.ipynb_checkpoints/FindingMino_side_by_side-checkpoint.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import fetch_openml\n",
    "import matplotlib.pyplot as plt\n",
    "import itertools\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from keras.utils.np_utils import to_categorical\n",
    "import tensorflow as tf\n",
    "from tensorflow import keras\n",
    "from tensorflow.keras import layers\n",
    "from tensorflow.keras.models import Sequential, load_model\n",
    "from keras.datasets import mnist\n",
    "import itertools\n",
    "import random\n",
    "random.seed(42)\n",
    "plt.style.use('dark_background')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "(train_images, train_labels), (test_images, test_labels) = mnist.load_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 28, 28)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_images.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Randomly sampling a subset of the data, to make the combinations more tractable. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(28, 28)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x14c0dc0a0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "image_A = train_images[0]\n",
    "print(image_A.shape)\n",
    "plt.imshow(image_A, cmap = plt.cm.binary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x10258b280>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "image_B = train_images[1]\n",
    "plt.imshow(image_B, cmap = plt.cm.binary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x11c887430>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "images_A_and_B = np.hstack((image_A, image_B))\n",
    "plt.imshow(images_A_and_B, cmap = plt.cm.binary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create mini training set so that it's not too computationally intensive\n",
    "sample_size = 40000\n",
    "X_train, X_val, y_train, y_val = train_images[:sample_size], train_images[sample_size:sample_size*2],  train_labels[:sample_size], train_labels[sample_size:sample_size*2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Randomly draw 40k training images\n",
    "\n",
    "num_images_chosen = 400000\n",
    "num_images_total = 40000\n",
    "\n",
    "combo_train_X = []\n",
    "combo_train_y = []\n",
    "\n",
    "for i in range(num_images_chosen):\n",
    "    \n",
    "    # Randomly draw indices\n",
    "    rand_A = random.randint(0, num_images_total-1)\n",
    "    rand_B = random.randint(0, num_images_total-1)\n",
    "    \n",
    "    # Concatenate images\n",
    "    image_A = X_train[rand_A]\n",
    "    image_B = X_train[rand_B]\n",
    "    concatenated_images = np.hstack((image_A, image_B))\n",
    "    \n",
    "    # Find the minimum label\n",
    "    intermediate_label_A = y_train[rand_A]\n",
    "    intermediate_label_B = y_train[rand_B]\n",
    "    minimum_label = min(intermediate_label_A, intermediate_label_B)\n",
    "    \n",
    "    # Append to lists\n",
    "    combo_train_X.append(concatenated_images)\n",
    "    combo_train_y.append(minimum_label)\n",
    "    \n",
    "combo_train_X = np.array(combo_train_X)\n",
    "combo_train_y = np.array(combo_train_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Randomly draw 20k validation images\n",
    "\n",
    "num_images_chosen = 10000\n",
    "num_images_total = 20000\n",
    "\n",
    "combo_val_X = []\n",
    "combo_val_y = []\n",
    "\n",
    "for i in range(num_images_chosen):\n",
    "    \n",
    "    # Randomly draw indices\n",
    "    rand_A = random.randint(0, num_images_total-1)\n",
    "    rand_B = random.randint(0, num_images_total-1)\n",
    "    \n",
    "    # Concatenate images\n",
    "    image_A = X_val[rand_A]\n",
    "    image_B = X_val[rand_B]\n",
    "    concatenated_images = np.hstack((image_A, image_B))\n",
    "    \n",
    "    # Find the minimum label\n",
    "    intermediate_label_A = y_val[rand_A]\n",
    "    intermediate_label_B = y_val[rand_B]\n",
    "    minimum_label = min(intermediate_label_A, intermediate_label_B)\n",
    "    \n",
    "    # Append to lists\n",
    "    combo_val_X.append(concatenated_images)\n",
    "    combo_val_y.append(minimum_label)\n",
    "    \n",
    "combo_val_X = np.array(combo_val_X)\n",
    "combo_val_y = np.array(combo_val_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_images = combo_train_X.reshape((combo_train_X.shape[0], 28, 56, 1))\n",
    "train_images = train_images.astype('float32')/ 255\n",
    "\n",
    "val_images = combo_val_X.reshape((combo_val_X.shape[0], 28, 56, 1))\n",
    "val_images = val_images.astype('float32')/255\n",
    "\n",
    "train_labels = to_categorical(combo_train_y)\n",
    "val_labels = to_categorical(combo_val_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = tf.keras.Sequential()\n",
