The Perceptron/Perceptron.ipynb

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   "source": [
    "## Perceptron\n",
    "\n",
    "### Definission\n",
    "The perceptron is an algorithm for **supervised learning** of binary classifiers. It is a type of linear classifier, i.e. a classification algorithm that makes its predictions based on a linear predictor function combining a set of weights with the feature vector.\n",
    "\n",
    "![The perceptron](https://raw.githubusercontent.com/Claudiooo/DeepLearningLearning/Group2/Images/perceptron_schematic_overview.png)\n",
    "\n",
    "### Implementation\n",
    "\n",
    "The purpose of this example is to find if a point is above or below a defined line with an affine function. This algorithm uses the **gradient descent** algorithm associated with a perceptron to learn how to classify the data. See *[Linear Regression](https://plot.ly/~nicolasconstanty/10)* for more informations about **gradient descent**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we can define or [activation function](https://www.wikiwand.com/en/Activation_function), the purpose to this function is to \"activate\" or not a neuron. In this case, we just active if the number is greater than 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def activationFunc(number):\n",
    "    return 1 if number > 0 else -1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the perceptron class, we want to send the input size and the [learning rate](https://www.wikiwand.com/en/Learning_curve) (In machine learning section) at the instanciation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Perceptron:\n",
    "    def __init__(self, size, learning_rate, activ_func):\n",
    "        self.size = size\n",
    "        self.weights = []\n",
    "        self.lr = learning_rate\n",
    "        self.activ_func = activ_func\n",
    "        self.initialize_weigth()\n",
    "        \n",
    "    def initialize_weigth(self):\n",
    "        for i in range(self.size):\n",
    "            self.weights.append(random.uniform(-1.0, 1.0))\n",
    "    \n",
    "    #This is our guess function using weighted sum of input\n",
    "    def guess(self, inputs):\n",
    "        sum = 0\n",
    "        for i in range(len(self.weights)):\n",
    "            sum += inputs[i] * self.weights[i]\n",
    "        return self.activ_func(sum)\n",
    "    \n",
    "    #This is the train function, witch is update the perceptron weight by calculating the error with target - guess\n",
    "    #This is the application of linear regression with a custom learning rate\n",
    "    def train(self, inputs, target):\n",
    "        value = self.guess(inputs)\n",
    "        error = target - value\n",
    "        for i in range(len(self.weights)):\n",
    "            self.weights[i] += error * inputs[i] * self.lr\n",
    "            \n",
    "    def valid(self, inputs, target):\n",
    "        value = self.guess(inputs)\n",
    "        error = target - value\n",
    "        return (error == 0)\n",
    "    \n",
    "    def getY(self, x):\n",
    "        m = - self.weights[0] / self.weights[1]\n",
    "        b = - self.weights[2] / self.weights[1]\n",
    "        return m * x + b\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the point class, we initialize a point with random position between -1 and 1, we feed also a label function in order to calculate the error during the training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Point:\n",
    "    def __init__(self, func):\n",
    "        self.x = random.uniform(-1.0, 1.0)\n",
    "        self.y = random.uniform(-1.0, 1.0)\n",
    "        #Point is above the line\n",
    "        if (self.y > func(self.x)):\n",
    "            self.label = 1\n",
    "        #Point is below the line\n",
    "        else:\n",
    "            self.label = -1\n",
    "        #Bias is needed to avoid to get stuck on zero in the weight computation\n",
    "        self.bias = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "#Global counter\n",
    "total_iteration = 0\n",
    "\n",
    "#Create bunch of point\n",
    "def initialise_data(size, function):\n",
    "    data = []\n",
    "    for i in range(size):\n",
    "        data.append(Point(function))\n",
    "    return data\n",
    "\n",
    "#Create run function\n",
    "def run(data, number_iteration, learning_rate):\n",
    "    return run_trained(data, number_iteration, Perceptron(3, learning_rate, activationFunc))\n",
    "\n",
    "#Create trainer functin\n",
    "def run_trained(data, number_iteration, perceptron):\n",
    "    global total_iteration\n",
    "    total_iteration += number_iteration\n",
    "    print(\"Training start for {0} iteration{1}...\".format(number_iteration, 's' if number_iteration > 1 else ''))\n",
    "    for i in range(number_iteration):\n",
    "        for point in data:\n",
    "            inputs = [point.x, point.y, point.bias]\n",
    "            #Call perceptron.train with current point data as input\n",
    "            perceptron.train(inputs, point.label)\n",
    "    print(\"After {0} iterations\".format(total_iteration))\n",
    "    return perceptron\n",
    "\n",
    "#Calculate the success percentage of a perceptron\n",
    "def calculate_success_percentage(data, perceptron):\n",
    "    trues = 0\n",
    "    for point in data:\n",
    "        inputs = [point.x, point.y, point.bias]\n",
    "        if (point.label - perceptron.guess(inputs) == 0):\n",
