dm_lab_2_fm.ipynb

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    "colab": {
      "name": "dm_lab-2_fm.ipynb",
      "provenance": [],
      "include_colab_link": true
    }
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
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      "source": [
        "<a href=\"https://colab.research.google.com/github/foxtrotmike/CS909/blob/master/dm_lab_2_fm.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H5YY8bbnZI9T"
      },
      "source": [
        "# Exercise-2\n",
        "## by Fayyaz Minhas\n",
        "## Gradient Descent and Perceptron\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "U1YPXeG3ZI9X"
      },
      "source": [
        "# Understanding gradient Descent\n",
        "\n",
        "We discussed how gradient descent works for solving optimization problems: By taking steps in a direction opposite to the gradient. Below is a very simple implementation for this method. Based on this, can you:\n",
        "1. Try to understand how Gradient Descent Works\n",
        "2. Can you find the  minima of the following function: $f(v)=2v^2-v$. You will need to update the implementation of the function and its derivative in the code for this.\n",
        "3. What happens when you use: $f(v)=sin(3v)$? Is this function convex?\n",
        "4. What do you think are the limitations of gradient descent for non-convex functions?\n",
        "5. What happens when you change the learning rate parameter (step size)?\n",
        "You can also look into questions posted as part of the self assessment exercise.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6vNkYFhYZI9Y",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "outputId": "f9fba5b3-52ca-4c74-a6f4-c86b63b152eb"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "def gd(f,df,v0=0.0,lr = 0.01,eps=1e-4,nmax=1000, history = True):\n",
        "    \"\"\"\n",
        "    Gradient descent optimization algorithm.\n",
        "\n",
        "    Parameters:\n",
        "    f (callable): The objective function to be minimized.\n",
        "                  It should take a single argument and return a scalar value.\n",
        "    df (callable): The gradient of the objective function.\n",
        "                   It should take a single argument and return the gradient as a scalar or numpy array.\n",
        "    v0 (float or numpy.ndarray): Initial starting point for the gradient descent algorithm.\n",
        "                                 Default is 0.0. Can be a scalar or numpy array for multi-dimensional inputs.\n",
        "    lr (float): Learning rate, determining the step size at each iteration. Default is 0.01.\n",
        "    eps (float): Convergence criterion. The algorithm stops if the step size is smaller than eps. Default is 1e-4.\n",
        "    nmax (int): Maximum number of iterations. Default is 1000.\n",
        "    history (bool): If True, the function returns the history of optimization steps. Default is True.\n",
        "\n",
        "    Returns:\n",
        "    tuple: Contains the optimal value, a boolean indicating convergence, and the history of iterations.\n",
        "           The history is returned as a tuple of numpy arrays representing the variable values and function values.\n",
        "    \"\"\"\n",
        "    Hv,Hf = [],[]\n",
        "    v = v0\n",
        "    if history:\n",
        "        Hv.append(v)\n",
        "        Hf.append(f(v))\n",
        "    for i in range(nmax):\n",
        "        dv = -lr*df(v) #gradient step\n",
        "\n",
        "        if history:\n",
        "            Hv.append(v)\n",
        "            Hf.append(f(v))\n",
        "        if np.linalg.norm(dv)<eps: # if the step taken is too small, we have converged\n",
        "            break\n",
        "        #import pdb; pdb.set_trace()\n",
        "        v = v+dv #gradient update\n",
        "    converged = np.linalg.norm(dv)<eps\n",
        "    return v,converged,(np.array(Hv),np.array(Hf))\n",
        "\n",
        "def plotGD(H,c):\n",
        "    \"\"\"\n",
        "    Plot the optimization steps of the gradient descent algorithm.\n",
        "\n",
        "    Parameters:\n",
        "    H (tuple of numpy.ndarray): History of iterations as returned by the gd function.\n",
        "                                It contains variable values and function values at each step.\n",
        "    c (bool): Convergence status as returned by the gd function.\n",
        "\n",
        "\n",
        "    This function generates a plot of the optimization steps.\n",
        "    \"\"\"\n",
        "    plt.figure()\n",
        "    Hv,Hf = H\n",
        "    if Hv.ndim == 1:\n",
        "        Hv = np.atleast_2d(Hv).T\n",
        "\n",
        "    plt.plot(Hf);plt.plot(Hv)\n",
        "    plt.xlabel('iterations');plt.legend(['Objective function']+['$V_'+str(i)+'$' for i in range(Hv.shape[1])])\n",
        "    str_title = 'Convergence in '+str(len(Hf))+' iterations.'\n",
        "    if not c: str_title = 'No '+str_title\n",
        "    plt.title(str_title)\n",
        "if __name__=='__main__':\n",
        "\n",
        "    #%% Single input variable\n",
        "\n",
        "\n",
        "    # Define the function f which is the objective function to be minimized.\n",
        "    # In this case, f is a simple quadratic function.\n",
        "    def f(v):\n",
        "        return v**2\n",
        "\n",
        "    # Define the derivative of the function f, denoted as df.\n",
        "    # This is required for the gradient descent algorithm to determine the direction of the steepest descent.\n",
        "    def df(v):\n",
        "        return 2*v\n",
        "\n",
        "    # Generate an array of values from -3 to 3, divided into 1000 intervals.\n",
        "    # This array represents the range of values over which we want to optimize the function.\n",
        "    v = np.linspace(-3, 3, 1000)\n",
        "\n",
        "    # Select a random initial point within the range of v for the gradient descent to start.\n",
        "    # This adds some randomness to the starting point of the optimization.\n",
        "    v0 = np.min(v) + (np.max(v) - np.min(v)) * np.random.rand()\n",
        "\n",
        "    # Call the gradient descent function 'gd' with the function f, its derivative df, and other parameters.\n",
        "    # v0: initial point, lr: learning rate, eps: convergence criterion, nmax: max iterations, history: store optimization steps.\n",
        "    vout, c, H = gd(f, df, v0=v0, lr=0.01, eps=1e-4, nmax=1000, history=True)\n",
        "\n",
        "    # Plot the gradient descent progress using the 'plotGD' function.\n",
        "    # It visualizes the optimization steps and the convergence of the algorithm.\n",
        "    plotGD(H, c)\n",
        "\n"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Optimize a two variable function using gradient descent\n",
        "\n",
        "See how this code solves the optimization problem for a two variable function. Check if the solution is actually valid by comparing it to the analytical solution."
      ],
      "metadata": {
        "id": "Y_hp_FQlHXuk"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "    #%% Two variable function\n",
        "    # Section for handling a two-variable optimization function\n",
        "\n",
        "    # Define a two-variable objective function 'f'.\n",
        "    # Here, 'f' is a simple quadratic function in two variables.\n",
        "    def f(v):\n",
        "        # v is expected to be a vector (or list) of two elements.\n",
        "        return np.array(v[0]**2 + (v[1]-1)**2)\n",
        "\n",
        "    # Define the gradient 'df' of the objective function 'f'.\n",
        "    # The gradient function returns a vector of partial derivatives.\n",
        "    def df(v):\n",
        "        # Returns the gradient of 'f' as a numpy array.\n",
        "        return np.array([2*v[0], 2*(v[1]-1)])\n",
        "\n",
        "    # Create a range of values for testing or visualization purposes.\n",
        "    # This is not directly used in the gradient descent for this 2-variable function.\n",
        "    v = np.linspace(-3, 3, 1000)\n",
        "\n",
        "    # Select a random initial point in 2D space for the gradient descent to start.\n",
        "    # This initial point is set to [-1.0, -1.0] in this case, but can be randomized or modified.\n",
        "    v0 = np.array([-1.0, -1.0])\n",
        "\n",
        "    # Perform the gradient descent optimization using the two-variable function 'f' and its gradient 'df'.\n",
        "    # The optimization will start from 'v0' and use the specified learning rate 'lr', convergence criterion 'eps',\n",
        "    # maximum number of iterations 'nmax', and it will store the history of optimization if 'history' is True.\n",
        "    vout, c, H = gd(f, df, v0=v0, lr=0.01, eps=1e-4, nmax=1000, history=True)\n",
        "\n",
        "    # Plot the gradient descent progress for the two-variable function.\n",
        "    # This visualizes how the optimization algorithm progresses over iterations.\n",
        "    plotGD(H, c)\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "fnrH5YQbHWxP",
        "outputId": "d3291b18-1c0d-4931-cb74-00eaf08df6f8"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "  ## Implementation of a very simple perceptron using the gradient descent function\n",
        "\n",