    "model.add(layers.Conv2D(32, (3,3), activation = 'relu', input_shape = (28,56,1)))\n",
    "model.add(layers.MaxPooling2D(2,2))\n",
    "model.add(layers.Conv2D(64, (3,3), activation = 'relu'))\n",
    "model.add(layers.MaxPooling2D(2,2))\n",
    "model.add(layers.Conv2D(64, (3,3), activation = 'relu'))\n",
    "# Adding a classifier\n",
    "model.add(layers.Flatten())\n",
    "model.add(layers.Dropout(0.5))\n",
    "model.add(layers.Dense(64, activation = 'relu'))\n",
    "model.add(layers.Dense(10, activation = 'softmax'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "conv2d (Conv2D)              (None, 26, 54, 32)        320       \n",
      "_________________________________________________________________\n",
      "max_pooling2d (MaxPooling2D) (None, 13, 27, 32)        0         \n",
      "_________________________________________________________________\n",
      "conv2d_1 (Conv2D)            (None, 11, 25, 64)        18496     \n",
      "_________________________________________________________________\n",
      "max_pooling2d_1 (MaxPooling2 (None, 5, 12, 64)         0         \n",
      "_________________________________________________________________\n",
      "conv2d_2 (Conv2D)            (None, 3, 10, 64)         36928     \n",
      "_________________________________________________________________\n",
      "flatten (Flatten)            (None, 1920)              0         \n",
      "_________________________________________________________________\n",
      "dropout (Dropout)            (None, 1920)              0         \n",
      "_________________________________________________________________\n",
      "dense (Dense)                (None, 64)                122944    \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 10)                650       \n",
      "=================================================================\n",
      "Total params: 179,338\n",
      "Trainable params: 179,338\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compile model\n",
    "opt = tf.keras.optimizers.RMSprop(learning_rate=0.0002)\n",
    "model.compile(optimizer = opt,\n",
    "             loss = 'categorical_crossentropy',\n",
    "             metrics = ['mae', 'accuracy'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/4\n",
      "4688/4688 [==============================] - 255s 54ms/step - loss: 0.3645 - mae: 0.0359 - accuracy: 0.8823\n",
      "Epoch 2/4\n",
      "4688/4688 [==============================] - 251s 54ms/step - loss: 0.1282 - mae: 0.0127 - accuracy: 0.9599\n",
      "Epoch 3/4\n",
      "4688/4688 [==============================] - 257s 55ms/step - loss: 0.0884 - mae: 0.0086 - accuracy: 0.9722\n",
      "Epoch 4/4\n",
      "4688/4688 [==============================] - 257s 55ms/step - loss: 0.0697 - mae: 0.0067 - accuracy: 0.9779\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.keras.callbacks.History at 0x11ca224c0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fit model\n",
    "model.fit(train_images, \n",
    "          train_labels, \n",
    "          epochs = 8, \n",
    "          batch_size = 64)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Val Accuracy: 0.983\n"
     ]
    }
   ],
   "source": [
    "y_predict = model.predict(val_images)\n",
    "#y_predict = y_predict.astype(int)\n",
    "\n",
    "\n",
    "correct = 0\n",
    "#check_baseline\n",
    "\n",
    "for label in range(len(val_labels)):\n",
    "    \n",
    "    if np.argmax(val_labels[label], axis=None, out=None) == np.argmax(y_predict[label], axis=None, out=None):\n",
    "        correct = correct + 1\n",
    "        \n",
    "print(\"Val Accuracy: \" + str(correct/len(val_labels)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Baseline for above is 10%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "313/313 [==============================] - 2s 4ms/step - loss: 0.0567 - mae: 0.0048 - accuracy: 0.9830\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[0.05668065324425697, 0.004844381473958492, 0.9829999804496765]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eval_model = model.evaluate(val_images, val_labels)\n",
    "eval_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Verify above by visually inspecting images from the predicted set\n",
    "num_val_images = 10000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted: 3\n",
      "True: 3\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "check_index = random.randint(0,num_val_images)\n",
    "plt.imshow(val_images[check_index], cmap = plt.cm.binary)\n",
    "print(\"Predicted: \" + str(np.argmax(y_predict[check_index])))\n",
    "print(\"True: \" + str(np.argmax(val_labels[check_index])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted: 0\n",
      "True: 0\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "check_index = random.randint(0,num_val_images)\n",
