maximizing-performance_upload.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import numpy as np\n",
    "import torch\n",
    "from torch import autograd\n",
    "import torch.nn.functional as F\n",
    "\n",
    "#Prepare the data.\n",
    "import torch\n",
    "import numpy as np\n",
    "from torch.autograd import Variable\n",
    "import torch.nn as nn\n",
    "from numpy import linalg as LA\n",
    "\n",
    "dtype = torch.FloatTensor\n",
    "\n",
    "images = np.load(\"./data/images.npy\")\n",
    "labels = np.load(\"./data/labels.npy\")\n",
    "\n",
    "images = np.reshape(images, (images.shape[0], images.shape[1] * images.shape[2]))\n",
    "\n",
    "images = images - images.mean()\n",
    "images = images/images.std() \n",
    "\n",
    "train_seqs = images[0:40000]\n",
    "val_seqs = images[40000:50000]\n",
    "\n",
    "train_labels = labels[0:40000]\n",
    "cv_labels = labels[40000:50000]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def accuracy(y, y_hat):\n",
    "    count = 0\n",
    "    for i in range(y.shape[0]):\n",
    "        if y[i] == y_hat[i]:\n",
    "            count += 1\n",
    "    return count/y.shape[0]\n",
    "\n",
    "import random\n",
    "def approx_train_accuracy():\n",
    "    model.eval()\n",
    "    i = np.random.choice(train_seqs.shape[0], size = 1000, replace=False)\n",
    "    x = Variable(torch.from_numpy(train_seqs[i].astype(np.float32)))\n",
    "    y = train_labels[i].astype(np.int)\n",
    "    \n",
    "    output = model(x)\n",
    "    y_hat = np.argmax(output.data.numpy(), axis =1)\n",
    "    acc = accuracy(y,y_hat)\n",
    "    return acc\n",
    "\n",
    "def val_accuracy():\n",
    "    model.eval()\n",
    "    i = np.random.choice(val_seqs.shape[0], size = 1000, replace=False)\n",
    "    x = Variable(torch.from_numpy(val_seqs[i].astype(np.float32)))\n",
    "    y = cv_labels[i].astype(np.int) \n",
    "    \n",
    "    output = model(x)\n",
    "    y_hat = np.argmax(output.data.numpy(), axis =1)\n",
    "    acc = accuracy(y,y_hat)\n",
    "\n",
    "    return acc\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     0  0.20  0.22\n",
      "   100  0.88  0.89\n",
      "   200  0.91  0.90\n",
      "   300  0.91  0.90\n",
      "   400  0.91  0.92\n",
      "   500  0.93  0.94\n",
      "   600  0.92  0.93\n",
      "   700  0.94  0.92\n",
      "   800  0.93  0.92\n",
      "   900  0.92  0.92\n",
      "  1000  0.93  0.93\n",
      "  1100  0.95  0.93\n",
      "  1200  0.93  0.93\n",
      "  1300  0.94  0.94\n",
      "  1400  0.92  0.92\n",
      "  1500  0.95  0.93\n",
      "  1600  0.93  0.94\n",
      "  1700  0.93  0.94\n",
      "  1800  0.93  0.93\n",
      "  1900  0.94  0.92\n",
      "  2000  0.95  0.93\n",
      "  2100  0.94  0.94\n",
      "  2200  0.92  0.93\n",
      "  2300  0.94  0.94\n",
      "  2400  0.93  0.93\n",
      "  2500  0.94  0.93\n",
      "  2600  0.93  0.94\n",
      "  2700  0.95  0.93\n",
      "  2800  0.95  0.94\n",
      "  2900  0.93  0.93\n",
      "  3000  0.95  0.93\n",
      "  3100  0.94  0.93\n",
      "  3200  0.94  0.94\n",
      "  3300  0.94  0.94\n",
      "  3400  0.95  0.94\n",
      "  3500  0.94  0.93\n",
      "  3600  0.94  0.95\n",
      "  3700  0.95  0.93\n",
      "  3800  0.95  0.94\n",
      "  3900  0.96  0.93\n",
      "  4000  0.94  0.94\n",
      "  4100  0.94  0.93\n",
      "  4200  0.95  0.94\n",
      "  4300  0.95  0.93\n",
      "  4400  0.96  0.94\n",
      "  4500  0.95  0.94\n",
      "  4600  0.93  0.93\n",
      "  4700  0.95  0.93\n",
      "  4800  0.94  0.93\n",
      "  4900  0.95  0.94\n"
     ]
    }
   ],
   "source": [
    "HEIGHT, WIDTH, NUM_CLASSES, NUM_OPT_STEPS = 26, 26, 5, 5000\n",
    "learning_rate = 0.01\n",
    "\n",
    "class MaxPerformanceCNNModel(torch.nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.conv1 = torch.nn.Conv2d(1, 16, kernel_size=3, stride=1)\n",
    "        \n",
    "        self.conv2 = torch.nn.Conv2d(16, 32, kernel_size=3, stride=1)\n",
    "        \n",
    "        self.conv3 = torch.nn.Conv2d(32, 64, kernel_size=3, stride=1)\n",
    "        \n",
    "        self.final_conv = torch.nn.Conv2d(64,5, kernel_size=1)\n",
    "        \n",
    "    \n",
    "    def forward(self, x):\n",
    "        \n",
    "        x = x.view(-1, HEIGHT, WIDTH).unsqueeze(1)\n",
    "        \n",
    "        x = F.max_pool2d(self.conv1(x), kernel_size=2, stride=2)\n",
    "        x = F.relu(x)\n",
    "        \n",
    "        x = self.conv2(x)\n",
    "        x = F.relu(x)\n",
    "        \n",
    "        x = self.conv3(x)\n",
    "        n, c, h, w = x.size()\n",
    "        x = F.max_pool2d(x, kernel_size=[h,w])\n",
    "        x = F.relu(x)\n",
    "        x = F.dropout(x)\n",
    "        \n",
    "        x = self.final_conv(x).view(-1, NUM_CLASSES)\n",
    "        \n",
    "        return x\n",
    "        \n",
    "\n",
    "model = MaxPerformanceCNNModel()\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr= learning_rate)\n",
    "\n",
    "def train(batch_size):\n",
    "    model.train()\n",
    "    \n",
    "    i = np.random.choice(train_seqs.shape[0], size = batch_size, replace=False)\n",
    "    x = Variable(torch.from_numpy(train_seqs[i].astype(np.float32)))\n",
    "    y = Variable(torch.from_numpy(train_labels[i].astype(np.int)))\n",
    "    \n",
    "    optimizer.zero_grad()\n",
    "    y_hat = model(x)\n",
    "    loss = F.cross_entropy(y_hat, y)\n",
    "    #loss = F.nll_loss(y_hat, y)\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    \n",
    "    return loss.data[0]\n",
    "\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr= 0.01)\n",
    "train_accs, val_accs = [], []\n",
    "batch_size = 300\n",
    "for i in range(5000):\n",
    "    l = train(batch_size)\n",
    "    if i % 100 == 0:\n",
    "        train_accs.append(approx_train_accuracy())\n",
    "        val_accs.append(val_accuracy())\n",
    "        print(\"%6d %5.2f %5.2f\" % (i, train_accs[-1], val_accs[-1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "max_train accuracy:  0.96\n",
      "max_val accuracy:  0.948\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAisAAAIkCAYAAADf+Gv9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJElaaoYVSZK01AwrkiRpqRlWJEnSUvv/qs5Fw2izJ4AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f121b711be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "t = np.arange(0,len(train_accs),1)\n",
    "\n",
    "s = train_accs\n",
    "k = val_accs\n",
    "print(\"max_train accuracy: \", max(train_accs))\n",
    "print(\"max_val accuracy: \", max(val_accs))\n",
    "plt.figure(figsize=(8,8), dpi = 80)\n",
    "plt.plot(t, s, t, k)\n",
    "\n",
    "plt.xlabel('number of iteration')\n",
    "plt.ylabel('accuracy')\n",
    "plt.title('Training/validation accuracy')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Description of the Model:\n",
    "\n",
    "Starting Point:\n",
    "\n",
    "A simple CNN with 2 convolutional layer and 1 final $1X1$ convolution layer.\n",
    "Used the following configuration:\n",
    "\n",
    "    a. strides = 2 in both conv layer. \n",
    "    b. Learning rate = 0.001, \n",
    "    c. batch size = 300 and \n",
    "    d. opt steps = 5000\n",
    "    e. Adam optimizer\n",
    "\n",
