Handwritten_Digit_Classification.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task 1: Introduction\n",
    "\n",
    "This graph describes the problem that we are trying to solve visually. We want to create and train a model that takes an image of a hand written digit as input and predicts the class of that digit, that is, it predicts the digit or it predicts the class of the input image.\n",
    "\n",
    "![Hand Written Digits Classification](images/1_1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import TensorFlow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using TensorFlow version 1.13.1\n"
     ]
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "\n",
    "tf.logging.set_verbosity(tf.logging.ERROR)\n",
    "print('Using TensorFlow version', tf.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task 2: The Dataset\n",
    "### Import MNIST"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tensorflow.keras.datasets import mnist\n",
    "(x_train, y_train), (x_test, y_test) = mnist.load_data()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Shapes of Imported Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_train shape: (60000, 28, 28)\n",
      "y_train shape: (60000,)\n",
      "x_test shape: (10000, 28, 28)\n",
      "y_test shape: (10000,)\n"
     ]
    }
   ],
   "source": [
    "print('x_train shape:', x_train.shape)\n",
    "print('y_train shape:', y_train.shape)\n",
    "print('x_test shape:', x_test.shape)\n",
    "print('y_test shape:', y_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot an Image Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "plt.imshow(x_train[0], cmap='binary')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Display Labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}\n"
     ]
    }
   ],
   "source": [
    "print(set(y_train))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# One Hot Encoding\n",
    "After this encoding, every label will be converted to a list with 10 elements and the element at index to the corresponding class will be set to 1, rest will be set to 0:\n",
    "\n",
    "| original label | one-hot encoded label |\n",
    "|------|------|\n",
    "| 5 | [0, 0, 0, 0, 0, 1, 0, 0, 0, 0] |\n",
    "| 7 | [0, 0, 0, 0, 0, 0, 0, 1, 0, 0] |\n",
    "| 1 | [0, 1, 0, 0, 0, 0, 0, 0, 0, 0] |\n",
    "\n",
    "### Encoding Labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tensorflow.keras.utils import to_categorical\n",
    "\n",
    "y_train_encoded = to_categorical(y_train)\n",
    "y_test_encoded = to_categorical(y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Validated Shapes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y_train_encoded shape: (60000, 10)\n",
      "y_test_encoded shape: (10000, 10)\n"