    "plt.imshow(val_images[check_index], cmap = plt.cm.binary)\n",
    "print(\"Predicted: \" + str(np.argmax(y_predict[check_index])))\n",
    "print(\"True: \" + str(np.argmax(val_labels[check_index])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted: 1\n",
      "True: 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "check_index = random.randint(0,num_val_images)\n",
    "plt.imshow(val_images[check_index], cmap = plt.cm.binary)\n",
    "print(\"Predicted: \" + str(np.argmax(y_predict[check_index])))\n",
    "print(\"True: \" + str(np.argmax(val_labels[check_index])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted: 0\n",
      "True: 0\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "check_index = random.randint(0,num_val_images)\n",
    "plt.imshow(val_images[check_index], cmap = plt.cm.binary)\n",
    "print(\"Predicted: \" + str(np.argmax(y_predict[check_index])))\n",
    "print(\"True: \" + str(np.argmax(val_labels[check_index])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted: 4\n",
      "True: 4\n"
     ]
    },
    {
     "data": {
      "image/png": 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Shv93OXl7FjMyzMGDB01BQYHJzs42e/bsMbNmzUr5XkqvXzfddJMpKioy+/btG6ytXr3arFixwkgyK1asMKtWrUp5n168/H6/KSoqMpLM+PHjzc8//2xmzZqVtvOVZMaNG2ckmaysLPPdd9+Z6667zmzZssXcd999RpJZt26dWbp0acr79Or11FNPmU2bNplPP/3USErruXZ1dZkpU6acUxvm3+Xkfdj1119vPv/888Gfq6qqTFVVVar/ASTklZeXd06Ad3Z2Gr/fb6SzodfZ2ZnyHhPx2rp1q5k3b96ImO+YMWPM999/b0pKSkxfX5/JzMw00tDvuc2vnJwc8+WXX5ry8vLBAE/XuUrOAT6cv8tJvYSSk5Oj7u7uwZ+PHDminJycZLaQMj6fT+FwWJIUDofl8/lS3JH38vLyVFRUpJaWlrSeb0ZGhtra2hSJRNTU1KRffvlFJ06c0JkzZySl1/f6zTff1HPPPaeBgQFJ0pQpU9J2rpJkjNH27dvV2tqqQCAgaXj/bzepZ6HgX8aYVLfgqXHjxqm+vl7Lly9Xf3//kD9Pp/kODAyoqKhIEydOVENDg6666qpUt5QQt99+uyKRiHbv3q25c+emup2kmDNnjnp7ezVt2jQ1NTWps7NzyHuG03c5qQHe09Oj6dOnD/6cm5urnp6eZLaQMseOHZPf71c4HJbf71ckEkl1S57JyspSfX29Nm3apIaGBknpPd9/nDx5Us3Nzbrhhhs0adIkZWZm6syZM2nzvS4tLdUdd9yh2267TaNHj9aECRO0du3atJzrP3p7eyWdPXivoaFBJSUlw/q7nNRLKKFQSFdccYXy8/OVnZ2txYsXq7GxMZktpExjY6MqKyslSZWVldq2bVuKO/JObW2tOjo6tGbNmsFaus536tSpmjhxoiRp9OjRuvnmm9XR0aHm5mbdc889ktJnvtXV1Zo+fboKCgq0ePFi7dy5Uw888EBazlWSxo4dq/Hjxw/+51tuuUXt7e3D/ruc1IvuCxYsMD///LM5ePCgqa6uTvkvARLx2rx5s+nt7TV//fWX6e7uNg8//LC59NJLzZdffmn2799vmpqazOTJk1Pepxev0tJSY4wxe/fuNW1tbaatrc0sWLAgbec7e/Zss3v3brN3716zb98+88ILLxhJpqCgwLS0tJgDBw6YTz75xPznP/9Jea9evubOnTv4S8x0nWtBQYHZs2eP2bNnj2lvbx/Mp+H8XeZWegCwFHdiAoClCHAAsBQBDgCWIsABwFIEOABYigAHAEsR4ABgqf8CLvNlBUf0gzwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "check_index = random.randint(0,num_val_images)\n",
    "plt.imshow(val_images[check_index], cmap = plt.cm.binary)\n",
    "print(\"Predicted: \" + str(np.argmax(y_predict[check_index])))\n",
    "print(\"True: \" + str(np.argmax(val_labels[check_index])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted: 7\n",
      "True: 7\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "check_index = random.randint(0,num_val_images)\n",
    "plt.imshow(val_images[check_index], cmap = plt.cm.binary)\n",
    "print(\"Predicted: \" + str(np.argmax(y_predict[check_index])))\n",
    "print(\"True: \" + str(np.argmax(val_labels[check_index])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted: 2\n",
      "True: 2\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "check_index = random.randint(0,num_val_images)\n",
    "plt.imshow(val_images[check_index], cmap = plt.cm.binary)\n",
    "print(\"Predicted: \" + str(np.argmax(y_predict[check_index])))\n",
    "print(\"True: \" + str(np.argmax(val_labels[check_index])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted: 9\n",
      "True: 9\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "check_index = random.randint(0,num_val_images)\n",
    "plt.imshow(val_images[check_index], cmap = plt.cm.binary)\n",
    "print(\"Predicted: \" + str(np.argmax(y_predict[check_index])))\n",
    "print(\"True: \" + str(np.argmax(val_labels[check_index])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted: 2\n",
      "True: 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "check_index = random.randint(0,num_val_images)\n",
    "plt.imshow(val_images[check_index], cmap = plt.cm.binary)\n",
    "print(\"Predicted: \" + str(np.argmax(y_predict[check_index])))\n",
    "print(\"True: \" + str(np.argmax(val_labels[check_index])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted: 2\n",
      "True: 2\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "check_index = random.randint(0,num_val_images)\n",
    "plt.imshow(val_images[check_index], cmap = plt.cm.binary)\n",
    "print(\"Predicted: \" + str(np.argmax(y_predict[check_index])))\n",
    "print(\"True: \" + str(np.argmax(val_labels[check_index])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "general_ML",
   "language": "python",
   "name": "general_ml"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}