        "  Now we will use the gradient descent function to implement a very simple perceptron. Let's assume we have a single feature and only two examples (one positive and one negative).\n",
        "\n",
        "  1. Look at the two examples and their labels in the code below and manually calculate the value of w which would enable correct classification for this example.\n",
        "\n",
        "  2. Check the implementation of the loss function and its derivatives as we will be using this as input to the gradient descent solver. Make sure that you understand how this code is solving the following optimization problem.\n",
        "\n",
        "  $$ min_w \\frac{1}{N}\\sum_{i=1}^N loss(y_i, f(x_i;w))$$\n",
        "\n",
        "  where $$f(x_i;w)=w^Tx_i$$ is the prediction function (not to be confused with $f$ in the above gd(f,df...)  function).\n",
        "\n",
        "  3. Check if the weight values returned by the gd function is indeed correct.\n",
        "  "
      ],
      "metadata": {
        "id": "gQv92z8SYPsf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "    #%% Implementation of a very simple perceptron using the gradient descent function\n",
        "\n",
        "    # Implementation of a simple perceptron using the gradient descent function\n",
        "\n",
        "    # X: Feature data, a 2D numpy array where each row represents a data point, and each column a feature.\n",
        "    # In this case, two data points with two features each.\n",
        "    X = np.array([[1, 3], [1, 5]])\n",
        "\n",
        "    # Y: Labels for the data points. Here, two labels (1 and -1).\n",
        "    Y = np.array([1, -1])\n",
        "\n",
        "    # Define the hinge loss function for a given data point (x, y) and weights w.\n",
        "    # Hinge loss is max(0, 1 - y * (w @ x)).\n",
        "    # Mathematically, L(y, w @ x) = max(0, 1 - y * (w @ x)).\n",
        "    def loss(y, x, w):\n",
        "        return max(0.0, 1 - y * (w @ x))\n",
        "\n",
        "    # Define the average loss across all data points for given weights w.\n",
        "    # This is the objective function to be minimized in gradient descent.\n",
        "    # Mathematically, L(w) = 1/N * Σ max(0, 1 - Yi * (w @ Xi)).\n",
        "    def loss_w(w):\n",
        "        return np.mean([loss(Y[i], X[i], w) for i in range(len(Y))])\n",
        "\n",
        "    # Define the derivative of the hinge loss function with respect to weights w for a given (x, y).\n",
        "    # The gradient is -y * x if 1 - y * (w @ x) > 0, else 0.\n",
        "    # Mathematically, dL(y, w @ x)/dw = -y * x if 1 - y * (w @ x) > 0, else 0.\n",
        "    def dloss(y, x, w):\n",
        "        if (1 - y * (w @ x)) < 0:\n",
        "            return np.zeros(x.shape)\n",
        "        else:\n",
        "            return -y * x\n",
        "\n",
        "    # Define the average gradient of the loss function across all data points for weights w.\n",
        "    # This function is used in gradient descent to update weights.\n",
        "    # Mathematically, dL(w)/dw = 1/N * Σ dL(Yi, w @ Xi)/dw.\n",
        "    def dloss_w(w):\n",
        "        return np.mean([dloss(Y[i], X[i], w) for i in range(len(Y))], axis=0)\n",
        "\n",
        "    # Assign the loss function and its derivative to variables for convenience.\n",
        "    f = loss_w\n",
        "    df = dloss_w\n",
        "\n",
        "    # Initialize weights (w) randomly. Here, w is a 2-element vector for two features.\n",
        "    v0 = 0.1 * np.random.randn(X.shape[1])\n",
        "\n",
        "    # Apply gradient descent to minimize the loss function and find the optimal weights.\n",
        "    vout, c, H = gd(f, df, v0=v0, lr=0.02, eps=1e-4, nmax=10000, history=True)\n",
        "\n",
        "    # Plot the optimization process for each weight separately.\n",
        "    # First plot is for the bias term, and the second plot is for the weight associated with the feature.\n",
        "    plotGD(H, c)\n",
        "\n"
      ],
      "metadata": {
        "id": "EchXT34SYJ3i",
        "outputId": "1514b33d-e8ba-4c51-98c1-9a5815e5550f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        }
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xeDlmiHrPRkI"
      },
      "source": [
        "## Importing plotit\n",
        "\n",
        "To use the code in the following exercises you will need to execute the cell below\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pWhbEdVpPQDk"
      },
      "source": [
        "from numpy.random import randn #importing randn\n",
        "import numpy as np #importing numpy\n",
        "import matplotlib.pyplot as plt #importing plotting module\n",
        "import itertools\n",
        "import warnings\n",
        "\n",
        "def plotit(X,Y=None,clf=None,  conts = None, ccolors = ('b','k','r'), colors = ('c','y'), markers = ('s','o'), hold = False, transform = None,extent = None,**kwargs):\n",
        "    \"\"\"\n",
        "    A function for showing data scatter plot and classification boundary\n",
        "    of a classifier for 2D data\n",
        "        X: nxd  matrix of data points\n",
        "        Y: (optional) n vector of class labels\n",
        "        clf: (optional) classification/discriminant function handle\n",
        "        conts: (optional) contours (if None, contours are drawn for each class boundary)\n",
        "        ccolors: (optional) colors for contours\n",
        "        colors: (optional) colors for each class (sorted wrt class id)\n",
        "            can be 'scaled' or 'random' or a list/tuple of color ids\n",
        "        markers: (optional) markers for each class (sorted wrt class id)\n",
        "        hold: Whether to hold the plot or not for overlay (default: False).\n",
        "        transform: (optional) a function handle for transforming data before passing to clf\n",
        "        kwargs: any keyword arguments to be passed to clf (if any)\n",
        "    \"\"\"\n",
        "    if clf is not None and X.shape[1]!=2:\n",
        "        warnings.warn(\"Data Dimensionality is not 2. Unable to plot.\")\n",
        "        return\n",
        "    if markers is None:\n",
        "        markers = ('.',)\n",
        "    eps=1e-6\n",
        "    d0,d1 = (0,1)\n",
        "    if extent is None:\n",
        "        minx, maxx = np.min(X[:,d0])-eps, np.max(X[:,d0])+eps\n",
        "        miny, maxy = np.min(X[:,d1])-eps, np.max(X[:,d1])+eps\n",
        "        extent = [minx,maxx,miny,maxy]\n",
        "    else:\n",
        "        [minx,maxx,miny,maxy] = extent\n",
        "    if Y is not None:\n",
        "        classes = sorted(set(Y))\n",
        "        if conts is None or len(conts)<2:\n",
        "            #conts = list(classes)\n",
        "            vmin,vmax = classes[0]-eps,classes[-1]+eps\n",
        "        else:\n",
        "            vmin,vmax= np.min(conts)-eps,np.max(conts)+eps\n",
        "\n",
        "    else:\n",
        "        vmin,vmax=-2-eps,2+eps\n",
        "        if conts is None or len(conts)<2:\n",
        "            conts = sorted([-1+eps,0,1-eps])\n",
        "        else:\n",
        "            vmin,vmax= np.min(conts)-eps,np.max(conts)+eps\n",
        "\n",
        "    if clf is not None:\n",
        "        npts = 150\n",
        "        x = np.linspace(minx,maxx,npts)\n",
        "        y = np.linspace(miny,maxy,npts)\n",
        "        t = np.array(list(itertools.product(x,y)))\n",
        "        if transform is not None:\n",
        "            t = transform(t)\n",
        "        z = clf(t,**kwargs)\n",
        "\n",
        "        z = np.reshape(z,(npts,npts)).T\n",
        "\n",
        "\n",
        "        plt.contour(x,y,z,conts,linewidths = [2],colors=ccolors,extent=extent, label='f(x)=0')\n",
        "        #plt.imshow(np.flipud(z), extent = extent, cmap=plt.cm.Purples, vmin = -2, vmax = +2); plt.colorbar()\n",
        "        plt.pcolormesh(x, y, z,cmap=plt.cm.Purples,vmin=vmin,vmax=vmax);plt.colorbar()\n",
        "        plt.axis(extent)\n",
        "\n",
        "    if Y is not None:\n",
        "        for i,y in enumerate(classes):\n",
        "\n",
        "            if colors is None or colors=='scaled':\n",
        "                cc = np.array([[i,i,i]])/float(len(classes))\n",
        "            elif colors =='random':\n",
        "                cc = np.array([[np.random.rand(),np.random.rand(),np.random.rand()]])\n",
        "            else:\n",
        "                cc = colors[i%len(colors)]\n",
        "\n",
        "            mm = markers[i%len(markers)]\n",
        "            plt.scatter(X[Y==y,d0],X[Y==y,d1], marker = mm,c = cc, s = 50)\n",
        "\n",
        "    else:\n",
        "        plt.scatter(X[:,d0],X[:,d1],marker = markers[0], c = 'k', s = 5)\n",
        "    plt.xlabel('$x_1$')\n",
        "    plt.ylabel('$x_2$')\n",
        "    if not hold:\n",
        "        plt.grid()\n",
        "        plt.show()\n",
        "    return extent"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Implementation of Perceptron\n",
        "\n",
        "Below is an implementation of a perceptron which will be discussed in class. It allows you to track the learning in each iteration and its effect on the decision boundary (if you set save_gif = True). See if you can figure out how the gradient descent based code gets mapped to this implementation."