    "# Performance Optimizations: Below are the steps followed to optimize the CNN to improve accuracy\n",
    "\n",
    "    1. Used max_pooling instead of avg_pooling after applying the convolution step.\n",
    "    2. Added 3rd convolution layer with relu activation and max pooling. Observed high overfitting but increased validation accuracy.\n",
    "    3. Changed the strides in the 3rd convolution layer to 1. This increased the validation accuracy by 1%\n",
    "    4. Included dropout before final convolution layer to reduce the overfitting trend.\n",
    "    5. Changed the order of relu and maxpooling in the first two convolutional layers to increase two layers.\n",
    "\n",
    "# Steps Tried but with negative impact on performance:\n",
    "\n",
    "    1. Added 4th convolution layer only to reduce the validation accuracy significantly.\n",
    "    2. Tried various loss function instead of Cross Entropy Loss. Not much change in accuracy.\n",
    "\n",
    "\n",
    "# Final Accuracy Settings:\n",
    "\n",
    "    1. 3 concolutional layer($3X3$) with relu and max pooling\n",
    "    1. Adam optimizer\n",
    "    2. Cross Entropy loss\n",
    "    3. Batch size = 300\n",
    "    4. Optimization steps: 5000\n",
    "    5. Learning rate = 0.001\n",
    "    \n",
    "    Highest Validation accuracy = 96%\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Testing on kaggle data set.\n",
    "#Generate a csv file with predictions.\n",
    "\n",
    "#load the test data.\n",
    "model.eval()\n",
    "test_data = np.load(\"./data/part_2_test_images.npy\")\n",
    "test_data = np.reshape(test_data, (test_data.shape[0], test_data.shape[1]*test_data.shape[2]))\n",
    "\n",
    "test_data = test_data - test_data.mean()\n",
    "test_data = test_data/test_data.std() \n",
    "\n",
    "output = np.empty((5000, 2), dtype=np.uint0)\n",
    "for i in range(test_data.shape[0]):\n",
    "    x = Variable(torch.from_numpy(test_data[i].astype(np.float32)))\n",
    "    out = model(x)\n",
    "    label = np.argmax(out.data.numpy(), axis =1)\n",
    "    output[i] = [i, label[0]]\n",
    "\n",
    "np.savetxt('out_exp2.csv', output, delimiter=\",\",fmt='%1.0f', header=\"id,label\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Failure Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "#identifying the 10 correct predictions and 10 incorrect predictions.\n",
    "\n",
    "#run the model and check for predictions\n",
    "correct = 0\n",
    "incorrect = 0\n",
    "model.eval()\n",
    "index = 0\n",
    "correct_predicted_input = []\n",
    "incorrect_predicted_input = []\n",
    "correct_labels = []\n",
    "while(correct < 10 or incorrect < 10):\n",
    "    x = Variable(torch.from_numpy(val_seqs[index].astype(np.float32)))\n",
    "    y = train_labels[index].astype(np.int)\n",
    "    \n",
    "    out = model(x)\n",
    "    y_hat = np.argmax(out.data.numpy(), axis =1)\n",
    "    \n",
    "    if ((y == y_hat) and (correct <10)) :\n",
    "        correct += 1\n",
    "        temp = x.view(-1, HEIGHT, WIDTH).unsqueeze(1)\n",
    "        correct_predicted_input.append(temp.data[0][0].numpy())\n",
    "        correct_labels.append(y)\n",
    "    elif ((y != y_hat) and (incorrect <10)) :\n",
    "        incorrect += 1\n",
    "        temp = x.view(-1, HEIGHT, WIDTH).unsqueeze(1)\n",
    "        incorrect_predicted_input.append(temp.data[0][0].numpy())\n",
    "    \n",
    "    index += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Display correctly predicted images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTeyHCoKt8IYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2910198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f121b379940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nGH4iTzH8RJ76P1aZ/5dlvzWhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2ebb208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nFOEHEkX4gUQRfiBRhB9IFOEHEvV/gfZV1nOzPzkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2c6cb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4wLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvpW3flQAADzJJREFUeJzt3XuMFWWax/HfoyKGm6CthHjDGYmJ\nGZDZIFnFqER3ZMwaGDFm+GPSk+i0ibfFINEoCV6i0c0yE2NWkx5RkbCMkwwTicHsIG5CJpoBJArt\nuK5gINxb4mUwchH62T+6nO3F7vc9nFPn0jzfT9I559RTXfVQ7c8651S9VebuAhDPKc1uAEBzEH4g\nKMIPBEX4gaAIPxAU4QeCIvxAUIQfCIrwA0Gd1siVmRmnE6Iqw4cPT9ZHjBiRrO/fvz+7jmPHjp1Q\nT63K3a2S+WoKv5nNkPSspFMlvejuT9eyPGAgEydOTNanTZuWrC9evDi7ji+//PKEehrsqn7bb2an\nSvp3ST+VdJmkOWZ2WVmNAaivWj7zT5W0xd0/dfcjkn4naWY5bQGot1rCf56kHX1e7yymARgE6v6F\nn5l1SOqo93oAnJhawr9L0gV9Xp9fTPt/3L1TUqfEt/1AK6nlbf96SRPM7GIzO13SzyWtLKctAPVW\n9Z7f3Y+a2T2S/lO9h/pecvcPS+sMJ41TTknvYx555JHsMhYuXJis9/T0JOvvvvtudh3vvPNOdp6T\nSU2f+d19laRVJfUCoIE4vRcIivADQRF+ICjCDwRF+IGgCD8QFOEHgmroxTwQ0/PPP5+s33nnndll\ndHZ2Jutz585N1g8ePJhdRzTs+YGgCD8QFOEHgiL8QFCEHwiK8ANBEX4gKHNv3JW1uIzXyae9vT07\nzyuvvJKs5y7UIUmPP/54pS2FV+lNO9jzA0ERfiAowg8ERfiBoAg/EBThB4Ii/EBQhB8IipN8kNTW\n1pasb9++PbuMt99+O1mfOTN/Z/fcHXnwfzjJB0AS4QeCIvxAUIQfCIrwA0ERfiAowg8ExU07kHTL\nLbck68OGDcsuY/78+ck6x/Cbo6bwm9k2SQckHZN01N2nlNEUgPorY88/3d33l7AcAA3EZ34gqFrD\n75L+ZGbvmVlHfzOYWYeZbTCzDTWuC0CJan3bf7W77zKzcyWtNrP/dve1fWdw905JnRIDe4BWUtOe\n3913FY/dkv4oaWoZTQGov6rDb2bDzWzkd88l/URSV1mNAaivqsfzm9kP1Lu3l3o/PvyHuz+Z+R3e\n9g8yb731VrJ+zjnnZJdx+eWXl9VO1caMGZOd59ChQ8n6wYMHy2qnriodz1/1Z353/1RS8/+qAKrC\noT4gKMIPBEX4gaAIPxAU4QeCIvxAUIQfCIqLebSo0aNHZ+c57bT0n2///vxI65EjRybr1157bbL+\nxBNPZNdRhgULFiTrd911V7I+bty47DqOHj2arF9//fXJ+tq1a5P1VsOeHwiK8ANBEX4gKMIPBEX4\ngaAIPxAU4QeC4jh/FcaOHZud58knk9c10a233pqsn3nmmSfUU39WrFiRnWfevHnJeu5cgq1bt55Q\nT/2p5FyB3HH+3L913bp12XXcfffdyfqDDz6YrHOcH8CgQPiBoAg/EBThB4Ii/EBQhB8IivADQXGc\nvx+XXnppsv7mm29ml5G7mcWyZcuS9Q8++CC7josvvjhZnz9/fnYZlRz/Tjl8+HB2ngceeCBZzx3D\nl6TnnnsuWb/vvvuyy8i55JJLkvXp06fXvI5Wwp4fCIrwA0ERfiAowg8ERfiBoAg/EBThB4Ii/EBQ\nIU/yGTJkSLL+2muvJetDhw7NruPKK69M1ru6urLLyDGzZH3q1KnZZTz11FM19fDCCy9k52lra0vW\nly5dml3G3LlzK+6pWt98802yPmzYsLr30EjZPb+ZvWRm3WbW1WfaWWa22sw+KR7H1LdNAGWr5G3/\nK5JmHDftIUlr3H2CpDXFawCDSDb87r5W0ufHTZ4paUnxfImkWSX3BaDOqv3MP9bd9xTP90oa8IqW\nZtYhqaPK9QCok5q/8HN3NzNP1DsldUpSaj4AjVXtob59ZjZOkorH7vJaAtAI1YZ/paT24nm7pNfL\naQdAo2Tf9pvZcknXSWozs52SFkp6WtLvzex2Sdsl3VbPJsvW0ZH+CmLSpEnJ+o033phdRxnH8XPc\n05+iZs3Kfw97xx13JOu5f2t3d/5N36pVq5L15cuXZ5fR09OTnadWp59+erKe296DTTb87j5ngNL1\nJfcCoIE4vRcIivADQRF+ICjCDwRF+IGgCD8QFOEHgrJGnrjQKuf2L1q0KFlvb29P1nMXp8DgtHbt\n2mT9yJEjyfoNN9xQZjtVc/f0VV4K7PmBoAg/EBThB4Ii/EBQhB8IivADQRF+IKiQN+349ttvk/Xc\nTT0w+ORucCJJEydOTNZffvnlstppCez5gaAIPxAU4QeCIvxAUIQfCIrwA0ERfiCokMf5c+OyOc5/\n8jn//POz84wePTpZ37x5c1nttAT2/EBQhB8IivADQRF+ICjCDwRF+IGgCD8QFOEHgsqe5GNmL0n6\nZ0nd7v6jYtqjkn4l6bNitofdfVW9miwbF/OI5+yzz655GXv37i2hk9ZRyZ7/FUkz+pn+G3efXPwM\nmuAD6JUNv7uvlfR5A3oB0EC1fOa/x8w2mdlLZjamtI4ANES14X9B0g8lTZa0R9KAd740sw4z22Bm\nG6pcF4A6qCr87r7P3Y+5e4+k30qampi3092nuPuUapsEUL6qwm9m4/q8/JmkrnLaAdAolRzqWy7p\nOkltZrZT0kJJ15nZZEkuaZukO+vYI4A6yIbf3ef0M3lxHXppmNmzZyfrO3bsaFAnQPNwhh8QFOEH\ngiL8QFCEHwiK8ANBEX4gKMIPBEX4gaBC3rHnoosuStZffPHFBnUCNA97fiAowg8ERfiBoAg/EBTh\nB4Ii/EBQhB8IKuRx/t27dyfrF154YYM6AZqHPT8QFOEHgiL8QFCEHwiK8ANBEX4gKMIPBBXyOP/m\nzZuT9UmTJjWoEzTKqFGjal7GoUOHSuikdbDnB4Ii/EBQhB8IivADQRF+ICjCDwRF+IGgCD8QVPYk\nHzO7QNKrksZKckmd7v6smZ0l6TVJ4yVtk3Sbu39Rv1bL09XVlazPnj07WR86dGh2HYcPHz6hnlBf\nV111VXaenp6eZH3jxo1ltdMSKtnzH5U0z90vk/SPku42s8skPSRpjbtPkLSmeA1gkMiG3933uPvG\n4vkBSR9JOk/STElLitmWSJpVryYBlO+EPvOb2XhJP5b0F0lj3X1PUdqr3o8FAAaJigf2mNkISX+Q\nNNfd/2Zmf6+5u5uZD/B7HZI6am0UQLkq2vOb2RD1Bn+Zu68oJu8zs3FFfZyk7v5+19073X2Ku08p\no2EA5ciG33p38YslfeTuv+5TWimpvXjeLun18tsDUC+VvO2fJukXkjab2fvFtIclPS3p92Z2u6Tt\nkm6rT4sA6iEbfnf/syQboHx9ue00Ru5iHqedlt4sEydOzK5jw4YNJ9QT6mvatGnZeTZt2pSsf/XV\nV2W10xI4ww8IivADQRF+ICjCDwRF+IGgCD8QFOEHgjL3fk/Jr8/KBjj/v9Ha2tqS9Y8//jhZ37p1\na3Yd11xzTbI+WG4AMWTIkGS97xiPgRw5cqSsdgZ0xhlnJOu7d+/OLmPZsmXJ+r333ntCPTWLu+f/\nKGLPD4RF+IGgCD8QFOEHgiL8QFCEHwiK8ANBEX4gqIov4Hky2b9/f7I+Z86cZH3VqlXZdaxevTpZ\nf+aZZ5L1XI+SNGHChGT9iiuuyC4jN8/kyZOT9a+//jq7jgULFiTrS5cuzS5j0qRJyfr999+frI8e\nPTq7jtxJPicb9vxAUIQfCIrwA0ERfiAowg8ERfiBoAg/EFTIi3nU6uabb87OkztmPHLkyLLaGdAX\nX3yRnWf9+vXJ+rp165L1KVPyt2CcMWNGdp5aHThwIFlftGhRdhmPPfZYWe00FRfzAJBE+IGgCD8Q\nFOEHgiL8QFCEHwiK8ANBEX4gqOxJPmZ2gaRXJY2V5JI63f1ZM3tU0q8kfVbM+rC7J69ycbKc5FOJ\nUaNGJevjx49P1s8999zsOrZt25asb9myJbuMRpg+fXqynrtgiCTt3LkzWX/jjTeS9YMHD2bXcbKo\n9CSfSq7kc1TSPHffaGYjJb1nZt9dpuY37v5v1TYJoHmy4Xf3PZL2FM8PmNlHks6rd2MA6uuEPvOb\n2XhJP5b0l2LSPWa2ycxeMrMxJfcGoI4qDr+ZjZD0B0lz3f1vkl6Q9ENJk9X7zqDfkRNm1mFmG8xs\nQwn9AihJReE3syHqDf4yd18hSe6+z92PuXuPpN9Kmtrf77p7p7tPcff88C8ADZMNv/XegH2xpI/c\n/dd9po/rM9vPJHWV3x6Aeqnk2/5pkn4habOZvV9Me1jSHDObrN7Df9sk3VmXDgHURaMv5vGZpO19\nJrVJyt+dovnos1yDoc/B0KP0/T4vcvdzKvnFhob/eys32zAYvgugz3INhj4HQ49SbX1yei8QFOEH\ngmp2+DubvP5K0We5BkOfg6FHqYY+m/qZH0DzNHvPD6BJmhZ+M5thZh+b2RYze6hZfeSY2TYz22xm\n77fSKcrFeIpuM+vqM+0sM1ttZp8Uj00dbzFAj4+a2a5ie75vZjc1s8eipwvM7L/M7K9m9qGZ/Usx\nvdW250B9VrVNm/K238xOlfQ/kv5J0k5J6yXNcfe/NryZDDPbJmmKu7fUMV8zu0bS15JedfcfFdP+\nVdLn7v508T/UMe7+YIv1+Kikr1tpKHhxtuq4vsPWJc2S9Eu11vYcqM/bVMU2bdaef6qkLe7+qbsf\nkfQ7STOb1Mug5O5rJX1+3OSZkpYUz5eo9z+Mphmgx5bj7nvcfWPx/ICk74att9r2HKjPqjQr/OdJ\n2tHn9U617jUCXNKfzOw9M+todjMZY4vrL0jSXvVefakVtexQ8OOGrbfs9ixjeD1f+OVd7e7/IOmn\nku4u3sq2PO/9PNeKh3IqGgreDP0MW/+7Vtqe1Q6vP16zwr9L0gV9Xp9fTGs57r6reOyW9EcNMHS5\nRez7brRl8djd5H6+p9Kh4I3W37B1teD2rGV4/fGaFf71kiaY2cVmdrqkn0ta2aReBmRmw4svVmRm\nwyX9RK09dHmlpPbiebuk15vYS79acSj4QMPW1WLbs/Th9e7elB9JN6n3G/+tkh5pVh+ZHn8g6YPi\n58NW6lPScvW+xftWvd+Z3C7pbElrJH0i6S1JZ7Vgj0slbZa0Sb3hGtcC2/Jq9b6l3yTp/eLnphbc\nngP1WdU25Qw/ICi+8AOCIvxAUIQfCIrwA0ERfiAowg8ERfiBoAg/ENT/AhJ4mEcLmdwsAAAAAElF\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2ec4e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nfzmD+JkRmickAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2e744e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2cdc668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n4ScyiuEnMup/AeJ7c0lIIBb9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2b32320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nP5Aowg8k6n8A+Rw3a5UfnuoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2b4fd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRfiBRBF+IFH/D1Dwd6eh4di9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2f4b390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def display(image):\n",
    "    plt.figure()\n",
    "    plt.imshow(image)\n",
    "    plt.set_cmap('gray')\n",
    "for i in range(len(correct_predicted_input)):\n",
    "    image = correct_predicted_input[i]\n",
    "    display(image)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Display incorrect Predictions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4wLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvpW3flQAAETdJREFUeJzt3WuMVVWaxvHnBVQMakKJQ8DGwVsk\nig5tECZcJiBeaByD/UFsjIZBoDqxTaaDJt5pjBkVsJEWiJGLNEqPPaKNoqINXhLGCy0XERGnpSAF\nTYHcpQFBEN75UAenBqm1TtW5s/6/hFTVeXet9ebAwz7n7LX3NncXgPS0KHUDAEqD8AOJIvxAogg/\nkCjCDySK8AOJIvxAogg/kCjCDySqVTEnMzOWEwIF5u6WzXY57fnNbKCZ/dXMaszsvlzGAlBc1ty1\n/WbWUtJXkq6VtEnSUklD3X1N4HfY8wMFVow9fw9JNe6+3t0PSfqjpME5jAegiHIJ/7mS/tbg502Z\nxwBUgIJ/4Gdm1ZKqCz0PgKbJJfx1kjo1+Pknmcf+H3efJmmaxHt+oJzk8rJ/qaSLzex8MztV0i8k\nzc9PWwAKrdl7fnf/3szukvRnSS0lPefuX+StszJ20UUXRbcZMWJEsH7++ecH63v27GlST821b9++\nYH3VqlXB+pIlS6JzfPXVV8E6V5MqjZze87v7AkkL8tQLgCJieS+QKMIPJIrwA4ki/ECiCD+QKMIP\nJIrwA4kq6sU8ykWPHj2C9bFjxwbr119/fXSOQ4cOBeu1tbXB+qmnnhqdI6Zly5bRbaqqqoL1M888\nM+c+1q1bF6xPmjQpOsasWbOC9f379zepJ7DnB5JF+IFEEX4gUYQfSBThBxJF+IFEEX4gUc2+dHez\nJivCZbwGDBgQ3Wb+/PAFh7Zv3x6sP/PMM9E5Zs6cGazv2LEjOkY5uOCCC4L1Xr16RccYNmxYsH7N\nNddEx9i5c2ewPnXq1GB9ypQp0Tlif++Voig37QBQuQg/kCjCDySK8AOJIvxAogg/kCjCDySK8AOJ\nqrhFPrFFPLEFPJL0xRfhGwtdd911wfo333wTnQPZe/PNN6PbdO3aNVjv2LFjsB67uIokTZgwIVgf\nN25csH7gwIHoHMXAIh8AQYQfSBThBxJF+IFEEX4gUYQfSBThBxJVVsf5+/fvHx3jjTfeCNZjx/Al\njuOXm4ULF0a3adUqfH+ZO+64I1gfM2ZMdI7YRUc2btwYrI8ePTo6x7x586Lb5Crb4/w53bHHzGol\n7ZV0RNL37t49l/EAFE8+btfV390r45pUAH7Ae34gUbmG3yUtNLPlZlZ9og3MrNrMlpnZshznApBH\nub7s7+PudWb2D5IWmdn/uPvihhu4+zRJ06TiXL0XQHZy2vO7e13m6zZJ8ySF730NoGw0O/xm1sbM\nzjz2vaTrJK3OV2MACqvZx/nN7ALV7+2l+rcP/+nu/xH6nRYtWvgpp5zSaH3Dhg3Reevq6oL1bG4A\nwXH88pKP4/xXX311zn306BF+4Rq78cdVV10VnWPRokXB+p133hkdo6amJlgv+HF+d18v6Z+a+/sA\nSotDfUCiCD+QKMIPJIrwA4ki/ECiCD+QKMIPJKqoF/No27ath2668fLLL0fHiF3MY/PmzdExli9f\nHqxPnz49WC/mc5aCclnkE9OiRXhfOXz48OgYjz/+eLB+9OjR6BjdunVrtLZjxw4dPnyYm3YAaBzh\nBxJF+IFEEX4gUYQfSBThBxJF+IFE5ePS3Vlr3bq1unTpktMYvXv3DtbN4oc4q6tPeK3RHwwaNChY\nj93cQZL27NkT3QaVJXYMfubMmdExVq5cGawvWxa/zm3fvn0brb3zzjvR3z+GPT+QKMIPJIrwA4ki\n/ECiCD+QKMIPJIrwA4kq6nH+mGzOk6+qqsp5npEjRwbrkydPDtYXL14crEtSz549g/WDBw9Gx8DJ\nZ926dTmP0a5du0ZrseseNMSeH0gU4QcSRfiBRBF+IFGEH0gU4QcSRfiBRBF+IFFFXeTj7jp8+HBO\nY7Rp0yZY379/f3SMGTNmBOuxhRjZXDDhkUceCdbvvffe6Bip2Lp1a3SbPn36FKGTwjv99NNL3cIP\nont+M3vOzLaZ2eoGj1WZ2SIzW5v52rawbQLIt2xe9v9e0sDjHrtP0rvufrGkdzM/A6gg0fC7+2JJ\nu457eLCk2ZnvZ0u6Kc99ASiw5n7g197dt2S+/1pS+8Y2NLNqM1tmZssOHDjQzOkA5FvOn/Z7/al4\njZ6O5+7T3L27u3cvpw87gNQ1N/xbzayDJGW+bstfSwCKobnhny/p2MXrh0l6LT/tACiW6HF+M3tR\nUj9J7cxsk6TfSHpC0ktmNkLSBklDspls7969eu+990JzRcd46aWXgvUbbrghm1aC3n///WB9ypQp\n0THuvvvuYH369OnBek1NTXSOk0Xo38Qxt912W7B+6aWXButr1qxpUk+FMnDg8QfOmi7073Pv3r1Z\njxMNv7sPbaQ0IOtZAJQdlvcCiSL8QKIIP5Aowg8kivADiSL8QKIIP5Aoy+YuOXmbzCw42aeffhod\no1u3bsF6y5Yto2McPXo0uk3I2WefHd1m8+bNwfr48eOD9YcffrhJPVWytm3jl4NYv359sB67wMrN\nN9/cpJ4KZe7cucH6lVdeGR3jwgsvDNbdPb5aTuz5gWQRfiBRhB9IFOEHEkX4gUQRfiBRhB9IVFFv\n2hEzb9686Dax4/zFsHPnzug2b731VrB+++23B+tjxoyJzlHMNRqFtHv37ug2jz32WLA+bty4YD2b\nm3588MEH0W1CLrnkkug2gwcPDtYnTpyYUw9NwZ4fSBThBxJF+IFEEX4gUYQfSBThBxJF+IFEldVx\n/kOHDpW6hbx54YUXgvXY8d5evXpF5/jwww+b1FMle/rpp4P1UaNGBesLFiyIzjFp0qRgPXZzkWyu\nwRC7qUbsOg/5xJ4fSBThBxJF+IFEEX4gUYQfSBThBxJF+IFEEX4gUdFFPmb2nKR/lbTN3btmHhsr\naZSk7ZnNHnD3+CqKhMQWlcQWNF177bXROVJa5PPdd98F63379g3Wn3rqqegc999/f7CejxupxC7i\nsmvXrpznyFY2e/7fSxp4gsefcvdumT8EH6gw0fC7+2JJxfvvCEBR5PKe/y4zW2Vmz5lZ/GZrAMpK\nc8P/jKQLJXWTtEXSbxvb0MyqzWyZmS1r5lwACqBZ4Xf3re5+xN2PSpouqUdg22nu3t3duze3SQD5\n16zwm1mHBj/+XNLq/LQDoFiyOdT3oqR+ktqZ2SZJv5HUz8y6SXJJtZJ+WcAeARRANPzuPvQED88s\nQC8nlQMHDgTrR44cCdbNLJ/tnPS2bt0arN96663RMT766KNgffLkycH6rFmzonPMmTMnuk2xsMIP\nSBThBxJF+IFEEX4gUYQfSBThBxJF+IFEEX4gUWV1x57t27fHN4q44oorotusXLky53liTjvttGC9\ndevWwXpskRCapl+/ftFtJk6cGKy/+uqrwfrIkSOb0lLJsecHEkX4gUQRfiBRhB9IFOEHEkX4gUQR\nfiBR5u7Fm8wsOFmbNm2iY9TW1gbrixYtio6RzYUdcnXPPfcE6xMmTAjW+/TpE50jpZt2xHTu3DlY\n/+STT6Jj1NXVBeuxG4Ps27cvOkcxuHtWV4Jhzw8kivADiSL8QKIIP5Aowg8kivADiSL8QKLK6jh/\nNsaOHRusP/TQQ9ExunTpEqzX1NQE6+ecc050jrVr1wbrCxcuDNaHDBkSnSMlbduGbwQdW/MQ+31J\n6tmzZ7C+cePG6BjlgOP8AIIIP5Aowg8kivADiSL8QKIIP5Aowg8kivADiYou8jGzTpKel9Rekkua\n5u6/M7MqSf8lqbOkWklD3H13ZKycF/m0a9cuWI8trpGkzz77LFgfMGBAsD516tToHMOHDw/WL7vs\nsmA9ttDoZNKrV6/oNnPmzAnW27dvH6zH/k4lacmSJdFtKkE+F/l8L+lud79U0j9L+pWZXSrpPknv\nuvvFkt7N/AygQkTD7+5b3H1F5vu9kr6UdK6kwZJmZzabLemmQjUJIP+a9J7fzDpL+qmkv0hq7+5b\