     ]
    }
   ],
   "source": [
    "print('y_train_encoded shape:',y_train_encoded.shape)\n",
    "print('y_test_encoded shape:', y_test_encoded.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Display Encoded Labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0., 0., 0., 1., 0., 0., 0., 0.], dtype=float32)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train_encoded[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task 4: Neural Networks\n",
    "\n",
    "### Linear Equations\n",
    "\n",
    "![Single Neuron](images/1_2.png)\n",
    "\n",
    "The above graph simply represents the equation:\n",
    "\n",
    "\\begin{equation}\n",
    "y = w1 * x1 + w2 * x2 + w3 * x3 + b\n",
    "\\end{equation}\n",
    "\n",
    "Where the `w1, w2, w3` are called the weights and `b` is an intercept term called bias. The equation can also be *vectorised* like this:\n",
    "\n",
    "\\begin{equation}\n",
    "y = W . X + b\n",
    "\\end{equation}\n",
    "\n",
    "Where `X = [x1, x2, x3]` and `W = [w1, w2, w3].T`. The .T means *transpose*. This is because we want the dot product to give us the result we want i.e. `w1 * x1 + w2 * x2 + w3 * x3`. This gives us the vectorised version of our linear equation.\n",
    "\n",
    "A simple, linear approach to solving hand-written image classification problem - could it work?\n",
    "\n",
    "![Single Neuron with 784 features](images/1_3.png)\n",
    "\n",
    "### Neural Networks\n",
    "\n",
    "![Neural Network with 2 hidden layers](images/1_4.png)\n",
    "\n",
    "This model is much more likely to solve the problem as it can learn more complex function mapping for the inputs and outputs in our dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Preprocessing the Examples\n",
    "\n",
    "### Unrolling N-dimensional Arrays to Vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_train_reshaped shape: (60000, 784)\n",
      "x_test_reshaped shape: (10000, 784)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "x_train_reshaped = np.reshape(x_train, (60000, 784))\n",
    "x_test_reshaped = np.reshape(x_test, (10000, 784))\n",
    "\n",
    "print('x_train_reshaped shape:', x_train_reshaped.shape)\n",
    "print('x_test_reshaped shape:', x_test_reshaped.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Display Pixel Values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0, 1, 2, 3, 9, 11, 14, 16, 18, 23, 24, 25, 26, 27, 30, 35, 36, 39, 43, 45, 46, 49, 55, 56, 64, 66, 70, 78, 80, 81, 82, 90, 93, 94, 107, 108, 114, 119, 126, 127, 130, 132, 133, 135, 136, 139, 148, 150, 154, 156, 160, 166, 170, 171, 172, 175, 182, 183, 186, 187, 190, 195, 198, 201, 205, 207, 212, 213, 219, 221, 225, 226, 229, 238, 240, 241, 242, 244, 247, 249, 250, 251, 252, 253, 255}\n"