      ],
      "metadata": {
        "id": "PWsQ1qc4bH45"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import imageio.v2 as imageio\n",
        "import os\n",
        "\n",
        "class Perceptron:\n",
        "    def __init__(self,alpha = 0.1, epochs = 200,save_gif = False):\n",
        "        self.alpha = alpha\n",
        "        self.epochs = epochs\n",
        "        self.W = np.array([0])\n",
        "        self.bias = np.random.randn()*0\n",
        "\n",
        "        self.save_gif = save_gif\n",
        "    def fit(self,Xtr,Ytr):\n",
        "        d = Xtr.shape[1]\n",
        "        self.W = np.random.randn(d)   #always start at zero or a random weight vectir\n",
        "\n",
        "        if self.save_gif:\n",
        "            plt.figure()\n",
        "            extent = [-1,+2,-1,+2]\n",
        "            plotit(Xtr,ytr,clf=self.score,conts=[0],extent = extent)\n",
        "            plt.title('epoch = '+str(0)+': w = '+(', '.join([f'{num:.3f}' for num in self.W]))+' b = '+f'{self.bias:.3f}')\n",
        "            ii = 0; filenames = [str(ii)+'.jpg']; plt.savefig(filenames[-1]); plt.close()\n",
        "\n",
        "        for e in range(self.epochs):\n",
        "            finished = True\n",
        "            for i,x in enumerate(Xtr):\n",
        "\n",
        "                if Ytr[i]*self.predict(np.atleast_2d(x))<1: #if error, use 1 on the RHS instead of 0 to implement hinge loss\n",
        "                    finished = False\n",
        "                    self.W += self.alpha*Ytr[i]*x\n",
        "                    self.bias += self.alpha*Ytr[i]\n",
        "                if self.save_gif:\n",
        "                    plt.figure()\n",
        "                    plotit(Xtr,ytr,clf=self.score,conts=[0],extent = extent)\n",
        "                    plt.plot(x[0],x[1],'r*')\n",
        "                    plt.title('epoch = '+str(e)+': w = '+(', '.join([f'{num:.3f}' for num in self.W]))+' b = '+f'{self.bias:.3f}')\n",
        "                    ii +=1; filenames.append(str(ii)+'.jpg'); plt.savefig(filenames[-1]); plt.close()\n",
        "            if finished: break\n",
        "        \"\"\"\n",
        "        #useful for l onger iterations\n",
        "        with imageio.get_writer('my_plots.gif', mode='I') as writer:\n",
        "            for filename in filenames:\n",
        "                image = imageio.imread(filename)\n",
        "                os.remove(filename)\n",
        "                writer.append_data(image,duration = 0.3)\n",
        "        \"\"\"\n",
        "        if self.save_gif:\n",
        "            imageio.mimsave('my_animation.gif', [imageio.imread(f) for f in filenames], duration=0.5)\n",
        "            for f in filenames: os.remove(f)\n",
        "\n",
        "    def score(self,x):\n",
        "        return np.dot(x,self.W) + self.bias\n",
        "\n",
        "    def predict(self,x):\n",
        "        return np.sign(self.score(x))\n",
        "\n",
        "if __name__=='__main__':\n",
        "    Xtr = np.array([[0,0],[0,1],[1,0],[1,1]])\n",
        "    ytr = np.array([-1,-1,-1,+1])\n",
        "    clf = Perceptron(alpha = 0.1)\n",
        "    clf.fit(Xtr,ytr)\n",
        "    z = clf.score(Xtr)\n",
        "    print(\"Prediction Scores:\",z)\n",
        "    y = clf.predict(Xtr)\n",
        "    print(\"Prediction Labels:\",y)\n",
        "    plotit(Xtr,ytr,clf=clf.score,conts=[0],\textent = [-1,+2,-1,+2])"
      ],
      "metadata": {
        "id": "GmNox4PLasmf",
        "outputId": "6581f329-d390-489c-d696-51cb806dacce",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 524
        }
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Prediction Scores: [-0.5        -0.455806   -0.01443895  0.02975505]\n",
            "Prediction Labels: [-1. -1. -1.  1.]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-13-6fddf3f24066>:63: UserWarning: The following kwargs were not used by contour: 'label'\n",
            "  plt.contour(x,y,z,conts,linewidths = [2],colors=ccolors,extent=extent, label='f(x)=0')\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RpKV63D0ZI9e"
      },
      "source": [
        "## Trying out Perceptron in sk-learn!\n",
        "\n",
        "Let's try a single Perceptron on the same toy problem. More help on using Perceptron in sk-learn is available [here](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.Perceptron.html). Here are some questions for you:\n",
        "\n",
        "1. What are your observations about the line that is drawn by this predictor?\n",
        "2. What happens to the line if you change the data?\n",
        "3. Is this line optimal?\n",
        "4. Can you predict the score and class label for a new test point, say [2,0]? Is this point classified correctly?\n",
        "5. You can use clf.coef_ and clf.intercept_ to get the weight vector and bias learned by the method. What do these weights and their signs tell you about your data?\n",
        "6. Try changing the data and observe how that impacts the weight vector. Solve the AND, OR and XOR problems.\n",
        "7. What happens when your data is not linearly separable?\n",
        "\n",
        "You can also look into questions posted as part of the self assessment exercise related to this.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "b1eqqLKMZI9e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 524
        },
        "outputId": "486e6120-8dfa-420e-e18b-595ea81e95cb"
      },
      "source": [
        "from sklearn.linear_model import Perceptron\n",
        "clf = Perceptron()\n",
        "X = np.array([[-1,0],[0,1],[4,4],[2,3]])\n",
