ML_Recognition_of_digits.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "149938de",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "from tensorflow import keras\n",
    "from tensorflow.keras import layers\n",
    "import matplotlib.pyplot as plt\n",
    "from tqdm import tqdm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "773c1396",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "example of a number and it's representation:\n",
      "5\n"
     ]
    },
    {
     "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": [
    "train_data, test_data = tf.keras.datasets.mnist.load_data(path=\"mnist.npz\")\n",
    "x_train = train_data[0].reshape(-1,784).astype(float) / 255\n",
    "y_train = train_data[1]\n",
    "number = 11\n",
    "plt.imshow(train_data[0][number], cmap='gray')\n",
    "print('example of a number and it\\'s representation:')\n",
    "print(y_train[number])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4b521b78",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"mnist_model\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "digits (InputLayer)          [(None, 784)]             0         \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 32)                25120     \n",
      "_________________________________________________________________\n",
      "dense_2 (Dense)              (None, 32)                1056      \n",
      "_________________________________________________________________\n",
      "predictions (Dense)          (None, 10)                330       \n",
      "=================================================================\n",
      "Total params: 26,506\n",
      "Trainable params: 26,506\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2022-02-11 17:19:06.857876: I tensorflow/core/platform/cpu_feature_guard.cc:145] This TensorFlow binary is optimized with Intel(R) MKL-DNN to use the following CPU instructions in performance critical operations:  SSE4.1 SSE4.2\n",
      "To enable them in non-MKL-DNN operations, rebuild TensorFlow with the appropriate compiler flags.\n",
      "2022-02-11 17:19:06.858258: I tensorflow/core/common_runtime/process_util.cc:115] Creating new thread pool with default inter op setting: 8. Tune using inter_op_parallelism_threads for best performance.\n"
     ]
    }
   ],
   "source": [
    "inputs = keras.Input(shape=(784,), name=\"digits\")\n",
    "x = layers.Dense(32, activation=\"relu\", name=\"dense_1\")(inputs)\n",
    "x = layers.Dense(32, activation=\"relu\", name=\"dense_2\")(x)\n",
    "outputs = layers.Dense(10, activation=\"softmax\", name=\"predictions\")(x)\n",
    "model = keras.Model(inputs=inputs, outputs=outputs, name=\"mnist_model\")\n",
    "loss = keras.losses.SparseCategoricalCrossentropy(from_logits=True)\n",
    "def loss1(true, pred):\n",
    "    val = 0.\n",
    "    for i in range(len(true)):\n",
    "        delta = pred[i, true[i]]\n",
    "        val -= np.log(delta)\n",
    "    return val / len(true)\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b18b6bdb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Layer dense_1 is casting an input tensor from dtype float64 to the layer's dtype of float32, which is new behavior in TensorFlow 2.  The layer has dtype float32 because it's dtype defaults to floatx.\n",
      "\n",
      "If you intended to run this layer in float32, you can safely ignore this warning. If in doubt, this warning is likely only an issue if you are porting a TensorFlow 1.X model to TensorFlow 2.\n",
      "\n",
      "To change all layers to have dtype float64 by default, call `tf.keras.backend.set_floatx('float64')`. To change just this layer, pass dtype='float64' to the layer constructor. If you are the author of this layer, you can disable autocasting by passing autocast=False to the base Layer constructor.\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([5, 8, 8, 7, 7, 2, 4, 5, 2, 5, 2, 9, 2, 2, 2, 5, 2, 2, 2, 2, 7, 2,\n",
       "       5, 7, 2, 2, 4, 5, 5, 5, 7, 2, 5, 5, 5, 7, 2, 5, 2, 2, 2, 4, 7, 5,\n",
       "       8, 7, 7, 2, 4, 5, 4, 2, 7, 5, 7, 2, 2, 9, 2, 2, 2, 5, 5, 5, 9, 5,\n",
       "       5, 5, 2, 2, 2, 5, 5, 2, 5, 5, 2, 5, 7, 5, 2, 5, 2, 2, 7, 2, 2, 9,\n",
       "       2, 9, 7, 5, 2, 2, 5, 2, 7, 4, 2, 5])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# untrained model\n",
    "logits = model(x_train, training=True)\n",
    "np.argmax(logits, 1)[0:100]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "35d74f67",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 2, 1, 0, 4, 1, 4, 9, 5, 9, 0, 6, 9, 0, 1, 5, 9, 7, 3, 4, 9, 6,\n",
       "       6, 5, 4, 0, 7, 4, 0, 1, 3, 1, 3, 4, 7, 2, 7, 1, 2, 1, 1, 7, 4, 2,\n",
       "       3, 5, 1, 2, 4, 4, 6, 3, 5, 5, 6, 0, 4, 1, 9, 5, 7, 8, 9, 3, 7, 4,\n",
       "       6, 4, 3, 0, 7, 0, 2, 9, 1, 7, 3, 2, 9, 7, 7, 6, 2, 7, 8, 4, 7, 3,\n",
       "       6, 1, 3, 6, 9, 3, 1, 4, 1, 7, 6, 9], dtype=uint8)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# what we would like to get\n",
    "test_data[1][0:100]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1267747f",
   "metadata": {},
   "source": [
    "# Training:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87ae5d96",
   "metadata": {},
   "source": [
    "### Number of optimization variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "189a7b47",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We are going to use (784+1) * 32 + (32+1) *32 + (32+1) *10 = 26506  optimization variables \n",
      "We take the value 'x+1' everytime in order to take into account the bias\n"
     ]
    }
   ],
   "source": [