     ]
    }
   ],
   "source": [
    "print(set(x_train_reshaped[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "\n",
    "### Data Normalization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_mean = np.mean(x_train_reshaped)\n",
    "x_std = np.std(x_train_reshaped)\n",
    "\n",
    "epsilon = 1e-10\n",
    "\n",
    "x_train_norm = (x_train_reshaped - x_mean) / (x_std + epsilon) \n",
    "x_test_norm = (x_test_reshaped - x_mean) / (x_std + epsilon)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Display Normalized Pixel Values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{-0.38589016215482896, 1.306921966983251, 1.17964285952926, 1.803310486053816, 1.6887592893452241, 2.8215433456857437, 2.719720059722551, 1.1923707702746593, 1.7396709323268205, 2.057868700961798, 2.3633385588513764, 2.096052433197995, 1.7651267538176187, 2.7960875241949457, 2.7451758812133495, 2.45243393406917, 0.02140298169794222, -0.22042732246464067, 1.2305545025108566, 0.2759611966059242, 2.210603629906587, 2.6560805059955555, 2.6051688630139593, -0.4240738943910262, 0.4668798577869107, 0.1486820891519332, 0.3905123933145161, 1.0905474843114664, -0.09314821501064967, 1.4851127174188385, 2.7579037919587486, 1.5360243604004349, 0.07231462467953861, -0.13133194724684696, 1.294194056237852, 0.03413089244334132, 1.3451056992194483, 2.274243183633583, -0.24588314395543887, 0.772349715676489, 0.75962180493109, 0.7214380726948927, 0.1995937321335296, -0.41134598364562713, 0.5687031437501034, 0.5941589652409017, 0.9378125553666773, 0.9505404661120763, 0.6068868759863008, 0.4159682148053143, -0.042236572029053274, 2.7706317027041476, 2.1342361654341926, 0.12322626766113501, -0.08042030426525057, 0.16140999989733232, 1.8924058612716097, 1.2560103240016547, 2.185147808415789, 0.6196147867316999, 1.943317504253206, -0.11860403650144787, -0.30952269768243434, 1.9942291472348024, -0.2840668761916362, 2.6306246845047574, 2.286971094378982, -0.19497150097384247, -0.39861807290022805, 0.2886891073513233, 1.7523988430722195, 2.3887943803421745, 2.681536327486354, 1.4596568959280403, 2.439706023323771, 2.7833596134495466, 2.490617666305367, -0.10587612575604877, 1.5614801818912332, 1.9051337720170087, 1.6123918248728295, 1.268738234747054, 1.9560454149986053, 2.6433525952501564, 1.026907930584471}\n"
     ]
    }
   ],
   "source": [
    "print(set(x_train_norm[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Creating a Model\n",
    "### Creating the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tensorflow.keras.models import Sequential\n",
    "from tensorflow.keras.layers import Dense\n",
    "\n",
    "model = Sequential([\n",
    "    Dense(128, activation='relu', input_shape=(784,)),\n",
    "    Dense(128, activation='relu'),\n",
