{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Demonstration: Neural network classifier "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-03-02T07:57:16.457264",
     "start_time": "2016-03-02T07:57:16.443739"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "from scipy.stats import multivariate_normal\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Developing a code for doing neural networks with back propagation\n",
    "\n",
    "One can identify a set of key steps when using neural networks to solve supervised learning problems:  \n",
    "  \n",
    "1. Collect and pre-process data  \n",
    "1. Define model and architecture  \n",
    "1. Choose cost function and optimizer  \n",
    "1. Train the model  \n",
    "1. Evaluate model performance on test data  \n",
    "1. Adjust hyperparameters (if necessary, network architecture)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The exercise \"build-your-own neural network\" provides a step-by-step guided recipe for coding a neural network from scratch in python."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction to tensorflow\n",
    "This short introduction uses Keras to:\n",
    "* Build a neural network that classifies images.\n",
    "* Train this neural network.\n",
    "* And, finally, evaluate the accuracy of the model.\n",
    "\n",
    "See [https://www.tensorflow.org/tutorials/quickstart/beginner](https://www.tensorflow.org/tutorials/quickstart/beginner) for more details"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See also the [Tensorflow classification tutorial](https://www.tensorflow.org/tutorials/keras/classification)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "You have tensorflow version: 2.13.0 (should be at least 2.0.0)\n"
     ]
    }
   ],
   "source": [
    "# Load tensorflow without optimization warning\n",
    "import os\n",
    "os.environ['TF_CPP_MIN_LOG_LEVEL'] = '1' \n",
    "\n",
    "import tensorflow as tf\n",
    "print('You have tensorflow version:', tf.__version__, '(should be at least 2.0.0)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load and prepare the [MNIST dataset](http://yann.lecun.com/exdb/mnist/). Convert the samples from integers to floating-point numbers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "mnist = tf.keras.datasets.mnist\n",
    "\n",
    "(x_train, y_train), (x_test, y_test) = mnist.load_data()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The images are 28x28 NumPy arrays, with pixel values ranging from 0 to 255. The labels are an array of integers, ranging from 0 to 9. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Explore the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 28, 28)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The shape of the training data\n",
    "x_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 0, 4, ..., 5, 6, 8], dtype=uint8)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Each training label is an integer\n",
    "y_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.imshow(x_train[0])\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For better performance (weights of natural size), scale these values to a range of 0 to 1 before feeding them to the neural network model. To do so, divide the values by 255. It's important that the training set and the testing set be preprocessed in the same way:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train, x_test = x_train / 255.0, x_test / 255.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To verify that the data is in the correct format and that you're ready to build and train the network, let's display the first 25 images from the training set and display the class name below each image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x1000 with 25 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,10))\n",
    "for i in range(25):\n",
    "    plt.subplot(5,5,i+1)\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "    plt.imshow(x_train[i], cmap=plt.cm.binary)\n",
    "    plt.xlabel(str(y_train[i]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Build the network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The basic building block of a neural network is the layer. Layers extract representations from the data fed into them. Hopefully, these representations are meaningful for the problem at hand.\n",
    "\n",
    "Most of deep learning consists of chaining together simple layers. Most layers, such as [`tf.keras.layers.Dense`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Dense), have parameters that are learned during training."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Build the [tf.keras.Sequential](https://www.tensorflow.org/api_docs/python/tf/keras/Sequential) model by stacking layers. Choose an optimizer and loss function for training:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = tf.keras.models.Sequential([\n",
    "  tf.keras.layers.Flatten(input_shape=(28, 28)),\n",
    "  tf.keras.layers.Dense(128, activation='relu'),\n",
    "  tf.keras.layers.Dropout(0.2),\n",
    "  tf.keras.layers.Dense(10, activation='softmax')\n",
    "])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first layer in this network, [`tf.keras.layers.Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten), transforms the format of the images from a two-dimensional array (of 28 by 28 pixels) to a one-dimensional array (of 28 * 28 = 784 pixels). Think of this layer as unstacking rows of pixels in the image and lining them up. This layer has no parameters to learn; it only reformats the data.\n",
    "\n",
    "After the pixels are flattened, the network consists two [`tf.keras.layers.Dense`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Dense) layers. These are densely connected, or fully connected, neural layers. The first Dense layer has 128 nodes (or neurons). The second (and last) layer is a 10-node softmax layer that returns an array of 10 probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the 10 classes.\n",