        "y = np.array([-1,-1,+1,+1])\n",
        "clf.fit(X,y)\n",
        "plotit(X,y,clf=clf.decision_function,conts=[0.0])\n",
        "print(\"Learned Weights: \",clf.coef_)\n",
        "print(\"Bias: \",clf.intercept_)"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-13-6fddf3f24066>:63: UserWarning: The following kwargs were not used by contour: 'label'\n",
            "  plt.contour(x,y,z,conts,linewidths = [2],colors=ccolors,extent=extent, label='f(x)=0')\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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yjBs3DoMGDcL169exatUqfPfdd5gzZ44nT4OIiMhtnvihyaysLMycORNjxozB2LFjsXbtWtTW1lqfbrr5Ptxk48aNSE1NdZjUW1NTg6VLl+LRRx9FeHg4zp8/jwULFmDQoEFITk5269xa49Fk5sqVK0hLS8Ply5fRrVs3REVFYffu3fj5z38OAKioqIBK1q//008/ISMjAzqdDj169EBsbCwOHDjQ4oRhIiIiatm0adPwww8/YPHixdDpdBg1ahQKCwutk4Jvvg8DwNmzZ/Hll19iz549Du2p1Wp8/fXXeP/993H9+nVERERg0qRJWL58ead+14xHk5mbZ0DfrKSkxO79mjVrsGbNmk6MiIiIyDMsTzO52zPj/D6ZmZnIzMxsdt3N92HA8uCOuYW5REFBQdbRlVvJ4xOAiYiICBBUlpdbbXjnfGW3KW4CMBEREZEz2DNDRESkBB74OYPbBZMZIiIiBWAu4zomM0RERAogqG79r2bfLjhnhoiIiLwae2aIiIiUgONMLmMyQ0REpADMZVzHYSYiIiLyauyZISIiUoIOmAAMH50AzGSGiIhIETpgnAm+mcxwmImIiIi8GntmiIiIFIATgF3HZIaIiEgBOuRL89ydc+OlOMxEREREXo09M0REREogwP35u77ZMcNkhoiISAkEQYDg5qQXd/f3VkxmiIiIFIBzZlzHOTNERETk1dgzQ0REpAB8NNt1TGaIiIiUgNmMyzjMRERERF6NPTNEREQKwAnArmMyQ0REpAAcZXIdh5mIiIjIq7FnhoiISAnYNeMyJjNEREQKwG8Adh2HmYiIiMirsWeGiIhIAQSV5eVuG76IyQwREZEScM6My5jMEBERKYCADshlOiQS7+OjHVJERER0u2DPDBERkQLwG4Bdx2SGiLyCOsBkW9azU5luQ5wz4zImM0SkaH1HVGDcYwcxJOEiamq34A8fr8HZA5Eo3R6PiycjPR0eESmAR/9588477yAqKgparRZarRbx8fH417/+1eo+27dvx9ChQ6HRaDBy5Eh89tlntyhaIrrVxvziKNLffh9DEr6BSm0GAKjUZgxJ+AZPvL0ZYx4q83CERB2nqWPG3Zez8vLy0L9/f2g0GsTFxeHw4cMtbrt582brl/s1vTQajd02ZrMZixcvRu/evREUFISkpCR88803zgfmBI8mM3369MGrr76KsrIyHD16FBMnTsTDDz+MU6dONbv9gQMH8Pjjj2P27Nk4fvw4UlNTkZqaipMnT97iyImos/UdUYGp8/8FQQDUfpLdOrWfBEEApj73GSJHXPRQhEQdq2nOjLsvZ2zbtg1ZWVnIycnBsWPHEB0djeTkZFy5cqXFfbRaLS5fvmx9fffdd3brX3/9dbz99tvIz8/HoUOHcMcddyA5ORkNDQ0uXZf28Ggy89BDD2HKlCkYPHgwfvazn+GVV15Bly5dcPDgwWa3f+utt5CSkoIXXngBw4YNw/LlyxETE4P169ff4siJqLONe+wgJLH1jyhJVCH+V81/XhBR2958801kZGQgPT0dw4cPR35+PoKDg1FQUNDiPoIgIDw83PoKCwuzrjObzVi7di1eeuklPPzww4iKisIHH3yA77//Hjt37uy081DMnBlRFLF9+3bU1tYiPj6+2W1KS0uRlZVlV5ecnNzmBdLr9dDr9db31dXVAACTyQSj0ehe4D7GZDLZLZXGbDZby5Jo+9e8SbTUiyZZnawsiqLd0lK2rJck27lKkuhQNpttdfIyIN20tMUmCBIEwVKvUtnq7cqNwypqta1FtexvrNrfsvTzlx0xwPavMimwsSza6syy5KCpLJhtdaJCPhHUASYMSbgIlToQTf9LzeYguyUAqNTAkPsqENRNgmhQSPAK5B+ksluSEzQC0HkdCvY6cAJw032uSWBgIAIDA+3qDAYDysrKkJ2dba1TqVRISkpCaWlpi4eoqalBv379IEkSYmJisHLlStxzzz0AgAsXLkCn0yEpKcm6fbdu3RAXF4fS0lJMnz7dvfNrgcf/9p84cQLx8fFoaGhAly5dsGPHDgwfPrzZbXU6nV0GCABhYWHQ6XStHiM3NxdLly51qN+3vwTBwcGuB+/Divd+7ukQFM8/0H6pUo20LNUSeoZfdaIl+YdbQAvl209N7ZZm62/ccPwX45Pvd3Y0t4e5BdGeDsHr1NXVoeg3t+ZYHfkwU2Sk/eT4nJwcLFmyxK7u6tWrEEWx2fvqmTNnmm1/yJAhKCgoQFRUFKqqqrB69WokJCTg1KlT6NOnj/V+7Mq92h0eT2aGDBmC8vJyVFVV4eOPP8bMmTOxb9++FhMaV2RnZ9v16FRXVyMyMhLjH5iAkJCQDjuOLzCZTCje+zkSJybBz8/jf3wcONMzY5SXjZYeFYNRlNVZ1uv1tp4Zvd62vr7BUq9vsPXuNcjK+npLuaFxKUmqxrhUuKrrifqGxmM20yYAGBr3M9YYbHV1tvYNNfrG9UaHfQDAUGspm+T71Jkc18v2EY32c1M8RR1gwh8+XmPtnQIsPTI3bhSga9cnIAj11npJFLD6V8+xZ6YV/kEqzC2IxrtPfAVjvTL+H3sNjaHtbRTo4sWL0Gq11vc398q4Kj4+3m70JCEhAcOGDcOGDRuwfPnyDjmGKzz+tz8gIACDBg0CAMTGxuLIkSN46623sGHDBodtw8PDUVlZaVdXWVmJ8PDwVo/RXPcaAPj5+cHf37+ZPagtSr128mRGFGQf2o1lAbY6s6wsSZZ/zqgl2TCN1DQMZGvGvmw5liA7jrwMNCUpTTvJhnvMKmusTceRxwFYbtIAIBv5gigb3RMbcxCTbKTUZLCdv0lvKRv1tjpjg+RQlt/clJLMoF6FswciMSThG4fJv4JQb01mRJMKZ//9M9RXqQAoJHYFM9ZLMDCZcYpK9pnS2Sw/NOnul+ZZlk1PCbemZ8+eUKvVLt1Xm/j7+2P06NE4d+4cAFj3q6ysRO/eve3aHDVqVDvPwnmKG0CVJMlufotcfHw8iouL7eqKiopanGNDRN7r4PZxUKlbv/Gq1BJKPx53iyIi6lw3P/Ls6qu9AgICEBsba3dflSQJxcXF7b6viqKIEydOWBOXAQMGIDw83K7N6upqHDp0qFPv1R7tmcnOzsbkyZPRt29f3LhxA1u2bEFJSQl2794NAEhLS8Ndd92F3NxcAMCzzz6L8ePH44033sDUqVOxdetWHD16FO+++64nT4OIOkHFyb7YtWYKpj73GSRRBZVsIrRoUkGllrBrzRR+cR7dPgS4/0uRTu6flZWFmTNnYsyYMRg7dizWrl2L2tpapKenA3C8Dy9btgzjxo3DoEGDcP36daxatQrfffcd5syZYzm8IGD+/PlYsWIFBg8ejAEDBuDll19GREQEUlNT3Ty5lnk0mbly5QrS0tJw+fJldOvWDVFRUdi9ezd+/vOfAwAqKiqgkvXrJyQkYMuWLXjppZewaNEiDB48GDt37sSIESM8dQpE1ImOfhKLyguhiP/VQQy5rwKAZfjt7L9/htKPxzGRIXLTtGnT8MMPP2Dx4sXQ6XQYNWoUCgsLrRN4b74P//TTT8jIyIBOp0OPHj0QGxuLAwcO2M1zXbBgAWprazF37lxcv34d999/PwoLCx2+XK8jCWbzLRwQVIjq6mp069YNlboruPPOOz0djlcxGo3YvacQyZNSlD9nRv4YduNk4JYmABsMLU8AbmiQTwC2lZsm6zbUNz8BuKHOYLf+meei8NNPAejRXY/Xc49ZJwDrGxzbBGyTfZsm+gK2SbsAYLihb1wvn+ArmyzcWG+sc5wULC/L1ytmzkwzgrpJePL9e5E/80jjHBlqr4AgFeZ9NBp5jx/nnBknqTRGfNHwKqqqqtqcg+KqpnvS//fL9xDg794TtgZjHTb8fU6nxqtEHp8ATETUHk1PK1mWvCHTbcjJOS8tteGL+M8bIiIi8mrsmSEiIlIClWB5uduGD2IyQ0REpAAd+Q3AvobDTEREROTV2DNDRESkAALcnwAsuP1FNd6JyQwREZEScM6MyzjMRERERF6NPTNEREQKwAnArmMyQ0REpACCSuiAX832zWyGyQwREZESsGvGZZwzQ0RERF6NPTNEREQKIHTAbzO5/dtOXorJDBERkQIIKsvL3TZ8kY+eNhEREd0u2DNDRESkABxmch2TGSIiIiXg00wu4zATEREReTX2zBARESkAJwC7jskMERGRAnDOjOt8NIcjIiKi2wV7ZoiIiJRAJVhe7rbhg5jMEBERKQCHmVzHZIaIiEgBBHTAk9kdEon34ZwZIiIi8mrsmSEiIlICzplxGZMZIiIiBeCcGddxmImIiIi8GntmiIiIFIA/zeQ6JjNERERKwDkzLuMwExEREXk19swQEREpACcAu47JDBERkQJYfjXbzWTGR8dbfPS0iYiI6HbBnhkiIiIlEOD+7xH45igTkxkiIiIl4JwZ13l0mCk3Nxf33nsvunbtitDQUKSmpuLs2bOt7rN582br//Cml0ajuUURExERdQ5BJXTIy1l5eXno378/NBoN4uLicPjw4Ra3/dOf/oT/+Z//QY8ePdCjRw8kJSU5bD9r1iyH+3RKSorTcTnDo8nMvn37MG/ePBw8eBBFRUUwGo2YNGkSamtrW91Pq9Xi8uXL1td33313iyImIiK6fWzbtg1ZWVnIycnBsWPHEB0djeTkZFy5cqXZ7UtKSvD444/jiy++QGlpKSIjIzFp0iRcunTJbruUlBS7+/RHH33Uqefh0WGmwsJCu/ebN29GaGgoysrK8MADD7S4nyAICA8Pb/dx9Ho99Hq99X11dTUAwGQywWg0Ohm1bzOZTHZLpTGbzdayJErWskm01IsmWZ2sLIqi3dJStqyXJNu5SpLoUDabbXXyMiDdtLTFJggSBMFSr1LZ6u3KaktZrba1qJb9jVX7W5Z+/rIjBtj+VSYFNpZFW51ZVDmUBbOtTlTwwLN/kMpuSe3Ha+cGjQA03KJjdcAwU9NXADfd55oEBgYiMDDQYfM333wTGRkZSE9PBwDk5+dj165dKCgowMKFCx22//DDD+3ev/fee/jb3/6G4uJipKWl2R3Pmfu0uxT10VVVVQUACAkJaXW7mpoa9OvXD5IkISYmBitXrsQ999zT4va5ublYunSpQ/2+/SUIDg52L2gfVbz