nMqWvVf+2AECFyPpGnWZ2hqRXJP3a3f9u9n9vK9zdG3s/b2bVkqpzbRRAfmW15zezU1Qf/D+4+58y\nD281sw6ZegdJ2070u+4+zd27u3v3fDQMID+i4bf6XfxMSV+6e8N7GM+XNCzz/TBJr+W/PQCFks3L\n/t6Sbpf0uZkdu7H9A5KekPSSmY2QtEESJ6ADFSQafnf/QFJjxw3jB0/zbMeOHcH6qFGjomPMnTs3\nWH/77beD9f79+0fnePLJJ4P1k+U4fqtW8f1H7AIrDz74YHSM2PMVu6HGihUronOkhhV+QKIIP5Ao\nwg8kivADiSL8QKIIP5Aowg8kquJu2pEPjz76aLAeOy69c+fO6BwDBw4M1levXh2sHzx4MDpHPnTt\n2jVYv/HGG4P1oUOHRue4/PLLg/Vnn302Osbo0aOD9W+//TY6Riq4aQeAIMIPJIrwA4ki/ECiCD+Q\nKMIPJIrwA4ki/ECiklzkE3PLLbcE6zNmzIiOccYZZ+TUQ+yiJZK0e3fwHik666yzomPEbnZx5MiR\nYP3jjz+OzjF+/Phg/fXXX4+OgeyxyAdAEOEHEkX4gUQRfiBRhB9IFOEHEkX4gURxnL8ZzjvvvOg2\nvXv3DtY7duwYrHfq1Ck6R1VVVbC+Z8+e6BhLly4N1hcsWBCsZ7MeAcXFcX4AQYQfSBThBxJF+IFE\nEX4gUYQfSBThBxJF+IFERRf5mFknSc9Lai/JJU1z99+Z2VhJoyRtz2z6gLsHV4ScLIt8gHKW7SKf\nbMLfQVIHd19hZmdKWi7pJklDJO1z9yezbYrwA4WXbfhbZTHQFklbMt/vNbMvJZ2bW3sASq1J7/nN\nrLOkn0r6S+ahu8xslZk9Z2Zt89wbgALKOvxmdoakVyT92t3/LukZSRdK6qb6Vwa/beT3qs1smZkt\ny0O/APIkq7P6zOwUSW9I+rO7TzxBvbOkN9w9eL9n3vMDhZe3s/rMzCTNlPRlw+BnPgg85ueSwjec\nB1BWsvm0v4+k/5b0uaSjmYcfkDRU9S/5XVKtpF9mPhwMjcWeHyiwvB3qyycz2y5pQ4OH2kmqhKtB\n0Gd+VUKfldCj9OM+/9Hdz8nmF4sa/h9NbrbM3buXrIEs0Wd+VUKfldCjlFufLO8FEkX4gUSVOvzT\nSjx/tugzvyqhz0roUcqhz5K+5wdQOqXe8wMokZKF38wGmtlfzazGzO4rVR8xZlZrZp+b2cpyWqKc\nOZ9im5mtbvBYlZktMrO1ma8lPd+ikR7Hmlld5vlcaWaDStljpqdOZva+ma0xsy/M7N8zj5fb89lY\nn816Tkvyst/MWkr6StK1kjZJWippqLuvKXozEWZWK6m7u5fVMV8z+xdJ+yQ9f2xZtZmNl7TL3Z/I\n/Ifa1t3vLbMex6qJp4IXWuC09X9TeT2feTu9Xirdnr+HpBp3X+/uhyT9UdLgEvVSkdx9saRdxz08\nWNLszPezVf8Po2Qa6bHsuPsWd1+R+X6vpGOnrZfb89lYn81SqvCfK+lvDX7epPK9RoBLWmhmy82s\nutTNRLRvsMT6a9Vffakcle2p4Medtl62z2c+Tq/nA7+4Pu5+paSfSfpV5qVs2fP693PleCgnq1PB\nS+EEp63/oJyez+aeXn+8UoW/TlLDO1H+JPNY2XH3uszXbZLmqf4tS7naeuxsy8zXbSXu50fcfau7\nH3H3o5Kmq0yez8xp669I+oO7/ynzcNk9nyfqs7nPaanCv1TSxWZ2vpmdKukXkuaXqJdGmVmbzAcr\nMrM2kq5TeZ+6PF/SsMz3wyS9VsJeTqgcTwVv7LR1ldnzmffT6929JH8kDVL9J/7rJD1Yqj4iPV4g\n6bPMny/KqU9JL6r+Jd5h1X9mMkLS2ZLelbRW0juSqsqwxxdUf3r4KtWHq0MZPJd9VP+SfpWklZk/\ng8rw+Wysz2Y9p6zwAxLFB35Aogg/kCjCDySK8AOJIvxAogg/kCjCDySK8AOJ+l9kP5hvP0FhigAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f120959e1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niuEncorhJ3Lq/wBIR0I3FpHGhAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2c11208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nyQEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f12095e4978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2ce4f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nKMIPJIrwA4ki/ECiCD+QKMIPJOp/Af7QJZpNi5n0AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f12095a2320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2b2f908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f121b3b1da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nsQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2e69470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n8BMF6v8Ag+Q2lYLQPPkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2eabef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2f24048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(len(incorrect_predicted_input)):\n",
    "    image = incorrect_predicted_input[i]\n",
    "    display(image)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Differences between two correct and incorrect classifications:\n",
    "\n",
    "    1. Some of incorrect classifications have multiple individual drawings in the same image.\n",
    "    2. Some inccorect prediction have images with very closely highlighted regions.\n",
    "    3. Most incorrect predictions have images which are tilted or rotated."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adding gaussian noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2913400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2ad2f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4wLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvpW3flQAAF7pJREFUeJzt3X1wldW1BvBnERNjCBC+EiIgQhSE\nSqE0ila8wqBWUQv2Q2UcBq0tjOgIVUaoV6e041RpVaDTKx20VrRVtMXWzNRCkTJQWkcJ1AtULhBo\nhMSQYEFJEPK57h85cVLKWes1OTnn0P38Zpgk5znZe+dNFufj3e/eoqogovB0S/UAiCg1WPxEgWLx\nEwWKxU8UKBY/UaBY/ESBYvETBYrFTxQoFj9RoM5KZmdZWVmanZ0dN29ubnbbaGlpMfMePXq4bdTX\n13eqj0SMMzMzs1PfDwDe7Mwosze9n8X6fSVKlOPp3ScjI8PMu3XzH+caGhrM3Due55xzjtuH14Y3\nBgAQkbhZY2Mjmpqa4t+hnU4Vv4hcB2AZgAwAz6rq49b9s7OzUVxcHDc/fvy42+cnn3xi5hMnTnTb\nKCsrM/OTJ0+a+UcffeT24Y0zPz/fzE+cOOH20djYaOZR/pC8Y37RRReZeVNTk9uHV3gff/yx20Zt\nba2Z5+bmmnmUwjxw4ICZez/rxRdf7Pbh/afujQGwj2d5ebn7/Z+2E/mepxCRDAD/A+B6AKMATBeR\nUR1tj4iSqzOv+S8FUKaq+1W1AcAqAFMTMywi6mqdKf6BAA62+7oidhsRnQG6/A0/EZkFYBYAnH32\n2V3dHRFF1JlH/koAg9t9PSh2279Q1RWqWqyqxVlZWZ3ojogSqTPFvwXAhSIyVESyANwGoCQxwyKi\nrtbhp/2q2iQi9wJYi9ZTfc+p6t87M5gop2O8c/SbN2922+jfv7+Ze6dbRo8e7fbhnS6sqqoy87q6\nOrcP75nUeeed57Zx1113mfnYsWPNPMo4vbkCa9euddv42c9+ZubePIDCwkK3D+80mXcqL8opYO94\neX+bgD1HpKKiwv3+Np16za+qbwB4ozNtEFFqcHovUaBY/ESBYvETBYrFTxQoFj9RoFj8RIFi8RMF\nKqmLebS0tJjXqUeZJOFNbImyMIR37bd3ffnBgwfNHPB/lp49e5r5yJEj3T5uvfVWM7/kkkvcNgoK\nCsx8/fr1Zl5TU+P2MW7cODP/xje+4bZx4403mvljjz1m5lF+Z94EmUmTJpm5t6BIFLt373bvY60F\nEWV9hTZ85CcKFIufKFAsfqJAsfiJAsXiJwoUi58oUCx+okBJlI0dEiU7O1uHDBkSN0/EOfoo6wR6\n/XgLhkRZcMFbq37Pnj1m7p1fB4DBgweb+Wuvvea2sWzZMjP31v6PsqmHd+75hhtucNu45557zLxf\nv35m/uijj7p9/OlPfzLzo0ePmnmUxWi8vwtrQ4421pyFQ4cOob6+PtKmHXzkJwoUi58oUCx+okCx\n+IkCxeInChSLnyhQLH6iQLH4iQKV1MU8VNWcNNK3b1+3jby8PDOPsiCIN8knJyfHzL3ddgDgc5/7\nnJlv2LDBzIuKitw+5s6da+ZRJiN5i3FceeWVZu5NWgGAffv2mfmaNWvcNrxJTz/4wQ/M/N5773X7\nOPfcc8189erVZu7t0gT4C8V4k6oAYMSIEXEzbyJSe3zkJwoUi58oUCx+okCx+IkCxeInChSLnyhQ\nLH6iQCX1PH92djaGDx8eN9+/f7/bRnV1tZkPGzbMbePYsWNmfuTIETOPsvjEwoULzdxblGTOnDlu\nH955ZW+hjihmzJhh5q+++qrbxt69e808yoIyH3zwgZl7x3vRokVuH3feeaeZDxo0yMznzZvn9lFY\nWGjmUY7F9u3b42bWpjin6lTxi0g5gFoAzQCaVLW4M+0RUfIk4pF/kqp+mIB2iCiJ+JqfKFCdLX4F\n8EcR2Sois053BxGZJSKlIlIaZd4yESVHZ5/2T1DVShHJB7BORP5PVTe1v4OqrgCwAgB69eqVvKWC\nicjUqUd+Va2MfawB8FsAlyZiUETU9Tpc/CLSXUR6tH0O4FoAOxM1MCLqWp152l8A4LexTQbOAvCS\nqpoXZouIuanGgAED3E6985jeOXzA32jCG8fSpUvdPqyNFQDga1/7mplHuTZ8/Pjx7n081jljwD9W\n3rlvADh+/LiZRzk37W1Q4l0n/+CDD7p9lJSUmPny5cvNfP78+W4fXhtRjsXIkSPjZqWlpe73t+lw\n8avqfgBjOvr9RJRaPNVHFCgWP1GgWPxEgWLxEwWKxU8UKBY/UaBY/ESBSupiHvX19ebCDllZWW4b\nPXv2NPMdO3a4bUybNs3Mn3nmGTP/29/+5vbxne98x8y9zS6amprcPsrKysz861//utvGli1bzNw7\nnpdffrnbh7dJSpTfu3e8vEUyomwu4k3yufrqq83cW/gEALZu3WrmGzdudNuora2Nm7W0tLjf34aP\n/ESBYvETBYrFTxQoFj9RoFj8RIFi8RMFisVPFKiknufv1q2bu1mFx1vk4qyz/B/p9ttvN/P6+noz\nr6mpcfuYMGGCmW/evNnMb7rpJrePV155xcyjLJh6//33m7l3bnv27NluHxdccIGZZ2Zmum28/PLL\nZu5tcuItWhJlHL/4xS/MfPLkyW4fP/nJT8x80qRJbhv9+/ePm+3bt8/9/jZ85CcKFIufKFAsfqJA\nsfiJAsXiJwoUi58oUCx+okAl9Tx/RkYGevXqFTe3rlNu07dvXzPv0aOH24a1cQgA5OTkmPmXv/xl\nt4+1a9eauXWuFgAWLlzo9vGXv/zFzKNsYHLDDTe497FE2STCmzcR5Xd24MABM29sbDTzKOsjePMR\nqqurzfy+++5z+3jiiSfM3FtrAvB/71HxkZ8oUCx+okCx+IkCxeInChSLnyhQLH6iQLH4iQLF4icK\nVFIn+TQ2NpoTJbyJLwBw4sQJMxcRt4133nnHzL/0pS+Z+YIFC9w+3nrrLTO/7bbb3DY83gYQ11xz\njduGN7Fl8eLFZl5RUeH20adPHzPPyMhw2/AW69izZ4+Z5+fnu30cP37czL1JaNu2bXP78P72oiyO\n8vzzz8fNvMVu2nMf+UXkORGpEZGd7W7rIyLrRGRv7GPvyD0SUVqI8rT/eQDXnXLbQgDrVfVCAOtj\nXxPRGcQtflXdBODIKTdPBbAy9vlKAP6EZCJKKx19zV+gqlWxzw8BKIh3RxGZBWAWEG2hRiJKjk6/\n26+qCkCNfIWqFqtqcZQ3dogoOTpa/NUiUggAsY/+WtZElFY6WvwlAGbGPp8J4PXEDIeIksV9zS8i\nLwOYCKCfiFQA+B6AxwG8KiJ3AXgfwC1ROsvMzMSAAQPi5nV1dW4bQ4cONfNHHnnEbWPkyJFmvmTJ\nEjP/wx/+4PZRVFRk5nPnzjXzKBuDDB8+3MxHjBjhtuF5++23zXzcuHFuG4cPHzZzb4EWAPjggw/M\n/NprrzXz/fv3u31UVla697FEWZTk6NGjZt6tm/94PGTIkLjZwYMH3e9v4xa/qk