    "print('We are going to use (784+1) * 32 + (32+1) *32 + (32+1) *10 =',(784+1)*32+(32+1)*32+(32+1)*10,' optimization variables ')\n",
    "print('We take the value \\'x+1\\' everytime in order to take into account the bias')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d784293",
   "metadata": {},
   "source": [
    "## Stochastic gradient descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1ba54737",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We use a constant step which is equals to 1/sqrt(K) =  0.011547005383792516 , where K is the number of iteration over the data\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|███████████████████████████████████████| 7500/7500 [04:59<00:00, 25.05it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The loop: 1 / 5 is done\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|███████████████████████████████████████| 7500/7500 [11:42<00:00, 10.67it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The loop: 2 / 5 is done\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|███████████████████████████████████████| 7500/7500 [05:15<00:00, 23.76it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The loop: 3 / 5 is done\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|███████████████████████████████████████| 7500/7500 [05:21<00:00, 23.30it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The loop: 4 / 5 is done\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|███████████████████████████████████████| 7500/7500 [05:49<00:00, 21.43it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The loop: 5 / 5 is done\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "number = len(x_train)//8\n",
    "step = 1/np.sqrt(number)\n",
    "print('We use a constant step which is equals to 1/sqrt(K) = ',step,', where K is the number of iteration over the data')\n",
    "losss = []\n",
    "\n",
    "def update_weights(model, update, alpha):\n",
    "    new_weights = model.trainable_weights.copy()\n",
    "    for i in range(len(new_weights)):\n",
    "        new_weights[i] = new_weights[i] -alpha * update[i]\n",
    "    model.set_weights(new_weights)\n",
    "\n",
    "number_of_loop = 5\n",
    "for inde in range(number_of_loop):\n",
    "    for k in tqdm(range(number)):\n",
    "        x_train_batch = x_train[k*8:k*8+8]\n",
    "        y_train_batch = y_train[k*8:k*8+8]\n",
    "        with tf.GradientTape() as tape:\n",
    "                logits = model(x_train_batch)\n",
    "                loss_value = loss(y_train_batch, logits)\n",
    "        grad = tape.gradient(loss_value, model.trainable_weights)\n",
    "        update_weights(model,grad,step)\n",
    "        ## Evaluate model\n",
    "        samples_for_evaluation = np.random.randint(0, 10000, 1000)\n",
    "        logits = model(x_train[samples_for_evaluation])\n",
    "        losss.append(loss(y_train[samples_for_evaluation], logits).numpy())\n",
    "    print('The loop:',inde+1,'/',number_of_loop,'is done')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9652f919",
   "metadata": {},
   "source": [
    "### Loss visualisation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b8af3d38",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x792 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The average loss over 8 items is about: 1.5346394 at the end of the training.\n"
     ]
    }
   ],
   "source": [
    "wide = 200\n",
    "loss_smmooth = [np.mean( np.asarray(losss[k:k+wide])) for k in range (len(losss)-wide)]\n",
    "plt.figure(1,figsize=(20,11))\n",
    "plt.plot(np.arange(len(loss_smmooth)),loss_smmooth)\n",
    "plt.grid()\n",
    "plt.title('evolution of loss function over iterations')\n",
    "plt.xlabel('number of iterations')\n",
    "plt.ylabel('loss over each epoc')\n",
    "plt.show()\n",
    "print('The average loss over 8 items is about:',np.mean(np.asarray(loss_smmooth[-4:-1])),'at the end of the training.')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d79f16a4",
   "metadata": {},
   "source": [
    "## Evaluation of the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b5b53907",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|█████████████████████████████████| 10000/10000 [00:00<00:00, 122272.22it/s]\n"
     ]
    }
   ],
   "source": [
    "predi = []\n",
    "data = (model.predict(test_data[0].reshape(-1,784).astype(float) / 255)*10).astype('int')\n",
    "for i in tqdm(range(len(test_data[0].reshape(-1,784)))):\n",
    "    L = data[i]\n",
    "    predi.append(np.where( L == np.max(L))[0][0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4cde06cb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Counter({0: 9294, -2: 103, 5: 92, 2: 73, 1: 62, -5: 60, 3: 57, -1: 41, 6: 40, 4: 37, -4: 32, -6: 29, 8: 23, -3: 22, 9: 15, -7: 11, 7: 9})\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.9294"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from collections import Counter\n",
    "print(Counter(test_data[1]-predi))\n",
    "rate = list(Counter(test_data[1]-predi).values())[0]/len(predi)\n",
    "rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3162f04e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "labels = 'Good prediction','Bad prediction'\n",
    "sizes = [rate*100,(1-rate)*100]\n",
    "explode = (0, 0.1)  # only \"explode\" the 2nd slice (i.e. 'Hogs')\n",
    "\n",
    "\n",
    "fig1, ax1 = plt.subplots()\n",
    "ax1.pie(sizes, explode=explode, labels=labels, autopct='%1.1f%%',\n",
    "        shadow=True, startangle=90,radius=1)\n",
    "ax1.axis('equal')  # Equal aspect ratio ensures that pie is drawn as a circle.\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}