3c0+HoHj+gfZLlWqkZamW0DP8qhMtyT/cAloo+465BdGeDsFr8do5r66uDkW/uUUH68AJwJGRkXbVOTk5WLJkiV2dwWBAWVkZsrOzrXUqlQpJSUkoLS1t1+Hq6upgNBod7tslJSUIDQ1Fjx49MHHiRKxYsQJ33nmn8+fTTopJZiRJwvz583HfffdhxIgRLW43ZMgQFBQUICoqClVVVVi9ejUSEhJw6tQp9OnTp9l9srOzkZWVZX1fXV2NyMhIjH9gQpuJE9kzmUwo3vs5Eicmwc9PMX98rJzpmTHKy0ZLj4rBKMrqLOv1elvPjF5vW1/fYKnXN9h69xpkZX29pdzQuJQkVWNcKlzV9UR9Q+Mxm2kTAAyN+xlrDLa6Olv7hhp943qjwz4AYKi1lE3yfepMjutl+4hG2zVRGv8gFeYWROPdJ76CsV65cSoRr50bNIa2t1GgixcvQqvVWt831ytz9epViKKIsLAwu/qwsDCcOXOmXcd58cUXERERgaSkJGtdSkoKfvnLX2LAgAE4f/48Fi1ahMmTJ6O0tBRqeVdzB1LM3WjevHk4efIkvvzyy1a3i4+PR3x8vPV9QkIChg0bhg0bNmD58uXN7tNS95qfnx/8/f2b2YPaotRrJ09mREH2od1YFmCrM8vKkmT554xakg3TSE3DQLZm7MuWYwmy48jLQFOS0rSTbLjHrLLG2nQceRwAIDUOD8lGviDKRvfExhzEJBspNRls52/SW8pGva3O2CA5lOU3NyUnM02M9RIMvCG7hNfOeSrZZ0pn68inmbRarV0y0xleffVVbN26FSUlJXYP4kyfPt1aHjlyJKKionD33XejpKQEiYmJnRKLIgZQMzMz8emnn+KLL75osXelJf7+/hg9ejTOnTvXSdERERF1vqZfzXb31V49e/aEWq1GZWWlXX1lZWWb811Wr16NV199FXv27EFUVFSr2w4cOBA9e/bs1Pu0R5MZs9mMzMxM7NixA3v37sWAAQOcbkMURZw4cQK9e/fuhAiJiIhuTwEBAYiNjUVxcbG1TpIkFBcX242A3Oz111/H8uXLUVhYiDFjxrR5nP/+97/48ccfO/U+7dFhpnnz5mHLli34xz/+ga5du0Kn0wEAunXrhqCgIABAWloa7rrrLuTm5gIAli1bhnHjxmHQoEG4fv06Vq1ahe+++w5z5szx2HkQERG5S4BzPSstteGMrKwszJw5E2PGjMHYsWOxdu1a1NbWWp9uuvke/Nprr2Hx4sXYsmUL+vfvb71vd+nSBV26dEFNTQ2WLl2KRx99FOHh4Th//jwWLFiAQYMGITk52b2Ta4VHk5l33nkHADBhwgS7+k2bNmHWrFkAgIqKCqhkExV++uknZGRkQKfToUePHoiNjcWBAwcwfPjwWxU2ERFRh/PENwBPmzYNP/zwAxYvXgydTodRo0ahsLDQOin45nvwO++8A4PBgF/96ld27TQ9LaVWq/H111/j/fffx/Xr1xEREYFJkyZh+fLlzc5d7SgeTWbM7ZhYVVJSYvd+zZo1WLNmTSdFRERE5FsyMzORmZnZ7Lqb78Hffvttq20FBQVh9+7dHRRZ+ynmaSYiIiJf5uwE3pba8EVMZoiIiBSAPzTpOiYzRERECsCeGdcp4ntmiIiIiFzFnhkiIiIF4DCT65jMEBERKQCHmVzHYSYiIiLyauyZISIiUgCh8T932/BFTGaIiIgUgMNMruMwExEREXk19swQEREpAHtmXMdkhoiISAH4aLbrOMxEREREXo09M0RERArAYSbXMZkhIiJSAmYzLmMyQ0REpADMZVzHOTNERETk1dgzQ0REpAB8msl1TGaIiIgUgMNMruMwExEREXk19swQEREpQQcMM/lq1wyTGSIiIgXgMJPrOMxEREREXo09M0RERAogNL7cbcMXMZkhIiJSAD6a7ToOMxEREZFXY88MERGRAgjogAnAHRKJ92EyQ0REpAAcZnIdkxkiIiIF4KPZruOcGSIiIvJq7JkhIiJSAA4zuY7JDBERkQJwmMl1HGYiIiIir+ZSMlNfX49Lly451J86dcrtgIiIiHxRU8+Muy9f5HQy8/HHH2Pw4MGYOnUqoqKicOjQIeu63/3udx0aHBERka9omjPj7ssXOZ3MrFixAmVlZSgvL8emTZswe/ZsbNmyBQBgNpudais3Nxf33nsvunbtitDQUKSmpuLs2bNt7rd9+3YMHToUGo0GI0eOxGeffebsaRARERGAvLw89O/fHxqNBnFxcTh8+HCr27d1DzabzVi8eDF69+6NoKAgJCUl4ZtvvunMU3A+mTEajQgLCwMAxMbGYv/+/diwYQOWLVvmdEa4b98+zJs3DwcPHkRRURGMRiMmTZqE2traFvc5cOAAHn/8ccyePRvHjx9HamoqUlNTcfLkSWdPhYiISDE8Mcy0bds2ZGVlIScnB8eOHUN0dDSSk5Nx5cqVZrdvzz349ddfx9tvv438/HwcOnQId9xxB5KTk9HQ0ODO5WmV08lMaGgovv76a+v7kJAQFBUV4fTp03b17VFYWIhZs2bhnnvuQXR0NDZv3oyKigqUlZW1uM9bb72FlJQUvPDCCxg2bBiWL1+OmJgYrF+/3tlTISIiUgxPDDO9+eabyMjIQHp6OoYPH478/HwEBwejoKCg2e3bugebzWasXbsWL730Eh5++GFERUXhgw8+wPfff4+dO3e6e4la1O5Hs2/cuIGuXbviz3/+M/z87HcLCAjARx99hMzMTLeCqaqqAmBJkFpSWlqKrKwsu7rk5ORWL5Jer4der7e+r66uBgCYTCYYjUY3IvY9JpPJbqk08qFOSZSsZZNoqRdNsjpZWRRFu6WlbFkvSbZzlSTRoWw22+rkZUC6aWmLTRAkCIKlXqWy1duV1ZayWm1rUS37q6f2tyz9/GVHDLB9kEmBjWXRVmcWVQ5lwWyrExX8ZQ3+QSq7JbUfr50bNALQeR0KnabpPtckMDAQgYGBdnUGgwFlZWXIzs621qlUKiQlJaG0tLTZdtu6B1+4cAE6nQ5JSUnW9d26dUNcXBxKS0sxffp0d06rRe3+6Pqf//kfFBYWok+fPi1uc99997kciCRJmD9/Pu677z6MGDGixe10Op11mKtJWFgYdDpdi/vk5uZi6dKlDvX79pcgODjY5Zh9WfHezz0dguL5B9ovVaqRlqVaQs/wq060JP+XVkALZd8xtyDa0yF4LV4759XV1aHoN7foYALc/6XIxv0jIyPtqnNycrBkyRK7uqtXr0IUxWbvqWfOnGm2+bbuwU1LZ+/T7mp3MjN69GjExcVh9+7dGDp0qLW+vLwcixYtcnsS7rx583Dy5El8+eWXbrXTnOzsbLtMsrq6GpGRkRj/wIRWe4HIkclkQvHez5E4Mcmhh04JnOmZMcrLRkuPisEoyuos6/V6W8+MXm9bX99gqdc32Hr3GmRlfb2l3NC4lCRVY1wqXNX1RH1D4zGbaRMADI37GWsMtro6W/uGGn3jeqPDPgBgqLWUTfJ96kyO62X7iEbbNVEa/yAV5hZE490nvoKxXrlxKhGvnRs0hra36SCWOS/ufgOwZXnx4kVotVpr/c29Mrebdt+NNm3ahJycHNx///3YuXMnQkND8dJLL+Fvf/sbpkyZ4lYQmZmZ+PTTT7F///5We34AIDw8HJWVlXZ1lZWVCA8Pb3Gf5rrXAMDPzw/+/v7N7EFtUeq1kyczoiD70G4sC7DVmWVlSbJ8Aqgl2TCN1DQMZGvGvmw5liA7jrwMNCUpTTvJhnvMKmusTceRxwEAUuPwkGzkC6JsdE9szEFMspFSk8F2/ia9pWzU2+qMDZJDWX5zU3Iy08RYL8HAG7JLeO2cp3LyKV13dOTPGWi1Wrtkpjk9e/aEWq126p7a1j24aVlZWYnevXvbbTNq1CinzsUZTg2gLl26FFlZWfj5z3+OESNG4MaNGygtLcUnn3zi0sHNZjMyMzOxY8cO7N27FwMGDGhzn/j4eBQXF9vVFRUVIT4+3qUYiIiIfFFAQABiY2Pt7qmSJKG4uLjFe2pb9+ABAwYgPDzcbpvq6mocOnSoU+/T7e6ZqaysxMqVK/GnP/0Jw4cPx5kzZzBr1iyMHTvW5YPPmzcPW7ZswT/+8Q907drVOp7WrVs3BAUFAQDS0tJw1113ITc3FwDw7LPPYvz48XjjjTcwdepUbN26FUePHsW7777rchxERESe5onfZsrKysLMmTMxZswYjB07FmvXrkVtbS3S09MBOH8PFgQB8+fPx4oVKzB48GAMGDAAL7/8MiIiIpCamureybWi3cnMgAEDMGTIEGzfvh1Tp05FYWEhpk2bhoqKCrzwwgsuHfydd94BAEyYMMGuftOmTZg1axYAoKKiAipZ335CQgK2bNmCl156CYsWLcLgwYOxc+fOVicNExERKZ0nfjV72rRp+OGHH7B48WLodDqMGjUKhYWF1gm8rtyDFyxYgNraWsydOxfXr1/H/fffj8LCQmg0GrfOrTXtTmYKCgrsHqlKSUnBF198gf/93//Ft99+i7y8PKcP3p5vDC4pKXGoe+yxx/DYY485fTwiIiKyl5mZ2eJXq7hyDxYEAcuWLcOyZcs6KsQ2tTuZae7Z8JiYGBw4cACTJ0/u0KCIiIh8jSeGmW4Xbj9b279/fxw4cKAjYiEiIvJdHfFDkT6azXTI10H26NGjI5ohIiIicpryvvWMiIjIB3liAvDtgskMERGRAnDOjOv4q2NERETk1dgzQ0REpAACOmCYye1fqvROTGaIiIgUQFAJEFRuJjNu7u+tmMwQEREpAOfMuI5zZoiIiMirsWeGiIhIAfhotuuYzBARESkAh5lcx2EmIiIi8mrsmSEiIlIADjO5jskMERGRAjCZcR2HmYiIiMirsWeGiIhIATgB2HVMZoiIiJSA2YzLOMxEREREXo09M0RERArACcCuYzJDRESkABxlch2TGSIiIgXgr2a7jnNmiIiIyKuxZ4aIiEgBOMzkOiYzRERECsAJwK7jMBMRERF5NfbMEBERKQB7ZlzHZIaIiEgBOGfGdRxmIiIiIq/GnhkiIiIF4DCT65jMEBERKYL7yQzgm8kMh5mIiIjIq7FnhoiISAE4Adh1TGaIiIgUgHNmXMdkhoiISAEsPTPuJjMdFIyX8ficmf379+Ohhx5CREQEBEHAzp07W92+pKTEmr3KXzqd7tYETERE5IOuXbuGGTNmQKvVonv37pg9ezZqampa3f7pp5/GkCFDEBQUhL59++KZZ55BVVWV3XbN3dO3bt3qVGwe75mpra1FdHQ0nnjiCfzyl79s935nz56FVqu1vg8NDe2M8IiIiG4Jpc+ZmTFjBi5fvoyioiIYjUakp6dj7ty52LJlS7Pbf//99/j++++xevVqDB8+HN999x2efPJJfP/99/j444/ttt20aRNSUlKs77t37+5UbB5PZiZPnozJkyc7vV9oaKjTJ0tERKRUgkqAoHJzmMnN/Vty+vRpFBYW4siRIxgzZgwAYN26dZgyZQpWr16NiIgIh31GjBiBv/3tb9b3d999N1555RX89re/hclkgp+fLQXp3r07wsPDXY7P48mMq0aNGgW9Xo8RI0ZgyZIluO+++1rcVq/XQ6/XW99XV1cDAEwmE4xGY6fHejsxmUx2S6Uxm83WsiRK1rJJtNSLJlmdrCyKot3SUraslyTbuUqS6FA2m2118jIg3bS0xSYIEgTBUq9S2ertympLWa22taiW/Y1V+1uWfv6yIwbYPsikwMayaKsziyqHsmC21YkK/kTwD1LZLan9eO3coBGABk8H4bym+1yTwMBABAYGutxeaWkpunfvbk1kACApKQkqlQqHDh3CI4880q52qqqqoNVq7RIZAJg3bx7mzJmDgQMH4sknn0R6erpT84cU/NHVvN69eyM/Px9jxoyBXq/He++9hwkTJuDQoUOIiYlpdp/c3FwsXbrUoX7f/hIEBwd3dsi3peK9n3s6BMXzD7RfqlQjLUu1hJ7hV51oSf4XOqCFsu+YWxDt6RC8Fq+d8+rq6lD0m1tzrI4cZoqMjLSrz8nJwZIlS1xuV6fTOUzn8PPzQ0hISLvnrF69ehXLly/H3Llz7eqXLVuGiRMnIjg4GHv27MHvf/971NTU4Jlnnml3fF6XzAwZMgRDhgyxvk9ISMD58+exZs0a/PnPf252n+zsbGRlZVnfV1dXIzIyEuMfmICQkJBOj/l2YjKZULz3cyROTHLIrJXAmZ4Zo7xstPSoGIyirM6yXq+39czo9bb19Q2Wen2DrXevQVbW11vKDY1LSVI1xqXCVV1P1Dc0HrOZNgHA0LifscZgq6uztW+o0TeuNzrsAwCGWkvZJN+nzuS4XraPaLRdE6XxD1JhbkE03n3iKxjrlRunEvHauUFjaHubDiI0/uduGwBw8eJFu3mlLfXKLFy4EK+99lqrbZ4+fdqtmADLfXfq1KkYPny4Q1L18ssvW8ujR49GbW0tVq1adXsnM80ZO3YsvvzyyxbXt9S95ufnB39//2b2oLYo9drJkxlRkH1oN5YF2OrMsrIkWT4A1JJsmEZqGgayNWNfthxLkB1HXgaakpSmnWTDPWaVNdam48jjAACpcXhINvIFUTa6JzbmICbZSKnJYDt/k95SNuptdcYGyaEsv7kpOZlpYqyXYOAN2SW8ds5TyT5TvIlWq7VLZlry/PPPY9asWa1uM3DgQISHh+PKlSt29SaTCdeuXWtzrsuNGzeQkpKCrl27YseOHW3eO+Li4rB8+XLo9fp2D43dFslMeXk5evfu7ekwiIiIXCfA/Z9WcnL/Xr16oVevXm1uFx8fj+vXr6OsrAyxsbEAgL1790KSJMTFxbW4X3V1NZKTkxEYGIh//vOf0Gg0bR6rvLwcPXr0cGqOj8eTmZqaGpw7d876/sKFCygvL0dISAj69u2L7OxsXLp0CR988AEAYO3atRgwYADuueceNDQ04L333sPevXuxZ88eT50CERGR25T8DcDDhg1DSkoKMjIykJ+fD6PRiMzMTEyfPt36JNOlS5eQmJiIDz74AGPHjkV1dTUmTZqEuro6/OUvf0F1dbV1YnKvXr2gVqvxySefoLKyEuPGjYNGo0FRURFWrlyJP/zhD07F5/Fk5ujRo3jwwQet75vmtsycORObN2/G5cuXUVFRYV1vMBjw/PPP49KlSwgODkZUVBQ+//xzuzaIiIi8jdK/Z+bDDz9EZmYmEhMToVKp8Oijj+Ltt9+2rjcajTh79izq6uoAAMeOHcOhQ4cAAIMGDbJr68KFC+jfvz/8/f2Rl5eH5557DmazGYMGDcKbb76JjIwMp2LzeDIzYcIEu3kON9u8ebPd+wULFmDBggWdHBURERHJhYSEtPgFeQDQv39/u/t5W/d3AEhJSbH7sjxXeTyZISIiImUPMykdkxkiIiIFUPowk5Lx6yCJiIjIq7FnhoiISAE4zOQ6JjNEREQKwGEm13GYiYiIiLwae2aIiIgUgMNMrmMyQ0REpAAcZnIdh5mIiIjIq7FnhoiISAHYM+M6JjNEREQKIDT+524bvojJDBERkUL4as+KuzhnhoiIiLwae2aIiIgUgI9mu47JDBERkQJwArDrOMxEREREXo09M0RERArAYSbXMZkhIiJSAA4zuY7DTEREROTV2DNDRESkABxmch2TGSIiIiUQGl/utuGDOMxEREREXo09M0RERArAYSbXMZkhIiJSAD7N5DomM0RERArAnhnXcc4MEREReTX2zBARESkAH2ZyHZMZIiIiBeAwk+s4zERERERejT0zRERECsCnmVzHZIaIiEgBOMzkOg4zERERkVdjzwwREZECcJjJdUxmqFXf1NfjhmiyvpdMlvJXtTVQ+dn++HRV+2FwUNAtj4+I6HbBZMZ1TGaoRd/U12NY2RG7uiCzGR8BePDE16i/6W/N6dh7mdAQEdEt5/E5M/v378dDDz2EiIgICIKAnTt3trlPSUkJYmJiEBgYiEGDBmHz5s2dHqcvkvfIdMb2RERk0zQB2N1XZ7l27RpmzJgBrVaL7t27Y/bs2aipqWl1nwkTJjjE9+STT9ptU1FRgalTpyI4OBihoaF44YUXYDI5dz/xeDJTW1uL6Oho5OXltWv7CxcuYOrUqXjwwQdRXl6O+fPnY86cOdi9e3cnR0pERNR5moaZ3H11lhkzZuDUqVMoKirCp59+iv3792Pu3Llt7peRkYHLly9bX6+//rp1nSiKmDp1KgwGAw4cOID3338fmzdvxuLFi52KzePDTJMnT8bkyZPbvX1+fj4GDBiAN954AwAwbNgwfPnll1izZg2Sk5M7K0wiIqJOpeRHs0+fPo3CwkIcOXIEY8aMAQCsW7cOU6ZMwerVqxEREdHivsHBwQgPD2923Z49e/Cf//wHn3/+OcLCwjBq1CgsX74cL774IpYsWYKAgIB2xefxZMZZpaWlSEpKsqtLTk7G/PnzW9xHr9dDr9db31dXVwMATCYTjEZjp8R5O5BMJgSZzXZ1Te9vrm/a3tPX0yyLSxIla9kkWupFk6xOVhZF0W5pKVvWS5JsArQkOpTNZludvAxINy1tsQmCBEGw1KtUtnq7stpSVqttLaplf2PV/paln7/siAG2DzIpsLEs2urMosqhLJhtdaKCPxH8g1R2S2o/Xjs3aASgwdNBOK/pPtckMDAQgYGBLrdXWlqK7t27WxMZAEhKSoJKpcKhQ4fwyCOPtLjvhx9+iL/85S8IDw/HQw89hJdffhnBwcHWdkeOHImwsDDr9snJyXjqqadw6tQpjB49ul3xKfijq3k6nc7upAEgLCwM1dXVqK+vR1AzE1Bzc3OxdOlSh/p9+0usF5Sa91EL9QU3bjjU6f79JXSdG45X8Q+0X6pUIy1LtYSe4VedaEn+L62AFsq+Y25BtKdD8Fq8ds6rq6tD0W88HYXzIiMj7d7n5ORgyZIlLren0+kQGhpqV+fn54eQkBDodC1/8v/mN79Bv379EBERga+//hovvvgizp49i7///e/Wdpu7pzetay+vS2ZckZ2djaysLOv76upqREZGYvwDExASEuLByJTtq9oaPHjia7u6ILMZBTdu4ImuXR2eZvpiZBSi7+hyK0N04EzPjFFeNlp6VAxGUVZnWa/X23pm9Hrb+voGS72+wdYb1SAr6+st5YbGpSSpGuNS4aquJ+obGo/ZTJsAYGjcz1hjsNXV2do31Ogb1xsd9gEAQ62lbJLvU2dyXC/bRzTaronS+AepMLcgGu8+8RWM9cqNU4l47dygMbS9TYfpiAm8lv0vXrwIrVZrrW2pV2bhwoV47bXXWm3x9OnTLkcjn1MzcuRI9O7dG4mJiTh//jzuvvtul9u9mdclM+Hh4aisrLSrq6yshFarbbZXBmi5e83Pzw/+/v7N7EEAoPLzc0hYmtQLgsM6lQKupzyZEQXZh3ZjWYCtziwrS5LlXNSSbJhGahoGsjVjX7YcS5AdR14GmpKUpp1kwz1mlTXWpuPI4wAAqXF4SDbyBfkDY2JjDmKSjeyZDLbzN+ktZaPeVmdskBzK8pubkpOZJsZ6CQbekF3Ca+c8VTND6t5Aq9XaJTMtef755zFr1qxWtxk4cCDCw8Nx5coVu3qTyYRr1661OB+mOXFxcQCAc+fO4e6770Z4eDgOHz5st03TPd6Zdr0umYmPj8dnn31mV1dUVIT4+HgPRUREROQ+T3xpXq9evdCrV682t4uPj8f169dRVlaG2NhYAMDevXshSZI1QWmP8vJyAEDv3r2t7b7yyiu4cuWKdRirqKgIWq0Ww4cPb3e7Hp8NVlNTg/LycusJXrhwAeXl5aioqABgGSJKS0uzbv/kk0/i//2//4cFCxbgzJkz+OMf/4i//vWveO655zwRPhER0W1v2LBhSElJQUZGBg4fPox///vfyMzMxPTp061PMl26dAlDhw619rScP38ey5cvR1lZGb799lv885//RFpaGh544AFERUUBACZNmoThw4fjd7/7Hb766ivs3r0bL730EubNm+fUhGWPJzNHjx7F6NGjrTOWs7KyMHr0aOsz5pcvX7YmNgAwYMAA7Nq1C0VFRYiOjsYbb7yB9957j49ld4Kuauc67pzdnoiIvMeHH36IoUOHIjExEVOmTMH999+Pd99917reaDTi7NmzqKurAwAEBATg888/x6RJkzB06FA8//zzePTRR/HJJ59Y91Gr1fj000+hVqsRHx+P3/72t0hLS8OyZcucis3jd58JEybYzXO4WXPf7jthwgQcP368E6MiABgcFITTsfc6/DaT7t9f4ouRUfxtJiKiDqT032YKCQnBli1bWlzfv39/u/t5ZGQk9u3b12a7/fr1c5g+4iyPJzOkbDcnKEajEToA0Xd08fhkXyKi24kAQIB72YiP/s6k54eZiIiIiNzBnhkiIiIlEOB+14qPds0wmSEiIlIApc+ZUTImM0RERAogNP7nbhu+iHNmiIiIyKuxZ4aIiEgJOGfGZUxmiIiIFIC5jOs4zERERERejT0zRERECiAIAgQ3H0dyd39vxWSGiIhICTjO5DIOMxEREZFXY88MERGRArBjxnVMZoiIiBSAc2Zcx2EmIiIi8mpMZoiIiMircZiJiIhIAfhDk65jMkNERKQAnDPjOg4zERERkVdjMkNERERejcNMRERECsA5M65jzwwRERF5NfbMEBERKYDQ+J+7bfgiJjNERERKwN8zcBmHmYiIiMirsWeGiIhIATgB2HVMZoiIiBSAo0yu4zATEREReTX2zBARESkBx5lcxmSGiIhIATjM5DomM0RERArAjhnXcc4MEREReTX2zBARESkBu2ZcxmSGiIhIIXwzFXEfh5mIiIjIqykimcnLy0P//v2h0WgQFxeHw4cPt7jt5s2bIQiC3Uuj0dzCaImIiDpe0yiTu6/Ocu3aNcyYMQNarRbdu3fH7NmzUVNT0+L23377rcP9uum1fft22Xk7rt+6datTsXl8mGnbtm3IyspCfn4+4uLisHbtWiQnJ+Ps2bMIDQ1tdh+tVouzZ89a3ws+OkZIRES3E2U/nD1jxgxcvnwZRUVFMBqNSE9Px9y5c7Fly5Zmt4+MjMTly5ft6t59912sWrUKkydPtqvftGkTUlJSrO+7d+/uVGweT2befPNNZGRkID09HQCQn5+PXbt2oaCgAAsXLmx2H0EQEB4efivDJCIi8lmnT59GYWEhjhw5gjFjxgAA1q1bhylTpmD16tWIiIhw2EetVjvcq3fs2IFf//rX6NKli1199+7d3bqvezSZMRgMKCsrQ3Z2trVOpVIhKSkJpaWlLe5XU1ODfv36QZIkxMTEYOXKlbjnnnta3F6v10Ov11vfV1dXAwBMJhOMRmMHnInvMJlMdkulMZvN1rIkStaySbTUiyZZnawsiqLd0lK2rJck27lKkuhQNpttdfIyIN20tMUmCBIEwVKvUtnq7cpqS1mttrWolv2NVftbln7