6PE/nbkxBR2uL0\nXqJAsfiJAsXiJwoUi58oUCx+okCx+IkCxeInClRSF/NoaGjAP/7xj7j5HXfc4bYxb948M/cW+wCA\nWbNmmfm6devM3Jpk0cZb+GHlypVmnpub6/bhTVxpaWlx2/BkZ2ebeZRdlrwde6IswOJNfrnzzjvN\nfPfu3W4f3gQxb7GZgQMHun389a9/NfMpU6a4bVgLk5x1VvSS5iM/UaBY/ESBYvETBYrFTxQoFj9R\noFj8RIFi8RMFKqnn+TMzM81zoQ8//LDbhre4xPe//323DW9BhWnT7MWI77//frcPb1MOb+OPwYMH\nu3148w2izBXwNDQ0mHmUTSKsBVwA4NixY24bXj/33XefmUfZEKagIO46tACAjz76yMzffPNNt48r\nr7zSzKMsCNK9e/e4WZTFQD69b+R7EtF/FBY/UaBY/ESBYvETBYrFTxQoFj9RoFj8RIFK6nn+nJwc\nfPGLX+xUGz/+8Y/NfO/evW4bo0ePNvO8vDwz79mzp9tHr169zNw7R++NAQA+/PBDM/c2JwGApqYm\nM/fO0d99991uH5Mn21s8LF261G3j97//vZl7P4d3rAB/ToN3PM877zy3D+/3GmU/S2suwGfZD5OP\n/ESBYvETBYrFTxQoFj9RoFj8RIFi8RMFisVPFCgWP1Gg3Ek+IvIcgBsB1KjqxbHbFgH4NoDDsbs9\npKpveG2pqjmR4uOPP3YHPGrUKDOPMsmnqqrKzL/61a+auTehBAAqKyvN3Jvk4y04AvibXYwZM8Zt\nw9vk4ac//amZb9q0ye1j1apVZr5mzRq3jcOHD5v56tWrzfy73/2u24e3scfWrVvN/IILLnD7mDNn\njpnv2rXLbWPjxo1xsyibqLSJ8sj/PIDrTnP7ElUdG/vnFj4RpRe3+FV1E4AjSRgLESVRZ17z3ysi\n20XkORHpnbAREVFSdLT4lwMoAjAWQBWAJ+PdUURmiUipiJRG2USTiJKjQ8WvqtWq2qyqLQCeAXCp\ncd8VqlqsqsXnnHNOR8dJRAnWoeIXkcJ2X94MYGdihkNEyRLlVN/LACYC6CciFQC+B2CiiIwFoADK\nAczuwjESURdwi19Vp5/m5p93pLNPPvnEPFf6u9/9zm3jm9/8pplHOe/c3Nxs5p///OfNvG/fvm4f\nw4YNM/N33nnHzPPz890+vHP0URZ2UFUzf+yxx8w8yvEuKysz8969/feLvUVFioqKzPzmm292+3jk\nkUfM3FugJcoiL95iNk8//bTbhrWBiff7bI8z/IgCxeInChSLnyhQLH6iQLH4iQLF4icKFIufKFAs\nfqJAyWeZFNBZOTk5OmLEiLh5lMUQfv3rX5t5SUlJp9vo37+/mS9evNjtY+rUqWbuLQjS2Njo9uHd\nJycnx22jvr7ezI8csa/mzs3NdfuwJqVEbcOb0DR+/Hgzj7Jjj7dYR79+/cz8qaeecvvwJgLNnu1P\nlrUmkP3mN79BTU2NvcpLDB/5iQLF4icKFIufKFAsfqJAsfiJAsXiJwoUi58oUEk9z5+VlaUFBQXx\nB+NsQgEADzzwgJnffffdnW7D2zjBO28NAMOHDzfzZ5991swXLFjg9rFu3Tozj/K7HTlypJmXlpaa\neZRNJjZv3mzmTz4Zd/3XT/3zn/80c299yB07drh95OXlmflLL71k5pdcconbx8MPP2zmL774otuG\nNX+jvLwcJ06c4Hl+IoqPxU8UKBY/UaBY/ESBYvETBYrFTxQoFj9RoNxNOxIpIyPDvHY7yqYHGzdu\nNPOJEye6bTz44INm/pWvfMXM6+rq3D68a+n37t1r5rfeeqvbx5o1a8z8iiuucNvYvXu3mXfv3t3M\nH330UbeP/fv3m/mWLVvcNkaNGmXm+/btM/Mo5+CXLFli5tZaFIA/DwAAXnjhBTP3Nh/xVFRURL4v\nH/mJAsXiJwoUi58oUCx+okCx+IkCxeInChSLnyhQLH6iQLmLeYjIYAAvACgAoABWqOoyEekD4BUA\n5wMoB3CLqh612urRo4eOGzfOyt0B19bWmvnYsWPdNpYtW2bmTz/9tJlHWXDBWxhizJgxZj5hwgS3\nj1WrVpn5L3/5S7eNGTNmmHl1dbWZe4tsAEBWVpaZ5+fnu21UVlaaubfhy/z5890+Ro8ebebLly83\n86VLl7p9ZGZmmrm3OYkn0Yt5NAF4QFVHAbgMwD0iMgrAQgDrVfVCAOtjXxPRGcItflWtUtVtsc9r\nAewCMBDAVAArY3dbCWBaVw2SiBLvM73mF5HzAXwBwNsAClS1KhYdQuvLAiI6Q0QufhHJBbAawDxV\nPdY+09Y3Dk775oGIzBKRUhEpjbL5JBElR6TiF5FMtBb+r1T1tdjN1SJSGMsLAdSc7ntVdYWqFqtq\nsfdmBxElj1v80rqe9s8B7FLV9nsQlwCYGft8JoDXEz88IuoqUc4rXAFgBoAdIvJu7LaHADwO4FUR\nuQvA+wBu6ZohElFXcItfVTcDiHfecPJn6ay5uRnHjh2Lm+/cudNt49xzzzXzkpISt43bb7/dzOfM\nmWPmUTYXWblypZm//rr9RGn79u1uH96CIVEMGjTIzP/85z+b+fjx490+vLkANTWnfcX4L7zNLq6+\n+mozP3TokNvH9OnTzbyqqsrMBw8e7PbhzavxNh8BAOu9My7mQUQuFj9RoFj8RIFi8RMFisVPFCgW\nP1GgWPxEgXKv50+k7OxsPf/88+PmQ4cOdds4++yzzdy77jtKG971/t4GEgCwfv16M3/yySfNPMpU\n6KNHzeUTcP3117ttvPXWW2ZeXl5u5lOmTHH7uOqqq8z8pptuctvwjsfq1avN/Ic//KHbh7dpjLcx\niLduAQAUFha69/EcPnw4blZeXo6TJ08m7Hp+IvoPxOInChSLnyhQLH6iQLH4iQLF4icKFIufKFAs\nfqJAJXWST25urlqbakQZi7UYCABkZ2e7bXibg3gLjX7rW99y+5g5c6aZNzc3m7k3SQgA3nvvPTPv\n27ev20ZTU5OZX3755WbubZYB+BtRbN682W1j8eLFZl5WVmbmQ4YMcfvwfifeoiNRJmZ59zl58qTb\nRq9eveJmW7duRW1tLSf5EFF8LH6iQLH4iQLF4icKFIufKFAsfqJAsfiJApXU8/yZmZnap0+fuPmA\nAQPcNrxz1/X19W4b3brZ/+ft2bPHzL2NLgB/A4f58+eb+WWXXeb24W2GUVDgb5zc0NBg5t5GKgcP\nHnT7eOKJJ8z8/fffd9u46KKLzNw7FlH+Lrw5It45+CjzKry/vSgbwuTl5cXNNmzYgKNHj/I8PxHF\nx+InChSLnyhQLH6iQLH4iQLF4icKFIufKFAsfqJAuZN8RGQwgBcAFABQACtUdZmILALwbQBt24c8\npKpvWG3l5eWptXuLt4gGAOzevdvM8/Pz3Tbq6urMPCcnx8yPHz/u9jF58mQz37Ztm5kfOnTI7aOo\nqMjMvUVLAH9HHm8SUCImtkT5Wb3f64EDB8w8yoSniooKM/d2lPKOJQD07t3bzL2/TcBe9KaioiLy\njj32EiutmgA8oKrbRKQHgK0isi6WLVFVe/oWEaUlt/hVtQpAVezzWhHZBWBgVw+MiLrWZ3rNLyLn\nA/gCgLdjN90rIttF5DkRsZ/PEFFaiVz8IpILYDWAeap6DMByAEUAxqL1mcFpt50VkVkiUioipd7r\nRyJKnkjFLyKZaC38X6nqawCgqtWq2qyqLQCeAXDp6b5XVVeoarGqFkfZwpiIksMtfmm9xvDnAHap\n6lPtbm+/0fjNAOxrP4korUR5t/8KADMA7BCRd2O3PQRguoiMRevpv3IAs7tkhETUJZK6mIeIHAbQ\nfuWGfgA+TNoAOo7jTKwzYZxnwhiBfx/nEFXtH+Ubk1r8/9a5SKmqFqdsABFxnIl1JozzTBgj0Llx\ncnovUaBY/ESBSnXxr0hx/1FxnIl1JozzTBgj0IlxpvQ1PxGlTqof+YkoRVJW/CJynYjsFpEyEVmY\nqnF4RKRcRHaIyLsiUprq8bSJXU9RIyI7293WR0TWicje2MeUXm8RZ4yLRKQydjzfFZEpqRxjbEyD\nRWSDiLwnIn8Xkbmx29PteMYbZ4eOaUqe9otIBoA9AK4BUAFgC4Dpqvpe0gfjEJFyAMWqmlbnfEXk\nvwDUAXhBVS+O3fYjAEdU9fHYf6i9VXVBmo1xEYC6dLoUPDZbtbD9ZesApgG4A+l1POON8xZ04Jim\n6pH/UgBlqrpfVRsArAIwNUVjOSOp6iYAR065eSqAlbHPV6L1DyNl4owx7ahqlapui31eC6DtsvV0\nO57xxtkhqSr+gQDa7/NUgfRdI0AB/FFEtorIrFQPxlEQW38BAA6hdfWldJS2l4Kfctl62h7PRFxe\nzzf8fBNUdRyA6wHcE3sqm/a09fVcOp7KiXQpeCqc5rL1T6XT8ezo5fWnSlXxVwJov5PloNhtaUdV\nK2MfawD8FnEuXU4T1W1XW8Y+1qR4PP8m6qXgyXa6y9aRhsezM5fXnypVxb8FwIUiMlREsgDcBqAk\nRWOJS0S6x95YgYh0B3At0vvS5RIAM2OfzwTwegrHclrpeCl4vMvWkWbHM+GX16tqSv4BmILWd/z3\nAfjvVI3DGeMwAP8b+/f3dBongJfR+hSvEa3vmdwFoC+A9QD2AngTQJ80HOOLAHYA2I7W4ipMg2M5\nAa1P6bcDeDf2b0oaHs944+zQMeUMP6JA8Q0/okCx+IkCxeInChSLnyhQLH6iQLH4iQLF4icKFIuf\nKFD/D+lx4morPvsjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2a76be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTxQpFj9RpFj8RJFi8RNF6v8BhQLkNNvFR38AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2a440b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2a2f630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2d28e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2d86860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4wLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvpW3flQAAFwpJREFUeJzt3XtsldWaBvDnpfQibcFSbhW506hQ\nHYWqGC8R7xgTITHkoJ6oUWq8BfVoRhmNqIkxEw8nmjMxqUcjKno0XiKJOoPiBVE5UhAV2nJTaotA\nVZCWW7tb3vmju07F7vf96G733sx6folpu5/dtZZf+7LbrvWtJaoKIgpPv3QPgIjSg8VPFCgWP1Gg\nWPxEgWLxEwWKxU8UKBY/UaBY/ESBYvETBap/KjvLzs7WvLy8hHmU1YaHDh3y+nDb2Ldvn5nn5OQk\nNQYA6NfP/nc1ShuerKyspMYA+Nf8mGOOMfPc3Fy3j9bW1qRyAGhrazPz9vZ2M/e+plHHYYnFYu5z\nrO9/IFoNWFpaWtDW1iZRnptU8YvIZQCeBJAF4B+q+rj1/Ly8PEydOjVhfvDgQbdP7zklJSVuGytX\nrjTz0aNHJzUGwP8ie21438wAUFxcbOZRvuG9f4QmT55s5hMmTHD7qKurM/Nt27a5bTQ2Npp5U1OT\nmR9//PFuHz/88IOZ9+9vl8v27dvdPkpLS83c+0fOU11dHfm5Pf6xX0SyAPwXgBkAJgGYIyKTetoe\nEaVWMr/znwFgs6p+p6qtAP4J4MreGRYR9bVkin8kgPouHzfEHyOio0Cf/8FPRCoAVADR/jhERKmR\nzCv/NgCjunx8fPyx31HVSlUtV9XyKH+JJ6LUSKb4VwEoFZFxIpID4E8AlvTOsIior/X4x35VbROR\n2wH8Dzqm+p5T1fXW5/Tr18+cAquvr0+YdfKm4bwpoShtFBQUmLmIP4163HHHmbm31mDXrl1uH95U\nXllZmdvGvHnzzPzEE09020hWlOmtTZs2mfnChQvN/OOPP3b78L5m3rToscce6/bR0NBg5lGmJK3v\njSNZP5LU7/yq+i6Ad5Npg4jSg8t7iQLF4icKFIufKFAsfqJAsfiJAsXiJwoUi58oUJLK47oKCgrU\nWngydOhQt43vv//ezL0NLgB/UUlLS4uZT5w40e3D2xjCW9A0YsQIt48bb7zRzK+//nq3De9e+8cf\nN7dowJo1a9w+xo0bZ+bTpk1z27jpppvM3FsU9fbbb7t9vPnmm2a+e/duM9+zZ4/bh7fPw4ABA9w2\nBg0alDCrqqpCU1NTpM08+MpPFCgWP1GgWPxEgWLxEwWKxU8UKBY/UaBY/ESBSumhHbFYzNzb3Jtf\nB/w54yjzzt5mHN5e9b/++qvbhzfn681tP/zww24f48ePd5/j8ebxP/30UzP39rIHgC1btpj5zp07\n3TaGDRtm5ldffbWZ33zzzW4fntdee83MvQNOAGDv3r1mHuV6RjmMJQq+8hMFisVPFCgWP1GgWPxE\ngWLxEwWKxU8UKBY/UaBY/ESBSukin5ycHHORTnV1tduGdyqKt1kC4G+YkJ+fb+beQg0AmDFjhpk/\n8MADZu6dGgQA8+fPN/PHHnvMbcPjna9obSzRaeDAgWYe5ZSlJ5980syHDx9u5hdeeKHbxw033GDm\n3jhff/11t48hQ4a4z/FYG7B4m8h0xVd+okCx+IkCxeInChSLnyhQLH6iQLH4iQLF4icKVErn+Vtb\nW81DNyZMmOC2kZOTY+ZR5lG9TRe89QaXX36524c3j79hwwYzX7x4sdvHJ598Yub33nuv28Ztt91m\n5l988YWZR1nzcODAATOP8nWvqakxc2+e/+DBg24f3qEcc+bMMfOVK1e6fTQ0NJj5SSed5LZhXfMj\n2egjqeIXka0AmgG0A2hT1fJk2iOi1OmNV/7pqvpzL7RDRCnE3/mJApVs8SuApSKyWkQqunuCiFSI\nSJWIVLW3tyfZHRH1lmR/7D9HVbeJyDAA74tIraou7/oEVa0EUAkAubm5qTsSmIhMSb3yq+q2+NtG\nAG8BOKM3BkVEfa/HxS8i+SJS2Pk+gEsArOutgRFR30rmx/