    "    Dense (10, activation='softmax')\n",
    "])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Activation Functions\n",
    "\n",
    "The first step in the node is the linear sum of the inputs:\n",
    "\\begin{equation}\n",
    "Z = W . X + b\n",
    "\\end{equation}\n",
    "\n",
    "The second step in the node is the activation function output:\n",
    "\n",
    "\\begin{equation}\n",
    "A = f(Z)\n",
    "\\end{equation}\n",
    "\n",
    "Graphical representation of a node where the two operations are performed:\n",
    "\n",
    "![ReLU](images/1_5.png)\n",
    "\n",
    "### Compiling the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense (Dense)                (None, 128)               100480    \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 128)               16512     \n",
      "_________________________________________________________________\n",
      "dense_2 (Dense)              (None, 10)                1290      \n",
      "=================================================================\n",
      "Total params: 118,282\n",
      "Trainable params: 118,282\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model.compile(\n",
    "    optimizer='sgd',\n",
    "    loss='categorical_crossentropy',\n",
    "    metrics=['accuracy']\n",
    ")\n",
    "\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Training the Model\n",
    "\n",
    "### Training the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/3\n",
      "60000/60000 [==============================] - 7s 124us/sample - loss: 0.3627 - acc: 0.8956\n",
      "Epoch 2/3\n",
      "60000/60000 [==============================] - 8s 131us/sample - loss: 0.1815 - acc: 0.9481\n",
      "Epoch 3/3\n",
      "60000/60000 [==============================] - 7s 118us/sample - loss: 0.1379 - acc: 0.9600\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.keras.callbacks.History at 0x7fcd587d95c0>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(x_train_norm, y_train_encoded, epochs=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluating the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000/10000 [==============================] - 1s 57us/sample - loss: 0.1282 - acc: 0.9615\n",
      "Test set accuracy: 96.14999890327454\n"
     ]
    }
   ],
   "source": [
    "_, accuracy = model.evaluate(x_test_norm, y_test_encoded)\n",
    "print('Test set accuracy:', accuracy*100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Predictions\n",
    "\n",
    "### Predictions on Test Set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of preds: (10000, 10)\n"
     ]
    }
   ],
   "source": [
    "preds = model.predict(x_test_norm)\n",
