "        print('EXTENDED')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SIMPLE My String\n",
      "EXTENDED\n"
     ]
    }
   ],
   "source": [
    "s = ExtendedClass()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "________"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Operation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Operation():\n",
    "    \"\"\"\n",
    "    An Operation is a node in a \"Graph\". TensorFlow will also use this concept of a Graph.\n",
    "    \n",
    "    This Operation class will be inherited by other classes that actually compute the specific\n",
    "    operation, such as adding or matrix multiplication.\n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, input_nodes = []):\n",
    "        \"\"\"\n",
    "        Intialize an Operation\n",
    "        \"\"\"\n",
    "        self.input_nodes = input_nodes # The list of input nodes\n",
    "        self.output_nodes = [] # List of nodes consuming this node's output\n",
    "        \n",
    "        # For every node in the input, we append this operation (self) to the list of\n",
    "        # the consumers of the input nodes\n",
    "        for node in input_nodes:\n",
    "            node.output_nodes.append(self)\n",
    "        \n",
    "        # There will be a global default graph (TensorFlow works this way)\n",
    "        # We will then append this particular operation\n",
    "        # Append this operation to the list of operations in the currently active default graph\n",
    "        _default_graph.operations.append(self)\n",
    "  \n",
    "    def compute(self):\n",
    "        \"\"\" \n",
    "        This is a placeholder function. It will be overwritten by the actual specific operation\n",
    "        that inherits from this class.\n",
    "        \n",
    "        \"\"\"\n",
    "        \n",
    "        pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example Operations\n",
    "\n",
    "### Addition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class add(Operation):\n",
    "    \n",
    "    def __init__(self, x, y):\n",
    "         \n",
    "        super().__init__([x, y])\n",
    "\n",
    "    def compute(self, x_var, y_var):\n",
    "         \n",
    "        self.inputs = [x_var, y_var]\n",
    "        return x_var + y_var"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multiplication"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class multiply(Operation):\n",
    "     \n",
    "    def __init__(self, a, b):\n",
    "        \n",
    "        super().__init__([a, b])\n",
    "    \n",
    "    def compute(self, a_var, b_var):\n",
    "         \n",
    "        self.inputs = [a_var, b_var]\n",
    "        return a_var * b_var"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Matrix Multiplication"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class matmul(Operation):\n",
    "     \n",
    "    def __init__(self, a, b):\n",
    "        \n",
    "        super().__init__([a, b])\n",
    "    \n",
    "    def compute(self, a_mat, b_mat):\n",
    "         \n",
    "        self.inputs = [a_mat, b_mat]\n",
    "        return a_mat.dot(b_mat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Placeholders"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Placeholder():\n",
    "    \"\"\"\n",
    "    A placeholder is a node that needs to be provided a value for computing the output in the Graph.\n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self):\n",
    "        \n",
    "        self.output_nodes = []\n",
    "        \n",
    "        _default_graph.placeholders.append(self)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Variable():\n",
    "    \"\"\"\n",
    "    This variable is a changeable parameter of the Graph.\n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, initial_value = None):\n",
    "        \n",
    "        self.value = initial_value\n",
    "        self.output_nodes = []\n",
    "        \n",
    "         \n",
    "        _default_graph.variables.append(self)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Graph():\n",
    "    \n",
    "    \n",
    "    def __init__(self):\n",
    "        \n",
    "        self.operations = []\n",
    "        self.placeholders = []\n",
    "        self.variables = []\n",
    "        \n",
    "    def set_as_default(self):\n",
    "        \"\"\"\n",
    "        Sets this Graph instance as the Global Default Graph\n",
    "        \"\"\"\n",
    "        global _default_graph\n",
    "        _default_graph = self"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A Basic Graph\n",
    "\n",
    "$$ z = Ax + b $$\n",
    "\n",
    "With A=10 and b=1\n",
    "\n",
    "$$ z = 10x + 1 $$\n",
    "\n",
    "Just need a placeholder for x and then once x is filled in we can solve it!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "g = Graph()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "g.set_as_default()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "A = Variable(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "b = Variable(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Will be filled out later\n",
    "x = Placeholder()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y = multiply(A,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "z = add(y,b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Session"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Traversing Operation Nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def traverse_postorder(operation):\n",