7hAN6KH4DRH8DLqvrf1ifEYjHznuii\noiK3U2+Ovra21m3jvPPOM/NTTjnFzBcuXOj24R128eCDD5r5L7/84vYRi8XMPDc3121j69atZl5Y\nWGjmUQ4w8eaef/jhB7eN5uZmM580aZKZr1vnvy6tWLHCzG+99VYz9w6UAfz9EaIcYGLtWZGSeX5V\n/Q7Av/X084kovTjVRxQoFj9RoFj8RIFi8RMFisVPFCgWP1GgWPxEgUrpZh4DBgxAWVlZwnz9+vVu\nG97GEN6hHoC/+GXevHlm/vnnn7t9XHPNNWbuLVaKsqmDd0CJdzgJ4G9y4W0+4W2iAQBtbW1m7n1N\nAaC83N4qwrtpLMoBJl9//bWZX3rppUnlAHD33Xeb+dixY902rK+ZavTbZ/jKTxQoFj9RoFj8RIFi\n8RMFisVPFCgWP1GgWPxEgUrpPD8AxDf/6NaIESPcz/ee421OAQBPPfVUUm089NBDbh9jxowx8/79\n7Usf5TCMzZs3u8/xrFmzxsxbWlrMPMpmHt61iLKZx9SpU83c2yTD21wFAM4880wz37Ztm5mfcMIJ\nbh9Dhw4180OHDrlt5OfnJ8yysrLcz+/EV36iQLH4iQLF4icKFIufKFAsfqJAsfiJAsXiJwpUSuf5\nW1tbUV9fnzAvKChw29i0aZOZ33HHHW4b1jwpAHz22WduGx5v/tu7jz7KPe4TJ048ojF1x7vmo0eP\nNnNvfh0A6urqzNy73x8ASkpKkupj8ODBbh/e95Z3kMqUKVPcPryva5QaaGpqSpgdyWG4fOUnChSL\nnyhQLH6iQLH4iQLF4icKFIufKFAsfqJAsfiJApXSRT5ZWVkoKipKmE+ePNlt46OPPjLz2bNnu218\n8cUXZl5ZWWnmpaWlbh/79+83c2/ThsLCQrePO++808x/+ukntw3vABLv4I/m5ma3j+LiYjOPsjDF\nO8xiy5YtZp6Tk+P24R2ksm7dOjOfNWuW24d3yIn3/Q0AZ599dsLM2izncO4rv4g8JyKNIrKuy2OD\nReR9EdkUf5u4ookoI0X5sf95AJcd9th9AJapaimAZfGPiego4ha/qi4HsOuwh68EsCj+/iIAM3t5\nXETUx3r6O/9wVd0ef38HgIS/yIhIBYAKINpNIESUGkn/tV87jgVNeDSoqlaqarmqlh/JzqJE1Ld6\nWvw7RaQEAOJvG3tvSESUCj0t/iUArou/fx2At3tnOESUKu7v/CLyCoDzAQwRkQYADwF4HMBrInIj\ngDoA/uQ6Og6AsOZjBw4c6Lbx/PPPm/mECRPcNubOnWvm3oYKUQ6Z8A7l8DaXOOuss9w+Zs60/84a\n5aCKr776ysy9Qyb27Nnj9uFtnjJs2DC3jXPOOcfMX331VTOPsmGIt6ahurrabcPjHQwyZMgQtw3v\n8JCo3OJX1TkJogt7ZQRElBZc3ksUKBY/UaBY/ESBYvETBYrFTxQoFj9RoFj8RIFK6WYehYWF5kYE\nUU5V8TZDeOKJJ9w2vE0uysrKzDzKYg9r0xIAyM3NNfNbbrnF7cNz1113uc/xFth4J/asWrXK7SMW\ni5n5jh073Db27t1r5oMGDTLzKIu/vMVbURY0ebzrXVtb67bhbQQTFV/5iQLF4icKFIufKFAsfqJA\nsfiJAsXiJwoUi58oUCmd529vb0dTU1PCPC8vz21j/PjxZr506VK3jdbWVjNfvny5mXsbXAD+vLN3\nQMmYMWPcPq666ioz9w6yAIDp06ebeX19vZl7G2AA/mYe3sYngL/BSr9+9uvY9u3bzRwAGhvt3ei8\nOXrv8wHg5JNPNvOXXnrJbcP63vKuw++eG/mZRPT/CoufKFAsfqJAsfiJAsXiJwoUi58oUCx+okCl\ndJ4/FouZBw6ce+65bhsdRwMm9s4777htePdDjxo1ysy9e8sBICcnx8y9dQAHDhxw+/DWK0RZK7B+\n/Xoz99YjRDkMw5t7PuaYY9w2vH527Tr8IOnfO3jwoNvHcccdZ+aFhYVmvm7dOrcPb2+DKGtdrANv\nRcT9/E585ScKFIufKFAsfqJAsfiJAsXiJwoUi58oUCx+okCx+IkC5S7yEZHnAFwBoFFVy+KPLQAw\nF0Dn6RfzVfVdr63s7GyMGDEiYf7zzz+7A/Y2j/AOwwCAkSNHmrm3uYS3sQTgL0oZOHBg0n14G1R4\nh5MA/kEpNTU1Zh5lnN6iqSibYKxcudLMvU1eoiye8a6Xd2iHtYCt08UXX2zm3vcFYNdJlEVXnaK8\n8j8P4LJuHv+bqp4a/88tfCLKLG7xq+pyAPbaSSI66iTzO//tIvKNiDwnIvbBdESUcXpa/E8DmADg\nVADbAfw10RNFpEJEqkSkyrupgYhSp0fFr6o7VbVdVQ8BeAbAGcZzK1W1XFXLrbuRiCi1elT8IlLS\n5cNZAPx7GYkoo0SZ6nsFwPkAhohIA4CHAJwvIqcCUABbAdzch2Mkoj7gFr+qzunm4Wd70pmqmhtQ\n7Nu3z23Dm8c/8cQT3TaqqqrM3Jv7jjJ/vmPHDjP3NvvYuHGj24e3qUiUOWNvUxFPdXW1+xxvbUaU\nDSi8a37ZZd3NRv+fKP+f3jW/4oorzLyhocHtw1rnAkRb69JbuMKPKFAsfqJAsfiJAsXiJwoUi58o\nUCx+okCx+IkCxeInClRKT+zJzs42T0VZunSp24Z3Yo+32AMAPvvsMzNvbm428ygn9hQXF5v5rFmz\nzNwbYxRZWVnuc7yFVd7imvz8fLcPb9HU5s2b3TY2bNhg5hdddJGZ19fXu31MnDjRzGtra8186NCh\nbh+ek046yX3Opk2bEmY8sYeIXCx+okCx+IkCxeInChSLnyhQLH6iQLH4iQKV0nn+WCxmbnIxefJk\nt42nn37azG+99Va3jTfeeMPMv/rqKzM/9thj3T5Gjx5t5oWFhWb++eefu314m3VE2RjCO/hj0qRJ\nZm5tztLJmpcG/GsBAIcOHUqqjQsuuMDtY+3atWburXlYsWKF24e3RsRaB9Ppu+++c58TBV/5iQLF\n4icKFIufKFAsfqJAsfiJAsXiJwoUi58oUCmd51dVWId1RpkzfuWVV8z8qquuctt49NFHzfymm24y\n84MHD7p9zJ8/332O5csvv3Sf492LH2XO2HuOd0hKFN7XtV8//zXIm0Nvb28389LSUreP9evXm7l3\n1uT48ePdPgoKCpLqAwBaWloSZt5+F13xlZ8oUCx+okCx+IkCxeInChSLnyhQLH6iQLH4iQLF4icK\nlLvIR0RGAXgBwHAACqBSVZ8UkcEAXgUwFsBWALNVdbfVlqqaizG8jSUAoKSkxMwfeeQRt42///3v\nZr5o0SIzj7L5xIABA8z82muvNfNBgwa5fUTZrMPjHTTRGweYeIuioiyaampqMnPvgJIoG2B433/e\n5illZWVuHwcOHDDz1atXu23k5eUlzKIsmPrtuRGe0wbgL6o6CcA0ALeJyCQA9wFYpqqlAJbFPyai\no4Rb/Kq6XVXXxN9vBlADYCSAKwF0vkQuAjCzrwZJRL3viH7nF5GxAE4D8C8Aw1W18+ekHej4tYCI\njhKRi19ECgC8AeBOVf3dL2DacTdBt3cUiEiFiFSJSJV38wURpU6k4heRbHQU/mJVfTP+8E4RKYnn\nJQAau/tcVa1U1XJVLY9yaiwRpYZb/NJx5u+zAGpUdWGXaAmA6+LvXwfg7d4fHhH1lSj3858N4M8A\nvhWRzo3N5wN4HMBrInIjgDoAs/tmiETUF9ziV9UVACRBfOGRdBaLxfDjjz8mzKNshuAdnPDyyy+7\nbYwdO9bM77nnHrcNz9atW828rq7OzPv39/9dHjZsmJlb17pTfX29mY8cOdLMi4uL3T6+//57M4/y\ntyBvPcGvv/5q5jNn+pNR3kYx3kYcl1xyiduHt0mLd60Aew0IN/MgIheLnyhQLH6iQLH4iQLF4icK\nFIufKFAsfqJApfTQjtzcXIwbNy5hHuVe5NNOO83Mo7TxzDPPmLk393366ae7fXj36y9ZssTMX3zx\nRbePJ554wsytA1I6eUuue+PAjcGDB5t5lLnp4cPt+8Y++OADM58yZYrbx/nnn2/m3vqQ8vJyt48F\nCxaYubdfBWDvJ1FbW+t+fie+8hMFisVPFCgWP1GgWPxEgWLxEwWKxU8UKBY/UaBY/ESBkiO5+T9Z\nhYWFOnXq1IT5kCFD3Da8gxWiHKhRU1Nj5t6iFO8ACcBfjDR37lwzP/fcc90+vI1Nli1b5rbx3nvv\nJdXHL7/84vbhHQxSWlrqttHY2O0Wkb+ZMWOGmVdUVLh9eBoaGszc28AFAO6//34zz8/Pd9vYuXNn\nwmzDhg3Yv39/os13foev/ESBYvETBYrFTxQoFj9RoFj8RIFi8RMFisVPFKiUzvMXFRXp9OnTE+a7\nd+922/DG29bW5rbR3Nxs5gMGDDDz3Nxctw9vIw1vzviCCy5w+/DmtmfP7vtDlLxrCURbe9HXWlpa\n3Od8+OGHZr548WIz976mgL8uYuDAgW4b1gYqa9euRXNzM+f5iSgxFj9RoFj8RIFi8RMFisVPFCgW\nP1GgWPxEgWLxEwXKXeQjIqMAvABgOAAFUKmqT4rIAgBzAXTu9jBfVd+12iooKNCysrKE+d69e90B\nDxo0yBuv28bGjRvN3FvkM2LECLePHTt2mLl1HYBoC572799v5gcOHHDbmDZtmpl7G5sUFRW5fezZ\ns8fMvdN4AH9xTF1dnZlHOcmmoKDAzL0FTd6mJYC/ECjKCUh5eXkJs9raWuzbty/SIp8ox3W1AfiL\nqq4RkUIAq0Xk/Xj2N1W1z4wioozkFr+qbgewPf5+s4jUABjZ1wMjor51RL/zi8hYAKcB+Ff8odtF\n5BsReU5E/J//iChjRC5+ESkA8AaAO1W1CcDTACYAOBUdPxn8NcHnVYhIlYhURTk1lohSI1Lxi0g2\nOgp/saq+CQCqulNV21X1EIBnAJzR3eeqaqWqlqtqeXZ2dm+Nm4iS5Ba/dPz5/FkANaq6sMvjXQ8S\nnwVgXe8Pj4j6SpS/9p8N4M8AvhWRtfHH5gOYIyKnomP6byuAm/tkhETUJ1K6mYeI/ASg64TsEAA/\np2wAPcdx9q6jYZxHwxiBP45zjKr6Cw6Q4uL/Q+ciVapanrYBRMRx9q6jYZxHwxiB5MbJ5b1EgWLx\nEwUq3cVfmeb+o+I4e9fRMM6jYYxAEuNM6+/8RJQ+6X7lJ6I0SVvxi8hlIrJBRDaLyH3pGodHRLaK\nyLcislZEqtI9nk7x+ykaRWRdl8cGi8j7IrIp/jat91skGOMCEdkWv55rReTydI4xPqZRIvKRiFSL\nyHoRmRd/PNOuZ6Jx9uiapuXHfhHJArARwMUAGgCsAjBHVatTPhiHiGwFUK6qGTXnKyLnAdgL4AVV\nLYs/9p8Adqnq4/F/UItU9d8zbIwLAOzNpFvB46tVS7retg5gJoDrkVnXM9E4Z6MH1zRdr/xnANis\nqt+paiuAfwK4Mk1jOSqp6nIAuw57+EoAi+LvL0LHN0baJBhjxlHV7aq6Jv5+M4DO29Yz7XomGmeP\npKv4RwKo7/JxAzJ3jwAFsFREVotIRboH4xge338BAHagY/elTJSxt4Ifdtt6xl7P3ri9nn/w852j\nqlMAzABwW/xH2YynHb/PZeJUTqRbwdOhm9vWf5NJ17Ont9cfLl3Fvw3AqC4fHx9/LOOo6rb420YA\nbyHBrcsZYmfn3Zbxt41pHs8fRL0VPNW6u20dGXg9k7m9/nDpKv5VAEpFZJyI5AD4E4AlaRpLQiKS\nH//DCkQkH8AlyOxbl5cAuC7+/nUA3k7jWLqVibeCJ7ptHRl2PXv99npVTct/AC5Hx1/8twD4j3SN\nwxnjeABfx/9bn0njBPAKOn7Ei6HjbyY3AigGsAzAJgAfABicgWN8EcC3AL5BR3GVZMC1PAcdP9J/\nA2Bt/L/LM/B6Jhpnj64pV/gRBYp/8CMKFIufKFAsfqJAsfiJAsXiJwoUi58oUCx+okCx+IkC9b8B\n3Z7jubmdLQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2d73198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nmMJPyswAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2970b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ni58oUix+okix+IkixeInitT/A9tLsYWCj/KlAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e292d278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import skimage\n",
    "gaussian_noise_images= []\n",
    "for i in range(len(correct_predicted_input)):\n",
    "    images = correct_predicted_input[i]\n",
    "    images = images/images.max()\n",
    "    new_image = skimage.util.random_noise(images, mode='gaussian')\n",
    "    gaussian_noise_images.append(new_image)\n",
    "    display(new_image)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 1\n",
      "3 1\n",
      "2 1\n",
      "2 1\n",
      "0 1\n",
      "0 1\n",
      "0 1\n",
      "1 1\n",
      "2 1\n",
      "2 1\n"
     ]
    }
   ],
   "source": [
    "# Predict with new images\n",
    "for i in range(len(gaussian_noise_images)):\n",
    "    x = Variable(torch.from_numpy(gaussian_noise_images[i].astype(np.float32)))\n",
    "    true_label = correct_labels[i]\n",
    "    out = model(x)\n",