+siMG2P5VJgU2lkVbnVlUOZQFs61O9Pg/b1rmH6SyW1L78dq5QSMADbfmUAI64GGmxmXTfa5JYGAgAgMDXW63tLQU3bt3tyYyAJCUlASVSoVDhw7hkUceabONsrIylJeXIy8vz2HdvHnzMGfOHAwcOBBPPvkk0tPTnRp18ehH19WrVyGKIsLCwuzqw8LCcObMmWb3GTJkCAoKChAVFYWqqiqsXr0aCQkJOHXqFPr06dPsPrm5uVi6dKlD/b79JQgODnb/RHxQ8d7PPR2C4vkH2i9VqpGWpVpCz/CrTrQk/wsd0ELZd8wtiPZ0CF6L1855dXV1KPqNp6NwXmRkpN37nJwcLFmyxOX2dDqdw9QPPz8/hISEQKfTtauNjRs3YtiwYUhISLCrX7ZsGSZOnIjg4GDs2bMHv//971FTU4Nnnnmm3fEp+N9hzYuPj0d8fLz1fUJCAoYNG4YNGzZg+fLlze6TnZ2NrKws6/vq6mpERkZi/AMTEBIS0ukx305MJhOK936OxIlJ8PNT3h8fZ3pmjPKy0dKjYjCKsjrLer3e1jOj19vW1zdY6vUNtt69BllZX28pNzQuJUnVGJcKV3U9Ud/QeMxm2gQAQ+N+xhqDra7O1r6hRt+43uiwDwAYai1lk3yfOpPjetk+otF2TZTGP0iFuQXRePeJr2CsV26cSsRr5waNoe1tFOjixYvQarXW9y31yixcuBCvvfZaq22dPn3a7Xjq6+uxZcsWvPzyyw7r5HWjR49GbW0tVq1a5T3JTM+ePaFWq1FZWWlXX1lZ2e6xM39/f4wePRrnzp1rcZuWutf8/Pzg7+/fzB7UFqVeO3kyIwqyD+3GsgBbnVlWliRL74dakg3TSE3DQLZm7MuWYwmy48jLQFOS0rSTbLjHrLLG2nQceRwAIDUOD8lGviDKRvfExhzEJBspNRls52/SW8pGva3O2CA5lOU3NyUnM02M9RIMvCG7hNfOeSrZZ0pn68jvzNNqtXbJTEuef/55zJo1q9VtBg4ciPDwcFy5csWu3mQy4dq1a+26X3/88ceoq6tDWlpam9vGxcVh+fLl0Ov17R4a82gyExAQgNjYWBQXFyM1NRWA5YO9uLgYmZmZ7WpDFEWcOHECU6ZM6cRIiYiIOtutf5qpV69e6NWrV5vbxcfH4/r16ygrK0NsbCwAYO/evZAkCXFxcW3uv3HjRvziF79o17HKy8vRo0cPp+b4eHycICsrCzNnzsSYMWMwduxYrF27FrW1tdanm9LS0nDXXXchNzcXgGVsbdy4cRg0aBCuX7+OVatW4bvvvsOcOXM8eRpERERuUfKvGQwbNgwpKSnIyMhAfn4+jEYjMjMzMX36dOuTTJcuXUJiYiI++OADjB071rrvuXPnsH//fnz22WcO7X7yySeorKzEuHHjoNFoUFRUhJUrV+IPf/iDU/F5PJmZNm0afvjhByxevBg6nQ6jRo1CYWGhdVJwRUUFVLK+/Z9++gkZGRnQ6XTo0aMHYmNjceDAAQwfPtxTp0BERHTb+/DDD5GZmYnExESoVCo8+uijePvtt63rjUYjzp49i7q6Orv9CgoK0KdPH0yaNMmhTX9/f+Tl5eG5556D2WzGoEGDrF/Z4gyPJzMAkJmZ2eKwUklJid37NWvWYM2aNbcgKiIiImoSEhLS4hfkAUD//v3t5i02WblyJVauXNnsPikpKXZflucqRSQzREREPk/ZXwCsaPwGJSIiIvJq7JkhIiJSAKHxP3fb8EXsmSEiIiKvxmSGiIiIvBqHmYiIiBRAyd8zo3TsmSEiIiKvxmSGiIiIvBqHmYiIiJSA40wuYzJDRESkAPzOPNcxmSEiIlICZjMu45wZIiIi8mrsmSEiIlIAdsy4jskMERGREnACsMs4zERERERejckMEREReTUOMxERESkA58y4jj0zRERE5NXYM0NERKQE7JpxGZMZIiIiBRAa/3O3DV/EYSYiIiLyauyZISIiUgIOM7mMyQwREZECMJdxHZMZIiIiJWA24zLOmSEiIiKvxp4ZIiIiRWDXjKuYzBARESkAUxnXcZiJiIiIvBp7ZoiIiJSAXTMuYzJDRESkAMxlXMdhJiIiIvJq7JkhIiJSAkGwvNxtwwexZ4aIiIi8mk/3zJysq0XXwADr+65qPwwOCvJgREREROQsn05mpp46iYYuXezqTsfey4SGiIhuOY4yuY7DTDe5IZo8HQIRERE5QRHJTF5eHvr37w+NRoO4uDgcPny41e23b9+OoUOHQqPRYOTIkfjss89uUaRERESdQxCEDnl1lldeeQUJCQkIDg5G9+7d27WP2WzG4sWL0bt3bwQFBSEpKQnffPON3TbXrl3DjBkzoNVq0b17d8yePRs1NTVOxebxZGbbtm3IyspCTk4Ojh07hujoaCQnJ+PKlSvNbn/gwAE8/vjjmD17No4fP47U1FSkpqbi5MmTtzhyIiIi32EwGPDYY4/hqaeeavc+r7/+Ot5++23k5+fj0KFDuOOOO5CcnIyGhgbrNjNmzMCpU6dQVFSETz/9FPv378fcuXOdis3jc2befPNNZGRkID09HQCQn5+PXbt2oaCgAAsXLnTY/q233kJKSgpeeOEFAMDy5ctRVFSE9evXIz8/v9lj6PV66PV66/uqqioAgKa21mHbGz/9hB/1BrfP63ZlMplQV1eHa9euwc/P4398HJjNZmtZEiVr2SRa6kV5nclWNhpFAIDB6Lher7cNPer1orXc0Fivb5CvN9rK9cbG9cbG2KoABMJs1qOh4QYaGtsyGmxtGgy2towmU2Pstj+PJsnWvghLvQRbnaSSlf0ay36yodMAWdloWa+StWlW266f4mgE1NXVARoDVGYFx6lEvHau0xiABvvPls5SXV3dYW3c3FZgYCACAwPdanvp0qUAgM2bN7dre7PZjLVr1+Kll17Cww8/DAD44IMPEBYWhp07d2L69Ok4ffo0CgsLceTIEYwZMwYAsG7dOkyZMgWrV69GRERE+4Ize5Berzer1Wrzjh077OrT0tLMv/jFL5rdJzIy0rxmzRq7usWLF5ujoqJaPE5OTo4ZAF988cUXX3y59Dp//ry7t7wW1dfXm8PDwzss1i5dujjU5eTkdFi8mzZtMnfr1q3N7c6fP28GYD5+/Lhd/QMPPGB+5plnzGaz2bxx40Zz9+7d7dYbjUazWq02//3vf293TB79p/XVq1chiiLCwsLs6sPCwnDmzJlm99HpdM1ur9PpWjxOdnY2srKyrO+vX7+Ofv36oaKiAt26dXPjDHxPdXU1IiMjcfHiRWi1Wk+H41V47dzD6+c6XjvXVVVVoW/fvggJCem0Y2g0Gly4cAEGQ8eMCpjNZoe5M+72yrii6b7c2j1bp9MhNDTUbr2fnx9CQkJava/fTHnjBJ2gpe61bt268S+2i7RaLa+di3jt3MPr5zpeO9epVJ07xVSj0UCj0XTqMZqzcOFCvPbaa61uc/r0aQwdOvQWReQajyYzPXv2hFqtRmVlpV19ZWUlwsPDm90nPDzcqe2JiIioec8//zxmzZrV6jYDBw50qe2m+3JlZSV69+5tra+srMSoUaOs29z8wI/JZMK1a9ecuq979GmmgIAAxMbGori42FonSRKKi4sRHx/f7D7x8fF22wNAUVFRi9sTERFR83r16oWhQ4e2+goICGi7oWYMGDAA4eHhdvfs6upqHDp0yHrPjo+Px/Xr11FWVmbdZu/evZAkCXFxce0+lscfzc7KysKf/vQnvP/++zh9+jSeeuop1NbWWp9uSktLQ3Z2tnX7Z599FoWFhXjjjTdw5swZLFmyBEePHkVmZma7jxkYGIicnByPjCF6O1471/HauYfXz3W8dq7jtbOpqKhAeXk5KioqIIoiysvLUV5ebvedMEOHDsWOHTsAWL43Z/78+VixYgX++c9/4sSJE0hLS0NERARSU1MBAMOGDUNKSgoyMjJw+PBh/Pvf/0ZmZiamT5/e/ieZAHj0aaYm69atM/ft29ccEBBgHjt2rPngwYPWdePHjzfPnDnTbvu//vWv5p/97GfmgIAA8z333GPetWvXLY6YiIjIt8ycObPZp6e++OIL6zYAzJs2bbK+lyTJ/PLLL5vDwsLMgYGB5sTERPPZs2ft2v3xxx/Njz/+uLlLly5mrVZrTk9PN9+4ccOp2ITGgxMRERF5JY8PMxERERG5g8kMEREReTUmM0REROTVmMwQERGRV/P5ZMaVnzT3ZXl5eejfvz80Gg3i4uJw+PBhT4fkFfbv34+HHnoIEREREAQBO3fu9HRIXiE3Nxf33nsvunbtitDQUKSmpuLs2bOeDstrvPPOO4iKirJ+8298fDz+9a9/eTosr/Tqq69aHzUm5fH5ZMaVnzT3Vdu2bUNWVhZycnJw7NgxREdHIzk52eHbG8lRbW0toqOjkZeX5+lQvMq+ffswb948HDx4EEVFRTAajZg0aRJqm/nFe3LUp08fvPrqqygrK8PRo0cxceJEPPzwwzh16pSnQ/MqR44cwYYNGxAVFeXpUKgFfDS70ebNmzF//nxcv37d06EoVlxcHO69916sX78egOXbmiMjI/H0009j4cKFHo7OewiCgB07dli/NIra74cffkBoaCj27duHBx54wNPheKWQkBCsWrUKs2fP9nQoXqGmpgYxMTH44x//iBUrVmDUqFFYu3atp8Oim/h8zwy1j8FgQFlZGZKSkqx1KpUKSUlJKC0t9WBk5EuqqqoAoFN/wfh2JYoitm7ditraWv78ixPmzZuHqVOn2n32kfL4xK9mk/uuXr0KURSb/Sn3M2fOeCgq8iWSJGH+/Pm47777MGLECE+H4zVOnDiB+Ph4NDQ0oEuXLtixYweGDx/u6bC8wtatW3Hs2DEcOXLE06FQG27LnpmFCxdCEIRWX7wBE3mXefPm4eTJk9i6daunQ/EqQ4YMQXl5OQ4dOoSnnnoKM2fOxH/+8x9Ph6V4Fy9exLPPPosPP/wQGo3G0+FQG27LnpnO/ElzX9WzZ0+o1WpUVlba1VdWVjr1M+1ErsjMzMSnn36K/fv3o0+fPp4Ox6sEBARg0KBBAIDY2FgcOXIEb731FjZs2ODhyJStrKwMV65cQUxMjLVOFEXs378f69evh16vh1qt9mCEJHdbJjO9evVCr169PB3GbSUgIACxsbEoLi62TlyVJAnFxcVO/WI5kTPMZjOefvpp7NixAyUlJRgwYICnQ/J6kiRBr9d7OgzFS0xMxIkTJ+zq0tPTMXToULz44otMZBTmtkxmnFFRUYFr167Z/aQ5AAwaNAhdunTxbHAKk5WVhZkzZ2LMmDEYO3Ys1q5di9raWqSnp3s6NMWrqanBuXPnrO8vXLiA8vJyhISEoG/fvh6MTNnmzZuHLVu24B//+Ae6du0KnU4HAOjWrRuCgoI8HJ3yZWdnY/Lkyejbty9u3LiBLVu2oKSkBLt37/Z0aIrXtWtXh7lZd9xxB+68807O2VIiF38J/LbRnp80J5t169aZ+/btaw4ICDCPHTvWfPDgQU+H5BW++OKLZv+czZw509OhKVpz1wyAedOmTZ4OzSs88cQT5n79+pkDAgLMvXr1MicmJpr37Nnj6bC81vjx483PPvusp8OgZvB7ZoiIiMir3ZZPMxEREZHvYDJDREREXo3JDBEREXk1JjNERETk1ZjMEBERkVdjMkNERERejckMEREReTUmM0REROTVmMwQERGRV2MyQ+SDPvroIwQFBeHy5cvWuvT0dERFRaGqqsqDkREROY8/Z0Dkg8xmM0aNGoUHHngA69atQ05ODgoKCnDw4EHcddddng6PiMgpPv+r2US+SBAEvPLKK/jVr36F8PBwrFu3Dv/3f/9nTWQeeeQRlJSUIDExER9//LGHoyUiah17Zoh8WExMDE6dOoU9e/Zg/Pjx1vqSkhLcuHED77//PpMZIlI8zpkh8lGFhYU4c+YMRFFEWFiY3boJEyaga9euHoqMiMg5TGaIfNCxY8fw61//Ghs3bkRiYiJefvllT4dEROQyzpkh8jHffvstpk6dikWLFuHxxx/HwIEDER8fj2PHjiEmJsbT4REROY09M0Q+5Nq1a0hJScHDDz+MhQsXAgDi4uIwefJkLFq0yMPRERG5hj0zRD4kJCQEZ86ccajftWuXB6IhIuoYfJqJiBwkJSXhq6++Qm1tLUJCQrB9+3bEx8d7OiwiomYxmSEiIiKvxjkzRERE5NWYzBAREZFXYzJDREREXo3JDBEREXk1JjNERETk1ZjMEBERkVdjMkNERERejckMEREReTUmM0REROTVmMwQERGRV2MyQ0RERF7t/weRhVzbXcaHpAAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Learned Weights:  [[2. 0.]]\n",