    "    \"\"\" \n",
    "    PostOrder Traversal of Nodes. Basically makes sure computations are done in \n",
    "    the correct order (Ax first , then Ax + b). Feel free to copy and paste this code.\n",
    "    It is not super important for understanding the basic fundamentals of deep learning.\n",
    "    \"\"\"\n",
    "    \n",
    "    nodes_postorder = []\n",
    "    def recurse(node):\n",
    "        if isinstance(node, Operation):\n",
    "            for input_node in node.input_nodes:\n",
    "                recurse(input_node)\n",
    "        nodes_postorder.append(node)\n",
    "\n",
    "    recurse(operation)\n",
    "    return nodes_postorder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Session:\n",
    "    \n",
    "    def run(self, operation, feed_dict = {}):\n",
    "        \"\"\" \n",
    "          operation: The operation to compute\n",
    "          feed_dict: Dictionary mapping placeholders to input values (the data)  \n",
    "        \"\"\"\n",
    "        \n",
    "        # Puts nodes in correct order\n",
    "        nodes_postorder = traverse_postorder(operation)\n",
    "        \n",
    "        for node in nodes_postorder:\n",
    "\n",
    "            if type(node) == Placeholder:\n",
    "                \n",
    "                node.output = feed_dict[node]\n",
    "                \n",
    "            elif type(node) == Variable:\n",
    "                \n",
    "                node.output = node.value\n",
    "                \n",
    "            else: # Operation\n",
    "                \n",
    "                node.inputs = [input_node.output for input_node in node.input_nodes]\n",
    "\n",
    "                 \n",
    "                node.output = node.compute(*node.inputs)\n",
    "                \n",
    "            # Convert lists to numpy arrays\n",
    "            if type(node.output) == list:\n",
    "                node.output = np.array(node.output)\n",
    "        \n",
    "        # Return the requested node value\n",
    "        return operation.output\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sess = Session()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "result = sess.run(operation=z,feed_dict={x:10})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "101"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "101"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "10*10 + 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Looks like we did it! **"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "g = Graph()\n",
    "\n",
    "g.set_as_default()\n",
    "\n",
    "A = Variable([[10,20],[30,40]])\n",
    "b = Variable([1,1])\n",
    "\n",
    "x = Placeholder()\n",
    "\n",
    "y = matmul(A,x)\n",
    "\n",
    "z = add(y,b)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sess = Session()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "result = sess.run(operation=z,feed_dict={x:10})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[101, 201],\n",
       "       [301, 401]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Activation Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1/(1+np.exp(-z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sample_z = np.linspace(-10,10,100)\n",
    "sample_a = sigmoid(sample_z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x171fcba0dd8>]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x171fc794240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sample_z,sample_a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Sigmoid as an Operation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Sigmoid(Operation):\n",
    " \n",
    "    \n",
    "    def __init__(self, z):\n",
    "\n",
    "        # a is the input node\n",
    "        super().__init__([z])\n",
    "\n",
    "    def compute(self, z_val):\n",
    "        \n",
    "        return 1/(1+np.exp(-z_val))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Classification Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_blobs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = make_blobs(n_samples = 50,n_features=2,centers=2,random_state=75)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[  7.3402781 ,   9.36149154],\n",
       "        [  9.13332743,   8.74906102],\n",
       "        [  1.99243535,  -8.85885722],\n",
       "        [  7.38443759,   7.72520389],\n",
       "        [  7.97613887,   8.80878209],\n",
       "        [  7.76974352,   9.50899462],\n",
       "        [  8.3186688 ,  10.1026025 ],\n",
       "        [  8.79588546,   7.28046702],\n",
       "        [  9.81270381,   9.46968531],\n",
       "        [  1.57961049,  -8.17089971],\n",
       "        [  0.06441546,  -9.04982817],\n",
       "        [  7.2075117 ,   7.04533624],\n",
       "        [  9.10704928,   9.0272212 ],\n",
       "        [  1.82921897,  -9.86956281],\n",
       "        [  7.85036314,   7.986659  ],\n",
       "        [  3.04605603,  -7.50486114],\n",
       "        [  1.85582689,  -6.74473432],\n",
       "        [  2.88603902,  -8.85261704],\n",
       "        [ -1.20046211,  -9.55928542],\n",
       "        [  2.00890845,  -9.78471782],\n",