    "    y_pred = np.argmax(out.data.numpy())\n",
    "    print(true_label, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Does the classifier still classify all 10 images correctly?\n",
    "\n",
    "Most predictions are incorrect. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Flip images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ntbX8Fzi6oQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e29ed160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQv+S+wEFp3QAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2d09f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2db5e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2dbeb38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4wLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvpW3flQAADylJREFUeJzt3XusVeWZx/HfM3ITQUUYjwRUSkNI\ntKg1aLzFOJm0immCSAIlQiBpevyjJmMyMRBHU+/WwXYyMcGEgvE4YaxNaEeskwCaiY4KDUgooNji\nBYPcyRkBL6jAM3+cxfQMst93n73Xvhye7ychZ5/1rPO+T3b8ufba62buLgDx/E2rGwDQGoQfCIrw\nA0ERfiAowg8ERfiBoAg/EBThB4Ii/EBQA5o5mZlxOiHQYO5u1axX15bfzG4xsz+b2ftmtqCesQA0\nl9V6br+ZnSHpL5J+IOkTSeskzXL3dxN/w5YfaLBmbPmvlvS+u3/o7l9L+o2kqXWMB6CJ6gn/GEk7\nev3+SbEMQD/Q8C/8zKxTUmej5wHQN/WEf6ekC3v9PrZY9v+4+2JJiyX2+YF2Us/H/nWSJpjZd8xs\nkKQfS1pRTlsAGq3mLb+7HzWzuyStlHSGpGfc/Z3SOgPQUDUf6qtpMj72Aw3XlJN8APRfhB8IivAD\nQRF+ICjCDwRF+IGgCD8QFOEHgiL8QFCEHwiK8ANBEX4gKMIPBEX4gaAIPxAU4QeCIvxAUIQfCIrw\nA0ERfiAowg8ERfiBoAg/EBThB4Jq+IM6o7rxxhuT9fnz5yfrEydOzM4xdOjQZL2aB7Js3bo1Wd+0\naVOyvnnz5uwce/bsya7TaEeOHMmus2HDhmT94MGDZbXTFtjyA0ERfiAowg8ERfiBoAg/EBThB4Ii\n/EBQVs2x4NImM2veZA105plnZtc5dOhQsr579+5kfeXKldk5vvjii2R90KBB2TEuvfTSZH3SpEnJ\n+rnnnpudo784fvx4sp475+GNN97IzrFs2bJkfe3atdkxctzdqlmvrpN8zGy7pMOSjkk66u6T6xkP\nQPOUcYbf37n7gRLGAdBE7PMDQdUbfpe0yszeNrPOU61gZp1mtt7M1tc5F4AS1fux/wZ332lm50ta\nbWbvufvrvVdw98WSFkunzxd+wOmgri2/u+8sfu6T9HtJV5fRFIDGqzn8ZnaWmQ0/8VrSDyVtKasx\nAI1V83F+Mxuvnq291LP78O/u/mjqbwYMGODDhw+vWL/kkkuy87711lt96LIxRowYkV2nu7s7WV+w\nYEGy/sQTT/Spp0YxSx8yHjt2bHaMkSNHltVOzc4+++zsOtddd12yfv3119dVl/LnRTz44IPZMXLr\nNPw4v7t/KOnyWv8eQGtxqA8IivADQRF+ICjCDwRF+IGgCD8QFOEHgmrqzTwuuOACnz17dsX6448/\nnh3jnHPOSda//PLLPvfVCLt27UrW16xZk6xPnz69zHbQBEOGDMmu09XVlaxPmTIlO0ZHR0fF2pEj\nR3T8+PGqTvJhyw8ERfiBoAg/EBThB4Ii/EBQhB8IivADQTX1OP+wYcM89RCIah56sHTp0mT9zjvv\n7HNfjXDfffcl6w8//HCy/tRTT2XnuPvuu5P13EMo0HzXXHNNsp47/0OSZsyYUbH2yiuvqLu7m+P8\nACoj/EBQhB8IivADQRF+ICjCDwRF+IGgynhEd9U+//xzrV27tmK9mgcWPPTQQ8n6zp07s2M88sgj\nyXoZx8dzcwwePDhZz50nIOUfADFv3rzsGJwL0FybNm2qe4zUg1IGDhxY9Ths+YGgCD8QFOEHgiL8\nQFCEHwiK8ANBEX4gKMIPBNXUk3xyHn300ew6Y8aMSdarOVHoqquuStbvueeeZP29997LzpFz//33\nJ+sHDx7MjrFw4cJkfeXKldkxli1bll0H5ZkzZ07dY2zcuLFirS8Prclu+c3sGTPbZ2Zbei07z8xW\nm9m24ueIqmcE0Baq+dj/rKRbTlq2QNKr7j5B0qvF7wD6kWz43f11Sd0nLZ4q6cRDx7ok3VZyXwAa\nrNZ9/g5331283iOp4pMDzaxTUmeN8wBokLq/8HN3N7OKtwB298WSFktSaj0AzVXrob69ZjZakoqf\n+8prCUAz1Br+FZLmFq/nSnqxnHYANEv2oR1m9rykmySNkrRX0s8l/Yek30q6SNLHkma4+8lfCp5q\nrIZ/7J87d252nUWLFiXrQ4cOTdaruSHD8uXLk/UPPvggWf/qq6+yczz99NPJ+qpVq7Jj3HHHHdl1\nUJ1BgwZl18ndbGb9+vXZMaZMmZKsu3tVD+3I7vO7+6wKpb+vZgIA7YnTe4GgCD8QFOEHgiL8QFCE\nHwiK8ANBEX4gqLa6mUcZurq6suu8/PLLyfrtt9+erM+YMSM7R+5mHQMGNP6tP//88xs+B/4qd8Kc\nJA0bNixZr+Ykn7Kw5QeCIvxAUIQfCIrwA0ERfiAowg8ERfiBoLI38yh1skD38Bs+fHiyPnLkyGR9\n5syZ2Tkee+yxZH3+/PnZMZ588snsOijPmjVrkvVDhw5lx7j55puT9Wpv5sGWHwiK8ANBEX4gKMIP\nBEX4gaAIPxAU4QeCOu2u528Xhw8fTtafffbZZD13TwFJeu2115L1JUuWZMdAc61bty5Znz17dpM6\nYcsPhEX4gaAIPxAU4QeCIvxAUIQfCIrwA0ERfiCo7M08zOwZST+StM/dv1cse0DSTyXtL1a7193/\nMztZoJt5jBo1Klnfv39/sr5w4cLsHLmbdTTzRi2ozpw5c5L15557LjvGhAkTKtZ27NihI0eOlHYz\nj2cl3XKK5f/i7lcU/7LBB9BesuF399cldTehFwBNVM8+/11mtsnMnjGzEaV1BKApag3/05K+K+kK\nSbsl/bLSimbWaWbrzax5TyAEkFVT+N19r7sfc/fjkn4t6erEuovdfbK7T661SQDlqyn8Zja616/T\nJG0ppx0AzZK9nt/Mnpd0k6RRZvaJpJ9LusnMrpDkkrZLurOBPQJogGz43X3WKRYvbUAvp5WjR4/W\n9fcfffRRdh2O4/c/27Ztq3uMcePGVazt3bu36nE4ww8IivADQRF+ICjCDwRF+IGgCD8QFOEHgiL8\nQFA8sadBPv3002T94MGDyfrll19eZjtoE7mbvFRj3759FWt9ObmMLT8QFOEHgiL8QFCEHwiK8ANB\nEX4gKMIPBJV9aEepkwV6aEfOkiVLkvWZM2dmx7j22muT9S1buLtaMw0ZMiS7zurVq5P1as7vGDt2\nbMXaZ599pmPHjpX20A4ApyHCDwRF+IGgCD8QFOEHgiL8QFCEHwiK4/wt0tHRkayvWbMmO8bgwYOT\n9Xnz5mXHyB13jiT3fk6aNClZX7RoUXaOK6+8MlmfNm1adoyXXnopWXd3jvMDqIzwA0ERfiAowg8E\nRfiBoAg/EBThB4Ii/EBQ2ZN8zOxCSc9J6pDkkha7+7+a2XmSXpA0TtJ2STPc/X8yY3GST5UmTpyY\nXeeFF15I1i+77LLsGN3d3cn6wIED66pXs86OHTuyYyxfvjxZv+iii5L13Ak6kjRhwoRkfcCA9DNu\ncu+lJM2aNStZX7VqVXaMnDJP8jkq6R/d/RJJ10j6mZldImmBpFfdfYKkV4vfAfQT2fC7+25331C8\nPixpq6QxkqZK6ipW65J0W6OaBFC+Pu3zm9k4Sd+X9EdJHe6+uyjtUc9uAYB+ouoHdZrZMEnLJd3t\n7ofM/rpb4e5eaX/ezDolddbbKIByVbXlN7OB6gn+Mnf/XbF4r5mNLuqjJZ3y0aHuvtjdJ7v75DIa\nBlCObPitZxO/VNJWd/9Vr9IKSXOL13MlvVh+ewAapZqP/ddLmiNps5ltLJbdK+kXkn5rZj+R9LGk\nGY1pEUAjcDOPfix3/LyzM/9Vy/jx45P1b775Jln/+uuvs3Pkxpg+fXp2jIsvvjhZ37VrV7K+efPm\n7By5h5zkxnjzzTezcxw4cCC7Tr24mQeAJMIPBEX4gaAIPxAU4QeCIvxAUIQfCIrj/MBphuP8AJII\nPxAU4QeCIvxAUIQfCIrwA0ERfiAowg8ERfiBoAg/EBThB4Ii/EBQhB8IivADQRF+ICjCDwRF+IGg\nCD8QFOEHgiL8QFCEHwiK8ANBEX4gKMIPBEX4gaCy4TezC83sv8zsXTN7x8z+oVj+gJntNLONxb9b\nG98ugLJkH9dlZqMljXb3DWY2XNLbkm6TNEPSZ+7+ZNWT8bguoOGqfVzXgCoG2i1pd/H6sJltlTSm\nvvYAtFqf9vnNbJyk70v6Y7HoLjPbZGbPmNmIknsD0EBVh9/MhklaLuludz8k6WlJ35V0hXo+Gfyy\nwt91mtl6M1tfQr8ASlLVI7rNbKCkP0ha6e6/OkV9nKQ/uPv3MuOwzw80WGmP6DYzk7RU0tbewS++\nCDxhmqQtfW0SQOtU823/DZL+W9JmSceLxfdKmqWej/wuabukO4svB1NjseUHGqzaLX9VH/vLYmb7\nJX3ca9EoSQea1kDt6LNc/aHP/tCj9O0+L3b3v63mD5sa/m9Nbrbe3Se3rIEq0We5+kOf/aFHqb4+\nOb0XCIrwA0G1OvyLWzx/teizXP2hz/7Qo1RHny3d5wfQOq3e8gNokZaF38xuMbM/m9n7ZragVX3k\nmNl2M9tcXLbcNqcoF9dT7DOzLb2WnWdmq81sW/GzpddbVOix7S4FT1y23m7vZ6mX17fkY7+ZnSHp\nL5J+IOkTSeskzXL3d5veTIaZbZc02d3b6pivmd0o6TNJz504rdrM/llSt7v/ovgf6gh3n99mPT6g\nPl4K3miJy9bnqb3ez9Iur5dat+W/WtL77v6hu38t6TeSpraol37J3V+X1H3S4qmSuorXXer5D6Nl\nKvTYdtx9t7tvKF4flnTisvV2ez8r9VmTVoV/jKQdvX7/RO17jwCXtMrM3jazzlY3k9HR6xTrPZI6\nWtlMQtteCn7SZett+36WcXk9X/jl3eDuV0qaIulnxUfZtuc9+3PteCinqkvBW+EUl63/n3Z6P2u9\nvP5krQr/TkkX9vp9bLGs7bj7zuLnPkm/V88uS7vae+Jqy+Lnvhb38y3uvtfdj7n7cUm/Vpu8n8Vl\n68slLXP33xWL2+79PFWftb6nrQr/OkkTzOw7ZjZI0o8lrWhRLxWZ2VnFFysys7Mk/VDtfenyCklz\ni9dzJb3Ywl5OqR0vBa902bra7P0s/fJ6d2/JP0m3qucb/w8k/VOr+sj0OF7Sn4p/77RTn5KeV89H\nvG/U853JTySNlPSqpG2SXpF0Xhv2+G/quTx8k3rCNboN3ssb1PORfpOkjcW/W9vw/azUZ03vKWf4\nAUHxhR8QFOEHgiL8QFCEHwiK8ANBEX4gKMIPBEX4gaD+FxKc4dFYbxoMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2dab7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e29ac048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ncAn1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e292d278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\noSd2EWrNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2970748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQKIIP5Aowg8kivADifp/3S0vliERLP8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e2a891d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4wLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvpW3flQAAEWZJREFUeJzt3XmMVXWWB/DvEejEAjQyakloasAG\nElmUHipobKOMSgvYERFR0CAqdmGCOgSCQ1DShSQqkxECLh0KISwiPSA7kU0yYqKGiKQolnJBKNKF\nrGFkCUIpnPmjLm01Vv3Oq/fu2+p8P0mlXt1z6/c7XurrW+4mqgoi8ueKbDdARNnB8BM5xfATOcXw\nEznF8BM5xfATOcXwEznF8BM5xfATOdU8k5OJSF4cTigiwXpBQYE5RsuWLVPq4aeffjLXOXnyZLB+\n8eLFlHqg/KSq4T/gSErhF5F+AGYAaAbgXVV9PZXxckXz5uHN0qNHD3OMW2+9NVi3Dqv+/vvvzTnW\nr18frJ85c8Ycg/xK+mW/iDQD8DaA/gC6AhgmIl3jaoyI0iuV9/y9AexV1X2qWgPgbwAGxtMWEaVb\nKuFvB+DvdX6ujpYRUR5I+wd+IlICoCTd8xBR46QS/oMA2tf5+bfRsn+iqmUAyoD8+bSfyINUXvZ/\nAaCziHQUkd8AGApgdTxtEVG6Jf3Mr6o/i8hzADagdlffXFXdHVtnaXTbbbcF6ytXrgzWCwsL42wn