            "Bias:  [-2.]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "97krRNHtZI9g"
      },
      "source": [
        "## Classifying digits\n",
        "Below is a code for classifying between MNIST digits (7 vs 9) using nearest neighbor and Perceptron classifiers. Please try to understand the code and answer the following questions."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DdYgrb4lZI9g",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "94ac91b4-6e1b-4ed5-e63b-fed759b2ed0c"
      },
      "source": [
        "import numpy as np\n",
        "from sklearn.datasets import load_digits\n",
        "import random\n",
        "from sklearn.neighbors import KNeighborsClassifier\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "digN,digP = 7,9\n",
        "X,y = load_digits(n_class=10, return_X_y=True) #load the digits dataset\n",
        "idx = (y==digP) + (y==digN) #Just focus on 7 and 9\n",
        "X,y = X[idx,:], y[idx]\n",
        "y[y==digN]=-1.0 #set (negative class)\n",
        "y[y==digP]=+1.0 #set (positive class)\n",
        "idx = list(range(len(y)))\n",
        "random.shuffle(idx) # Just shuffle the data\n",
        "X,y = X[idx,:], y[idx]\n",
        "plt.gray();plt.matshow(X[0].reshape((8,-1)))\n",
        "# show an example. we need to reshape to show as an image.\n",
        "\n",
        "Ntr = 15 #select number of training examples\n",
        "Xtr,Ytr = X[:Ntr], y[:Ntr] #get training examples\n",
        "Xtt,Ytt = X[Ntr:], y[Ntr:] #get validation (test) examples\n",
        "\n",
        "clf = KNeighborsClassifier(n_neighbors=1)\n",
        "clf = clf.fit(Xtr, Ytr)\n",
        "Z = clf.predict(Xtt)\n",
        "print('Accuracy of kNN:',np.mean(Z==Ytt))\n",
        "plt.gray();plt.matshow(Xtt[0].reshape((8,-1))); plt.title('Predicted:'+str(Z[0]))\n",
        "error_idx = np.nonzero(Ytt!=np.sign(Z))[0][0] # show one error example\n",
        "plt.gray();plt.matshow(Xtt[error_idx].reshape((8,-1))); plt.title('Misclassified: Predicted as '+str(Z[error_idx])) # show a misclassification\n",
        "\n",
        "\n",
        "\n"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy of kNN: 0.9651162790697675\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Misclassified: Predicted as -1')"
            ]
          },
          "metadata": {},
          "execution_count": 16
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 0 Axes>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 480x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 480x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 480x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aPWp7xpDZI9i"
      },
      "source": [
        "1. What is the relationship between accuracy over test examples and training set size for the classifier? How can you design an experiment to do this?\n",
        "2. What is the impact of changing the value of k in the nearest neighbor classifier? Which value of k gives you the best validation performance?\n",
        "3. Here, we are using each pixel as a feature. Can you extract better features that allow you to do better classification?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B4mgVXMNZI9i"
      },
      "source": [
        "## Using Perceptron for Digit Classification\n",
        "\n",
        "Use the codes provided above and compare the predictive performance of a perceptron for this problem. Compare the performance of the perceptron to the k-NN classifier. Which one is better and what is your intuition as to why that is the case.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vChQd0jQTUk-"
      },
      "source": [
        "# Your code goes here"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vP8LOePATY6K"
      },
      "source": [
        "Once you have trained and evaluated your perceptron, execute the following cell to show the internal representation of the weights of the perceptron (clf). What is your intuition about this?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6G73hKgKTn6Z",
        "outputId": "9cd3f511-c135-4dbd-83c3-ac0f8608ec43",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 193
        }
      },
      "source": [
        "plt.gray();plt.matshow(clf.coef_.reshape((8,-1)))"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "error",
          "ename": "AttributeError",
          "evalue": "'KNeighborsClassifier' object has no attribute 'coef_'",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-18-94696b628956>\u001b[0m in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m;\u001b[0m\u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmatshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mclf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcoef_\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;31mAttributeError\u001b[0m: 'KNeighborsClassifier' object has no attribute 'coef_'"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 0 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LcvbJV_jTYDE"
      },
      "source": []
    }
  ]
}