       "        [  7.68945113,   9.01706723],\n",
       "        [  6.42356167,   8.33356412],\n",
       "        [  8.15467319,   7.87489634],\n",
       "        [  1.92000795,  -7.50953708],\n",
       "        [  1.90073973,  -7.24386675],\n",
       "        [  7.7605855 ,   7.05124418],\n",
       "        [  6.90561582,   9.23493842],\n",
       "        [  0.65582768,  -9.5920878 ],\n",
       "        [  1.41804346,  -8.10517372],\n",
       "        [  9.65371965,   9.35409538],\n",
       "        [  1.23053506,  -7.98873571],\n",
       "        [  1.96322881,  -9.50169117],\n",
       "        [  6.11644251,   9.26709393],\n",
       "        [  7.70630321,  10.78862346],\n",
       "        [  0.79580385,  -9.00301023],\n",
       "        [  3.13114921,  -8.6849493 ],\n",
       "        [  1.3970852 ,  -7.25918415],\n",
       "        [  7.27808709,   7.15201886],\n",
       "        [  1.06965742,  -8.1648251 ],\n",
       "        [  6.37298915,   9.77705761],\n",
       "        [  7.24898455,   8.85834104],\n",
       "        [  2.09335725,  -7.66278316],\n",
       "        [  1.05865542,  -8.43841416],\n",
       "        [  6.43807502,   7.85483418],\n",
       "        [  6.94948313,   8.75248232],\n",
       "        [ -0.07326715, -11.69999644],\n",
       "        [  0.61463602,  -9.51908883],\n",
       "        [  1.31977821,  -7.2710667 ],\n",
       "        [  2.72532584,  -7.51956557],\n",
       "        [  8.20949206,  11.90419283]]),\n",
       " array([1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1,\n",
       "        0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0,\n",
       "        0, 0, 0, 1]))"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x171fd905908>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAD8CAYAAAB0IB+mAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIPABIBL/D5PGxRKMfbENAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x171fd90e6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "features = data[0]\n",
    "plt.scatter(features[:,0],features[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x171fda56588>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAD8CAYAAAB0IB+mAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nHy2kWeYNBdmQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x171fd90e710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "labels = data[1]\n",
    "plt.scatter(features[:,0],features[:,1],c=labels,cmap='coolwarm')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x171fda674e0>]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAD8CAYAAAB0IB+mAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEELECAl8IYSIERL4QggRI/4f6TNn7LH9POcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x171fda192e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# DRAW A LINE THAT SEPERATES CLASSES\n",
    "x = np.linspace(0,11,10)\n",
    "y = -x + 5\n",
    "plt.scatter(features[:,0],features[:,1],c=labels,cmap='coolwarm')\n",
    "plt.plot(x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Defining the Perceptron\n",
    "\n",
    "$$ y = mx + b $$\n",
    "\n",
    "$$ y = -x + 5 $$\n",
    "\n",
    "$$ f1 = mf2 + b , m=1$$\n",
    "\n",
    "$$ f1 = -f2 + 5 $$\n",
    "\n",
    "$$ f1 + f2 - 5 = 0 $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Convert to a Matrix Representation of Features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ w^Tx + b = 0 $$\n",
    "\n",
    "$$   \\Big(1, 1\\Big)f - 5 = 0 $$\n",
    "\n",
    "Then if the result is > 0 its label 1, if it is less than 0, it is label=0\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example Point\n",
    "\n",
    "Let's say we have the point f1=2 , f2=2 otherwise stated as (8,10). Then we have:\n",
    "\n",
    "$$ \n",
    "\\begin{pmatrix} \n",
    "1 , 1\n",
    "\\end{pmatrix} \n",
    "\\begin{pmatrix} \n",
    "8 \\\\\n",
    "10\n",
    "\\end{pmatrix} + 5 =  $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([13])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([1, 1]).dot(np.array([[8],[10]])) - 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or if we have (4,-10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-11])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([1,1]).dot(np.array([[4],[-10]])) - 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using an Example Session Graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "g = Graph()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "g.set_as_default()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = Placeholder()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "w = Variable([1,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "b = Variable(-5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "z = add(matmul(w,x),b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = Sigmoid(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sess = Session()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99999773967570205"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sess.run(operation=a,feed_dict={x:[8,10]})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0590222692562472e-07"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sess.run(operation=a,feed_dict={x:[0,-10]})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Great Job!"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}