\naWfPng3Wly9fbo6xaNGiYH3Dhg3BOq8Elb9Ses+vqh8C+DCmXogog3h4L5FTDD+RUww/kVMMP5FT\nDD+RUww/kVMMP5FTksmDNDJxeO/gwYPNdRYuXBisf/fdd8H6iy++aM7x+eefB+s1NTXB+k033WTO\n8fjjjwfrw4YNM8e44YYbgvW1a9cG68OHDzfn+OGHH8x1KD6JXsyDz/xETjH8RE4x/EROMfxETjH8\nRE4x/EROMfxETuXdfv7u3bsH6+Xl5eYYW7ZsCdatYwXyZb91s2bNzHWefvrpYH3mzJnBenV1tTnH\nkCFDgvVE/s0ocdzPT0RBDD+RUww/kVMMP5FTDD+RUww/kVMMP5FTDD+RU3l3kM+YMWOC9WnTpplj\nXH/99cH68ePHG9VTU9arV69gfdmyZeYY1vYeOXKkOcbixYvNdagWD/IhoiCGn8gphp/IKYafyCmG\nn8gphp/IKYafyKnm2W6gsW6//fZg/euvvzbH4H78X7Rq1SpYf/TRR4P1NWvWmHN07tw5WH///ffN\nMTp16hSsT5kyxRyD/llK4ReRKgCnAVwA8LOqFsfRFBGlXxzP/P+uqnwqJcozfM9P5FSq4VcAG0Xk\nSxEpqW8FESkRkW0isi3FuYgoRqm+7L9DVQ+KyPUANonIV6r6Sd0VVLUMQBmQmbv0ElFiUnrmV9WD\n0fejAFYA6B1HU0SUfkmHX0RaikjrS48B/BHArrgaI6L0SuVlfyGAFSJyaZz3VXV9LF0F3HjjjcH6\n7t27091CkzJ06NBgffz48SnPMXbs2GC9qqrKHGPy5MnBekVFRbC+atUqcw5vkg6/qu4DcEuMvRBR\nBnFXH5FTDD+RUww/kVMMP5FTDD+RUww/kVMMP5FTeXcxD8vFixez3UJesW7Kcfbs2WD9o48+MueY\nMGFCsN6hQwdzjG7dugXr8+bNC9at/04A2Ldvn7lOU8JnfiKnGH4ipxh+IqcYfiKnGH4ipxh+IqcY\nfiKn8m4//+nTp4P1Nm3aZKiTpuGhhx4K1mtqaoL1kydPmnNY/yYtWrQwx7AuOrJ9+/ZgfenSpeYc\n1g1hzp8/b46RT/jMT+QUw0/kFMNP5BTDT+QUw0/kFMNP5BTDT+RU3u3n37FjR7D+xBNPZKiTpmHA\ngAHB+rp164L14cOHm3MsXrw4WD916pQ5hrWO9e++fr19P5kxY8YE61OnTjXHyCd85idyiuEncorh\nJ3KK4SdyiuEncorhJ3KK4SdyiuEnckpUNXOTiQQnExFzjLKysmD9mWeeMcfo2LFjsF5VVWWO4YV1\nIY6ioiJzjMrKymA9ExfJ+OCDD8x17rnnnmC9S5cuwfqxY8ca1VO6qKodJCTwzC8ic0XkqIjsqrOs\njYhsEpFvo+/XpNIsEWVeIi/75wHod9myCQA2q2pnAJujn4koj5jhV9VPAJy4bPFAAPOjx/MBPBhz\nX0SUZsme2FOoqoeix4cBFDa0ooiUAChJch4iSpOUz+pTVQ19kKeqZQDKAPsDPyLKnGR39R0RkbYA\nEH0/Gl9LRJQJyYZ/NYAR0eMRAFbF0w4RZYq5n19EFgPoA+BaAEcA/AXASgBLABQBOADgEVW9/EPB\n+sYKTtahQwez4f3795vrWF544YVg/c0330x5DuuYBetYgwMHDphzXLhwoVE9eZbI35Z1PMKCBQuC\n9VGjRjWmpbRJdD+/+Z5fVYc1UAofEUFEOY2H9xI5xfATOcXwEznF8BM5xfATOcXwEznF8BM5lVMX\n87jqqqvMMU6ePJlyH3v27AnWu3XrlvIckyZNCtZfeeWVYH3jxo3mHAMHDgzWz507Z45BvygtLQ3W\nX3755WC9uLjYnKO8vLwxLSUltot5EFHTxPATOcXwEznF8BM5xfATOcXwEznF8BM5lVP7+RNh7Se9\n5ZZbUp0Cffr0Cda3bt1qjnHiRPjaJrt37w7WE9ln/NRTTwXr8+bNM8egXxQUFATr1gVW1q5da85h\n/ZvFgfv5iSiI4SdyiuEncorhJ3KK4SdyiuEncorhJ3Iq5Xv1ZdqsWbOC9XfeeSflOZ599tlgvaKi\nwhzjyiuvDNbffffdYD2R/fzt2rUz10m39u3bm+s0a9YsWK+qqoqpm9ScPXs2WF+6dGmw/thjj5lz\nWH9b58+fN8eIC5/5iZxi+ImcYviJnGL4iZxi+ImcYviJnGL4iZxi+ImcMi/mISJzAfwJwFFV7R4t\nKwXwZwDHotUmquqH5mQxXMzj6quvDtarq6vNMVq1ahWs19TUBOvXXXedOUdlZWWwbt2gxOoRAEpK\nSoL12bNnm2NYrBuDrFy50hzjwoULwfr48ePNMaZPn26uk2533nlnsL5lyxZzjEGDBgXriWxPS5wX\n85gHoF89y6eras/oyww+EeUWM/yq+gmA8DWpiCjvpPKe/zkRqRCRuSJyTWwdEVFGJBv+vwL4HYCe\nAA4BeKOhFUWkRES2ici2JOciojRIKvyqekRVL6jqRQCzAfQOrFumqsWqap+mRkQZk1T4RaRtnR8H\nAdgVTztElCnm+fwishhAHwDXikg1gL8A6CMiPQEogCoAo9LYIxGlQd7dtMMyevRoc5233norWF++\nfHmwPnjwYHOOTp06BesvvfRSsJ7IBUPefvvtYN06XiERM2bMCNati1MA9r7rIUOGmGPcfPPNwfqu\nXel/8XnFFeEXytZNPQDg008/DdaHDh3aqJ7qw5t2EFEQw0/kFMNP5BTDT+QUw0/kFMNP5BTDT+QU\nw0/kVJM7yEfEPr7BOujk3nvvDdZ79eplzvHVV1+Z6+SDfv3qu5TDL9atW2eOMWnSpGB94sSJ5hjW\nAU2JXBAk3d54o8Hz2/7BOigqkQvFWHcW4kE+RBTE8BM5xfATOcXwEznF8BM5xfATOcXwEzllXskn\n3yRy3MLIkSOD9R07dgTrS5YsMefo06dPsH7iRH5cDf3uu+9OeQzrAivWRTIAoHnz3P9TTeTYjoKC\ngmC9devW5hjWfv5E8ZmfyCmGn8gphp/IKYafyCmGn8gphp/IKYafyKnc33maBsePHw/WrZtIbNiw\nwZxj06ZNwXrfvn2D9Vw5DsA6R93algDQv3//YL2qqsoco7S01Fwn24qKisx1fvzxx2D9yJEjcbVj\n4jM/kVMMP5FTDD+RUww/kVMMP5FTDD+RUww/kVMMP5FT5k07RKQ9gAUACgEogDJVnSEibQD8D4AO\nAKoAPKKq/2eMlbk7hKTRXXfdZa6zdu3aYP3w4cPB+ogRI8w5PvvsM3MdypyFCxea61g3fOnatWvK\nfcR5046fAYxT1a4AbgMwWkS6ApgAYLOqdgawOfqZiPKEGX5VPaSq26PHpwFUAmgHYCCA+dFq8wE8\nmK4miSh+jXrPLyIdAPwewFYAhap6KCodRu3bAiLKEwmf2CMirQAsAzBGVU/VvSGmqmpD7+dFpARA\nSaqNElG8EnrmF5EWqA3+IlVdHi0+IiJto3pbAEfr+11VLVPVYlUtjqNhIoqHGX6pfYqfA6BSVafV\nKa0GcOkj6REAVsXfHhGlSyIv+/8AYDiAnSJSHi2bCOB1AEtEZCSAAwAeSU+LRJQO5n7+WCdrIvv5\nE1FcHH6X89577wXrnTp1Mud47bXXgvUpU6aYY9TU1JjrUC3r5iI7d+40x7AuXHL//fc3pqV6xbmf\nn4iaIIafyCmGn8gphp/IKYafyCmGn8gphp/IKe7nz5KCgoJgferUqeYYo0ePDtbLy8uDdQAYO3Zs\nsP7xxx+bY3jx/PPPB+szZ840x3j44YeD9WXLljWqp/pwPz8RBTH8RE4x/EROMfxETjH8RE4x/ERO\nMfxETjH8RE7xIJ881rdv32B91qxZ5hgdO3YM1rds2RKsr1plX73tm2++Cdb37t1rjrF///5gvXnz\n8EWpevToYc4xefLkYP2+++4L1tesWWPO8cADD5jrpIoH+RBREMNP5BTDT+QUw0/kFMNP5BTDT+QU\nw0/kFPfzN2EtWrQw13nyySeD9XHjxgXrXbp0Meeoe1PXXFZdXR2sv/rqq8H6nDlzzDkycZMU7ucn\noiCGn8gphp/IKYafyCmGn8gphp/IKYafyCmGn8gp8yAfEWkPYAGAQgAKoExVZ4hIKYA/AzgWrTpR\nVT80xuJBPk1M69atzXU6d+6cUh0AioqKgvXz588H68eOHQvWAWDFihXB+rlz58wxckGiB/mEL39S\n62cA41R1u4i0BvCliGyKatNV9b+TbZKIsscMv6oeAnAoenxaRCoBtEt3Y0SUXo16zy8iHQD8HsDW\naNFzIlIhInNF5JqYeyOiNEo4/CLSCsAyAGNU9RSAvwL4HYCeqH1l8EYDv1ciIttEZFsM/RJRTBIK\nv4i0QG3wF6nqcgBQ1SOqekFVLwKYDaB3fb+rqmWqWqyqxXE1TUSpM8MvtedjzgFQqarT6ixvW2e1\nQQB2xd8eEaVLIp/2/wHAcAA7RaQ8WjYRwDAR6Yna3X9VAEalpUMiSotMX8zjGIADdRZdC+B4xhpI\nHvuMVz70mQ89Ar/u819V9bpEfjGj4f/V5CLb8uGzAPYZr3zoMx96BFLrk4f3EjnF8BM5le3wl2V5\n/kSxz3jlQ5/50COQQp9Zfc9PRNmT7Wd+IsqSrIVfRPqJyNcisldEJmSrD4uIVInIThEpz6VDlKPz\nKY6KyK46y9qIyCYR+Tb6ntXzLRrosVREDkbbs1xEBmSzx6in9iLyvyKyR0R2i8h/RMtzbXs21GdS\n2zQrL/tFpBmAbwD0BVAN4AsAw1R1T8abMYhIFYBiVc2pfb4icieAMwAWqGr3aNl/ATihqq9H/0O9\nRlX/M8d6LAVwJpdOBY+OVm1b97R1AA8CeBK5tT0b6vMRJLFNs/XM3xvAXlXdp6o1AP4GYGCWeslL\nqvoJgBOXLR4IYH70eD5q/zCypoEec46qHlLV7dHj0wAunbaea9uzoT6Tkq3wtwPw9zo/VyN3rxGg\nADaKyJciUpLtZgyF0fUXAOAwaq++lIty9lTwy05bz9ntGcfp9fzAz3aHqv4bgP4ARkcvZXOe1r6f\ny8VdOQmdCp4N9Zy2/g+5tD2TPb3+ctkK/0EA7ev8/NtoWc5R1YPR96MAVqCBU5dzxJFLZ1tG349m\nuZ9fSfRU8Eyr77R15OD2TOX0+stlK/xfAOgsIh1F5DcAhgJYnaVeGiQiLaMPViAiLQH8Ebl96vJq\nACOixyMArMpiL/XKxVPBGzptHTm2PWM/vV5Vs/IFYABqP/H/DsBL2erD6PFGADuir9251CeAxah9\nifcTaj8zGQngXwBsBvAtgI8AtMnBHhcC2AmgArXhapsD2/IO1L6krwBQHn0NyMHt2VCfSW1THuFH\n5BQ/8CNyiuEncorhJ3KK4SdyiuEncorhJ3KK4SdyiuEncur/AQPhjgo3KGQ8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11e292bc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from skimage import transform\n",
    "#from sklearn.preprocessing import normalize\n",
    "flip_image= []\n",
    "for i in range(len(correct_predicted_input)):\n",
    "    images = correct_predicted_input[i]\n",
    "    images = images/images.max()\n",
    "    flip_image.append((transform.rotate(images, 90)))\n",
    "\n",
    "for j in range(len(flip_image)):\n",
    "    display(flip_image[j])\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 1\n",
      "3 1\n",
      "2 1\n",
      "2 1\n",
      "0 1\n",
      "0 1\n",
      "0 1\n",
      "1 1\n",
      "2 1\n",
      "2 1\n"
     ]
    }
   ],
   "source": [
    "# Predict the label of flipped images\n",
    "for i in range(len(flip_image)):\n",
    "    x = Variable(torch.from_numpy(flip_image[i].astype(np.float32)))\n",
    "    true_label = correct_labels[i]\n",
    "    out = model(x)\n",
    "    y_pred = np.argmax(out.data.numpy())\n",
    "    print(true_label, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analysis:\n",
    "\n",
    "When flipped images are given to model, the model failed to predict the correct output almost all the cases. This means that the trained model is not invariant to change in image orientation. \n",
    "\n",
    "This is a issue: A good CNN model should be invariant towards change in image orientation.\n",
    "\n",
    "To improve the model, training procedure has to be modified. The training procedure should include data augmentation technique to better predict on these changed images."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Kaggle Submission Details:\n",
    "\n",
    "Username : vijayilla"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}