    "print('Shape of preds:', preds.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting the Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 25 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,12))\n",
    "\n",
    "start_index = 0\n",
    "\n",
    "for i in range(25):\n",
    "    plt.subplot(5, 5, i+1)\n",
    "    plt.grid(False)\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "    \n",
    "    pred = np.argmax(preds[start_index+i])\n",
    "    gt = y_test[start_index+i]\n",
    "    \n",
    "    col='g'\n",
    "    if pred != gt:\n",
    "        col = 'r'\n",
    "        \n",
    "    plt.xlabel('i={}, pred={}, gt={}'.format(start_index+i, pred, gt), color=col)\n",
    "    plt.imshow(x_test[start_index+i], cmap='binary')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VG3QUE2kLca67wzDciWxiOpXGvqOTtpoGaYq0h7A7MYHZuYzVpVCJGO5ENjEwPIGMWrtBRzHRcAhzGcW+kUmrS6ESMdyJbMKOM2VM87syccaMYzDciWwiNmTAV+NBV7Pf6lJOsqE1AK9H2O/uIAx3IpvojRvY1BpEjdd+b8v6Wi/WNfs5191B7PdXRFSl+myyQUcxUe7K5CgMdyIbGEumEB+ftmV/uykSDmHfyCSmU2mrS6ESMNyJbKA3Pg7AnoOppmh7CKrZWT1kfwx3Ihsw+7LtHO6cMeMsDHciG4jFDayor0H7inqrSymqq9kPn9fDQVWHYLgT2UAsbmBz+wqILLY3jj3UeD3Y0BrgdEiHYLgTWUxVEbPZBh3FRNs5Y8YpGO5EFjs8Ng1jes4R4R4Jh3Do+BSM6ZTVpdBpMNyJLBZzwEwZk7lDVD9nzNgew53IYrF4NijtuNRvofkZM+x3tz2GO5HFYvFxrF5Zj5UNtVaXclodjQ1oqPVyxowDMNyJLNYbd8ZgKgB4PIJIOMi57g7AcCeyUCqdwe7ExPwm1E4Q4RozjsBwJ7LQvqOTSKXV1guGFYq2h5AwZjA6OWt1KXQKDHciC/WaG3SE7bf7UjHdXIbAERjuRBaKxQ14PYKNbQGrSylZlOHuCAx3Igv1xg2sbwmgrsZrdSklC6+ow4r6Goa7zTHciSzU55BlB/KJSHYZgjgHVe2M4U5kkcmZORwYTWKzA05eKtQdDiE2ZEBVrS6FimC4E1mkzwFruBcTDYcwNpXCsDFjdSlUBMOdyCKx3EyZze3OmSljMpchiHEZAttiuBNZpDduwO/zoqOxwepSliwSDgLgjBk7Y7gTWaRvyEB3OASPx74bdBTTHKxDS7CO4W5jDHcii8TihiMHU02RcBAxLkNgWwx3IgskjBmMTM46cjDVFAmH0D9kIJPhjBk7YrgTWcAciHRyuEfbQ0jOpnHo+JTVpdAiGO5EFog5eBqkKcJlCGyN4U5kgVh8HC1BH1qCdVaXcsbMGTPcuMOeGO5EFog5aIOOYkL1tVi9sp5b7tkUw52owjIZRd/QhKOW+S0m0h7ijBmbYrgTVdjBY0lMpdKItgetLuWsRcMh7B6ewFw6Y3UpVKCkcBeR60UkJiIDInLHIvd/RkReE5FXRORxEVm3/KUSucP8Bh0OXHagUCQcwmw6g/2jSatLoQKnDXcR8QK4B8BWAFsA3CwiWwoOexlAj6peAOAhAHctd6FEbhGLGxA5MSDpZOa4Afvd7aeUlvvFAAZUdY+qzgL4CYAb8w9Q1SdV1fzo/jWAjuUtk8g9YnEDnU1++H01Vpdy1ja2BiHCGTN2VEq4rwFwMO/6YO62Yj4E4NGzKYrIzXrj4/NzxJ2uwefFuiY/57rbUCnhvtiqRouebywiHwTQA+AbRe6/VUR2isjORCJRepVELjGdSmPfSBKbHT4NMl8kHOLSvzZUSrgPAlibd70DwOHCg0TkWgBfAHCDqi66gr+qfl9Ve1S1p7W19UzqJXK03YkJpDPq+Dnu+aLtIewbSWJmLm11KZSnlHB/EUC3iKwXER+AmwA8nH+AiFwI4B+RDfbh5S+TyB1ObNDhnnCPhENIZxR7EpNWl0J5ThvuqjoH4DYAOwDsAvCgqr4qIl8WkRtyh30DQBDA/xaR34rIw0UejqiqxeIGfF4P1jUHrC5l2XCNGXsqabheVbcD2F5w2xfzLl+7zHURuVJsyMDGtiBqve45f3B9SwA1HmG/u8245y+MyAFiccNVXTIA4KvxYENrgC13m2G4E1XIWDKFI2PTrhpMNUXCIfRxjRlbYbgTVYgb1nAvJhoO4cBoEsnZOatLoRyGO1GFzIe7S05gyted+5362Xq3DYY7UYXE4uMI1dfgnJX1Vpey7MxvI1yGwD4Y7kQVYg6miix20rezdTb5UVfj4QJiNsJwJ6oAVUWvC3ZfKsbrEXSHg+gbZreMXTDciSrgyNg0jOk5V/a3myLhEFvuNsJwJ6qAEzNlnL9BRzGRcAjx8WmMJVNWl0JguBNVhHn2pptb7ubv1jfM1rsdMNyJKiAWN3DOynqs9NdaXUrZRMwZM+yasQWGO1EF9MYN12zQUczqlfUI1tWgn9MhbYHhTlRmc+kMdg9PuG5NmUIigkg4yLnuNsFwJyqzfSOTmE1nXDsNMp+5K5Pqopu1UQUx3InKrDfu3jVlCkXCIRxLpnB0YtbqUqoew52ozGJxA16PYGNr0OpSys78AOPyv9ZjuBOVWSxuoKvZj/par9WllB13ZbIPhjtRmcWGDGx28clL+VqCPjQFfAx3G2C4E5VRcnYOB0aTVdHfDmRnzHS3BTnX3QYY7kRl1Dc0AdXqGEw1RdtDud+bM2asxHAnKqNYfByAu5cdKBQJhzAxM4fDY9NWl1LVGO5EZRSLT6Ch1ovOJr/VpVQMZ8zYA8PdwVLpDB56aRCP/eEIvwLbVGxoHJFwEB6P+zboKCbSlgt39rtbqsbqAmjpVBU7Xh3C1x/rxd6jkwCA169dhS9sOxcXr2+yuDrKF4sbuHpzm9VlVNRKfy3CK+q4DIHFGO4O8/KBY/jrR3Zh5/5j6G4L4ge39OB4MoVv7Ijhff/4PN6+JYw7tm7Ghio4Ycbujk7M4OjErKvXcC8mEg6xW8ZiDHeHODCSxNd39OKRV46gJViHr777dXjvRR2o8WZ71ra97hzc99xefPfJAbz9W8/gA2/qxCev6UZzsM7iyqtXXxWs4V5MNBzC/b/ej3RG4a2iLik7Ybjb3PHkLL7zxAD+1/P7UOPx4BPXdOMv3roBgbqF/+safF587KpNeF/PWtz9eB8eeOEAfvabQ/joVRvx3y9bXxVnR9pNNa0pUyjSHsLMXAYHR5PoaglYXU5VYrjb1MxcGvc/vx9//8QAjOkU3nvRWnzm7RGEV9Sf8udaQ3X4qz96Hf7s0vX42qO9uOuxGH74/H589roo/ugNa6pqYM9qsbiB5oAPraHq+/ZkLkMQGzIY7hZhuNuMquIXrxzBXTt6cXB0CldEWnHnts1LPn19U1sQ997Sg+d3j+Ar23fhMw/+Dj/41V58Ydu5uHRTS5mqp3y9Q0ZVttoBoLstO+bTFzdw3XntFldTnRjuNvLivlH89SO78NuDx7G5PYT7P3QxLu9uPavHfPPGZvzbxy7D/33lMO56LIYP3PsCrt7chju3bkZ3FfYFV0omo+gfMvC+nrVWl2KJQF0N1jY1cMaMhRjuNrAnMYGvP9aLHa8OoX1FPb7xngvw7jd2LNtAlMcjuPENa3Ddee345//Yh3ueHMB1f/cMbrq4E5+6thttoVN39dDSDR6bQnI27frdl04lGg6hf2jC6jKqFsPdQiMTM/j24/144IUDqKvx4LNvj+BDb9mABl95Bj/ra734yBUb8b6etfj24/344a/34+cvH8JHrtiID1++Hn6fc/8c0hnF7waP4zf7j6ElWIdNbUFsaA1Y9jv1mssOVHG4R8IhPBVLYHYuA18Nz5esNOe+mx1sOpXGfc/txfee3I1kKo2bL16LT14TqdjAW1PAhy/dcB5uubQLdz3Wi2/+sg8PvLAft78tij++aPm+MZTb0YkZPNOXwFOxBJ7tT+BYMnXSMWtWNWBjWxCbWoPY2BbI/RtEc8AHkfL9nuaqiG7fFPtUIuEQ5jKKfSOTVf06WIXhXkGZjOLnvz2Ev9kRw+GxaVx7bvaEo01t1pxwtL4lgO998CLs3DeKv3pkFz7301dw33N78flt5+KtkbPr6y+HdEbx24PH8XRsGE/1JfD7Q2NQza4hftXmNlwZbcMlG5pwPJnC7uEJDAxPYCAxgd2JCfx47yimUun5x1rlr80GfWsQm9rM4A9hTWPDsny49Q4ZWNvUcNKU1WoyP2MmbjDcLVC9f3kV9h8DR/GVR3fhD4fGcUHHSnzz/W/AJRuarS4LANDT1YT/89FLsf33cXztsV340/v+E5d3t+Dz287FuedYe3Zlfuv8mf4EjidT8AjwhrWr8OlrI7gq2obzVq9YMMWzLVR/UphkMorDY1PYnZjEwHA28AeGJ/D/dg3hX3cenD+ursaD9S0BbGrLhX4u/Ne3BJZ0rkBf3EA0XH1npubb0BqA1yM8U9UiDPcy6x8y8NVHe/FE7zDWrGrA3Te9Ae+6YLXt5puLCN5xwTm4dkvb/Pz6bd9+Fu+9qAOfeVsU7SsrM+ha2Dp/ZXAMQLZ1fnWudf7W7has8vuW9Lgej6Cj0Y+ORj+uKPhWcmxydj7szX9/N3gcj/z+CMz12ESAtY3+XOAHFgR/YS0zc2nsOTpZ9VMA62u96Gr2M9wtwnAvk2FjGt/6ZT/+9cUDCNTV4M6tm3HLpV22P1O0rsaLD1++Ae+5qAPfeWIA//L8fjz8u8O49fINuPWKjQiWoZvh6MQMno4l8FRftu/cbJ1f2NmI298WwZWLtM6XU2PAh55AE3q6Fi66Np1KY09icj7wBxIT2D08gV8NHMXsXGb+uJagDxtaT7T062s9SGe0qgdTTdH2EHYdsS7cp2bTODCaxP6RSRwYTaLBl11+eV1TAKtX1c8v3+FGDPdllpydw73P7sU/PL0bs3MZ3HJpFz5xdTcaA0traVptld+Hv3znFvzpm7tw145efPuJAfzoPw/i02/rxvt71p7Vm8JsnT8VG8ZTsWzfOQC0BOtwzeYwroy24vIzaJ0vt/paL7asXoEtqxd2r6QzikPHpjCQMLKt/eFJDCQm8MgrRzA2dWJQt/DnqlF3WwiP/iGO6VS6LA0bVcXxZAr7zQAfSc5f3j+SxLAxU/RnazyCNY0N2bBv9