    "            trues += 1\n",
    "    return trues / float(len(data))\n",
    "\n",
    "#Print the success percentage\n",
    "def print_success_percentage(number):\n",
    "    print(\"Success : {0} %\".format(number))    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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     "name": "stdout",
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     "text": [
      "2.2.1\n"
     ]
    }
   ],
   "source": [
    "from plotly import __version__\n",
    "from plotly.offline import download_plotlyjs, init_notebook_mode, plot, iplot\n",
    "\n",
    "init_notebook_mode(connected=True)\n",
    "\n",
    "import plotly.plotly as py\n",
    "import plotly.graph_objs as go\n",
    "import plotly.figure_factory as FF\n",
    "\n",
    "print (__version__) # requires version >= 1.9.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def display_current_state(data, perceptron, func):\n",
    "    px = []\n",
    "    py = []\n",
    "    colors = []\n",
    "    for i in range (0, len(data)):\n",
    "        px.append(data[i].x)\n",
    "        py.append(data[i].y)\n",
    "        colors.append('rgba(76, 175, 80, 0.95)' if perceptron.valid([data[i].x, data[i].y, data[i].bias], data[i].label) else 'rgba(244, 67, 54, 0.95)')\n",
    "    #Define dot traces\n",
    "    trace = go.Scatter(\n",
    "        x = px, y = py,\n",
    "        name= 'Points',\n",
    "        mode='markers',\n",
    "        marker=dict(\n",
    "            color=colors,\n",
    "            line=dict(\n",
    "                color='rgba(0, 0, 0, 1.0)',\n",
    "                width=1,\n",
    "            ),\n",
    "                symbol='circle',\n",
    "                size=10,\n",
    "            )\n",
    "        )\n",
    "    xTab = [-1, 1]\n",
    "    #Y = M * X + B\n",
    "    yTab = [func(-1), func(1)]\n",
    "\n",
    "    #Define best fit trace\n",
    "    trace1 = go.Scatter(\n",
    "        x = xTab,\n",
    "        y = yTab,\n",
    "        name = 'Best fit',\n",
    "        line = dict(\n",
    "            width = 2,\n",
    "            color = 'rgb(69, 32, 39)'\n",
    "        )\n",
    "    )\n",
    "    \n",
    "    xTab1 = [-1, 1]\n",
    "    #Y = M * X + B\n",
    "    yTab1 = [perceptron.getY(xTab1[0]), perceptron.getY(xTab1[1])]\n",
    "    #Define best fit trace\n",
    "    trace2 = go.Scatter(\n",
    "        x = xTab1,\n",
    "        y = yTab1,\n",
    "        name = 'Best fit predicted',\n",
    "        line = dict(\n",
    "            color = 'rgb(103, 58, 183)'\n",
    "        )\n",
    "    )\n",
    "\n",
    "    #Define the layout\n",
    "    layout = go.Layout(\n",
    "        title='Random points and current best fit',\n",
    "        plot_bgcolor='rgb(230, 230,230)',\n",
    "        showlegend=True,\n",
    "        xaxis=dict(range=[-1, 1]),\n",
    "        yaxis=dict(range=[-1, 1])\n",
    "    )\n",
    "    \n",
    "\n",
    "    #Draw the final graph\n",
    "    fig = go.Figure(data=[trace, trace1, trace2], layout=layout)\n",
    "    iplot(fig, filename='dot_Jan')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training start for 1 iteration...\n",
      "After 1 iterations\n",
      "Success : 60.199999999999996 %\n"
     ]
    },
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    {
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     "text": [
      "Training start for 5 iterations...\n",
      "After 6 iterations\n",
      "Success : 99.8 %\n"
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    {
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     "text": [
      "Training start for 5 iterations...\n",
      "After 11 iterations\n",
      "Success : 100.0 %\n"
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points and current best fit\", \"showlegend\": true, \"yaxis\": {\"range\": [-1, 1]}}, {\"showLink\": true, \"linkText\": \"Export to plot.ly\"})});</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "if __name__ == \"__main__\":\n",
    "    # y = mx + b\n",
    "    func = lambda x : 1.5 * x + 0.74\n",
    "    size = 1000\n",
    "    data = initialise_data(size, func)\n",
    "    p = run(data, 1, 0.001)\n",
    "    percent = calculate_success_percentage(data, p) * 100\n",
    "    print_success_percentage(percent)\n",
    "    display_current_state(data, p, func)\n",
    "    while percent != 100:\n",
    "        p = run_trained(data, 5, p)\n",
    "        percent = calculate_success_percentage(data, p) * 100\n",
    "        print_success_percentage(percent)\n",
    "        display_current_state(data, p, func)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Links\n",
    "\n",
    "#### Youtube\n",
    " * [Siraj Raval - How to Make a Neural Network - Intro to Deep Learning #2](https://www.youtube.com/watch?v=p69khggr1Jo&index=3&list=PL2-dafEMk2A7YdKv4XfKpfbTH5z6rEEj3)\n",
    " * [The Coding Train - 10.2: Neural Networks: Perceptron Part 1](https://www.youtube.com/watch?v=ntKn5TPHHAk&list=PLRqwX-V7Uu6aCibgK1PTWWu9by6XFdCfh&index=2)\n",
    " * [The Coding Train - 10.3: Neural Networks: Perceptron Part 2](https://www.youtube.com/watch?v=DGxIcDjPzac&index=3&list=PLRqwX-V7Uu6aCibgK1PTWWu9by6XFdCfh)\n",
    " \n",
    "#### Web\n",
    " * [Wikipedia - Perceptron](https://www.wikiwand.com/fr/Perceptron)\n",
    " * [ataspinar - The perceptron](http://ataspinar.com/2016/12/22/the-perceptron/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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