qOzyY/OpsD8ZaePl0gp64CLyPUA7gbgBXCvqn6t4P46AP8C4CIAIwDer6r7TvWYPT09unPnzjMs237SGcVPXxrE3/4yhqHxGWw9vx2fu34z1rvk1OuXDxzDV7bvwov7jmFTWxCf37YZV0XbSp5xkjByfeeLtM6vjLSWvXVeCaqKkclZDAxPYDqVxpXR6lrqdzHbf38EH33gN/jFx9+C89esPKPHyGQUQ8Y09o+cCO39o8lskI9MYnx6bsHx4RV1WNcUQGezH13NfnQ2B7CuKRvYU6k09o8kcWB0MvdvMteyTy74YAayjY11zX6sa/Jjbe4DIBv8AbQEyzvb6lRE5CVV7TntcacLdxHxAugD8DYAgwBeBHCzqr6Wd8xHAVygqh8RkZsA/BdVff+pHtdN4f50XwJf3b4LvXEDF3auwl++41xctM5966qb68h/7dFd2DeSxJs3NOML7zh30TdttnV+DE/FEie1zq+ItNqmdU7lNTA8gWu/+TT+9r2vxx9f1FH0uNm5DAaP5Yd2LshHkzg4msRMXjdYjUfQ0dgwH9pmS7urJYC1jf4zPk9kLJnC/vzQH0li/2j228CR8WnkR6U/170z3+rPq2X1qgbUlrG7p9RwL+V7x8UABlR1T+6BfwLgRgCv5R1zI4Av5S4/BOA7IiJahu2BDh2fwsHRJLwegUcEXo/AKwKPB3mXs/96PScuezw46bb8x/AIlvxJvOvIOL6yfRee7T+KziY/vvtf34it57db9olebiKC689vx9Wb2/CjF/bj7sf78c6//xXefeEa3H5dFD6vZ751/kxfAmNT2db5Gzsb8dm3Z/vOt5zj7NY5LU1Xsx8+rwd9wwYmZuYKuk5OtKAPH59CJi8tGmq9WNfsx4aWAK7e3DYfouXsK1/pr8UF/lW4oGPVSfdNp9IYPDaFA6Mn6j8wksSeo5N4qi+xYAzG6xGsXlU//+3hxAdQ9no5xq0WU0rL/T0ArlfVD+eu/wmAN6nqbXnH/CF3zGDu+u7cMUeLPe6Zttz/4end+NqjvUv+uVJ4JPcBkf8hsegHRvaDYv9oEisbavGJq7vxwUvWVd1ZeOPTKXz3yd2477m9UFWk0tm/JbN1ftXmVly+qRUr/bUWV0pW2nr3s+gbMpDOLMyapoAvL7Szrd9sN4ofrcE6xzSS8ruNTrT4kziQ++ZxvODkuuaAD5/fdu4pv8mcynK23Bd7hQs/EUo5BiJyK4BbAaCzs7OEpz7Zu16/GhesWYm0KtIZRUYV6QzyLp/4d8H9qshkCu6fvy3v/rzj8m9LZ7DwflW86/Wr8eFx5Y5nAAAD4UlEQVS3bKja8FpRX4s7tm7GBy/pxD89tw+N/lq2zukkH796E57pS+RasbkBy2Y/VtS7433j8QjOWdmAc1Y2LHruythUCgdywW9283Q0NpS9rlJa7m8G8CVVvS53/U4AUNWv5h2zI3fM8yJSAyAOoPVU3TJu6nMnIqqUUlvupfQjvAigW0TWi4gPwE0AHi445mEAt+QuvwfAE+XobyciotKctltGVedE5DYAO5CdCnmfqr4qIl8GsFNVHwbwAwD3i8gAgFFkPwCIiMgiJQ3bqup2ANsLbvti3uVpAO9d3tKIiOhMVdf0DiKiKsFwJyJyIYY7EZELMdyJiFyI4U5E5EIlrQpZlicWSQDYf4Y/3gKg6NIGVYivx0J8PU7ga7GQG16Pdap62n0wLQv3syEiO0s5Q6ta8PVYiK/HCXwtFqqm14PdMkRELsRwJyJyIaeG+/etLsBm+HosxNfjBL4WC1XN6+HIPnciIjo1p7bciYjoFBwX7iJyvYjERGRARO6wuh6riMhaEXlSRHaJyKsi8kmra7IDEfGKyMsi8gura7GaiKwSkYdEpDf3d/Jmq2uyioh8Ovc++YOI/FhE6q2uqdwcFe65zbrvAbAVwBYAN4vIFmursswcgNtV9VwAlwD4WBW/Fvk+CWCX1UXYxN0AHlPVzQBejyp9XURkDYBPAOhR1fORXbrc9cuSOyrckbdZt6rOAjA36646qnpEVX+Tu2wg+8ZdY21V1hKRDgDvAHCv1bVYTURWAHgrsnstQFVnVfW4tVVZqgZAQ26nOD+AwxbXU3ZOC/c1AA7mXR9ElQcaAIhIF4ALAbxgbSWW+zsAnwOQOd2BVWADgASAf8p1U90rIgGri7KCqh4C8DcADgA4AmBMVf/d2qrKz2nhXtJG3NVERIIAfgrgU6o6bnU9VhGRdwIYVtWXrK7FJmoAvBHA91T1QgCTAKpyjEpEGpH9hr8ewGoAARH5oLVVlZ/Twn0QwNq86x2ogq9XxYhILbLB/oCq/szqeix2GYAbRGQfst11V4vID60tyVKDAAZV1fw29xCyYV+NrgWwV1UTqpoC8DMAl1pcU9k5LdxL2ay7KoiIINufuktVv2l1PVZT1TtVtUNVu5D9u3hCVV3fOitGVeMADopINHfTNQBes7AkKx0AcImI+HPvm2tQBYPLJe2hahfFNuu2uCyrXAbgTwD8XkR+m7vt87n9bokA4OMAHsg1hPYA+G8W12MJVX1BRB4C8BtkZ5m9jCo4U5VnqBIRuZDTumWIiKgEDHciIhdiuBMRuRDDnYjIhRjuREQuxHAnInIhhjsRkQsx3ImIXOj/A+vM6NGGkFgnAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(preds[8])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}