    "\n",
    "In between the Dense layers is a [`tf.keras.layers.Dropout`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Dropout) layer. Dropout consists in randomly setting a fraction rate of input units to 0 at each update during training time, which helps prevent overfitting."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can print a summary of the model that also shows the number of parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential\"\n",
      "_________________________________________________________________\n",
      " Layer (type)                Output Shape              Param #   \n",
      "=================================================================\n",
      " flatten (Flatten)           (None, 784)               0         \n",
      "                                                                 \n",
      " dense (Dense)               (None, 128)               100480    \n",
      "                                                                 \n",
      " dropout (Dropout)           (None, 128)               0         \n",
      "                                                                 \n",
      " dense_1 (Dense)             (None, 10)                1290      \n",
      "                                                                 \n",
      "=================================================================\n",
      "Total params: 101770 (397.54 KB)\n",
      "Trainable params: 101770 (397.54 KB)\n",
      "Non-trainable params: 0 (0.00 Byte)\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Other useful commands for storing and retrieving tensorflow models are:\n",
    "- For saving a `model` after training: `tf.keras.models.save_model(model, 'filename.keras')`\n",
    "- For load a pre-trained model: `tf.keras.models.load_model('filename.keras')`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before the model is ready for training, it needs a few more settings. These are added during the model's compile step:\n",
    "\n",
    "* *Loss function* — This measures how accurate the model is during training. You want to minimize this function to \"steer\" the model in the right direction.\n",
    "* *Optimizer* — This is how the model is updated based on the data it sees and its loss function.\n",
    "* *Metrics* — Used to monitor the training and testing steps. The following example uses accuracy, the fraction of the images that are correctly classified. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.compile(optimizer='adam',\n",
    "              loss='sparse_categorical_crossentropy',\n",
    "              metrics=['accuracy'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train and evaluate the model:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The simplest way to fit data is to just specify a number of epochs. If unspecified, `batch_size` will default to 32. During training the data will be fed through the network this many times. Here we keep the verbosity during training at a minimum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "history = model.fit(x_train, y_train, epochs=10,verbose=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['loss', 'accuracy'])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "history.history.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.9150833487510681,\n",
       " 0.9578333497047424,\n",
       " 0.9685333371162415,\n",
       " 0.9734333157539368,\n",
       " 0.9771833419799805,\n",
       " 0.9800500273704529,\n",
       " 0.9817500114440918,\n",
       " 0.9834499955177307,\n",
       " 0.9850666522979736,\n",
       " 0.9857833385467529]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "history.history['accuracy']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Make predictions and evaluate accuracy\n",
    "Next, compare how the model performs on the test dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Test accuracy: 0.980\n"
     ]
    }
   ],
   "source": [
    "test_loss, test_acc = model.evaluate(x_test,  y_test, verbose=0)\n",
    "\n",
    "print(f'\\nTest accuracy: {test_acc:5.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the model trained, you can use it to make predictions about some images."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.4696879e-07, 3.8383258e-10, 2.5593865e-08, 1.7151525e-06,\n",
       "       3.7908587e-14, 8.1841262e-10, 1.8726145e-17, 9.9999052e-01,\n",
       "       3.7903551e-09, 7.4352351e-06], dtype=float32)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictions = model.predict(x_test, verbose=0)\n",
    "\n",
    "# Let's look at the prediction for the first test image\n",
    "predictions[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Check the normalization of the output probabilities\n",
    "np.sum(predictions[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Which prob is largest?\n",
    "np.argmax(predictions[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Examining the test label shows that this classification is correct:\n",
    "y_test[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Some helper functions for nice plotting\n",
    "def plot_image(i, predictions_array, true_label, img):\n",
    "  predictions_array, true_label, img = predictions_array, true_label[i], img[i]\n",
    "  plt.xticks([])\n",
    "  plt.yticks([])\n",
    "\n",
    "  plt.imshow(img, cmap=plt.cm.binary)\n",
    "\n",
    "  predicted_label = np.argmax(predictions_array)\n",
    "  if predicted_label == true_label:\n",
    "    color = 'green'\n",
    "  else:\n",
    "    color = 'red'\n",
    "\n",
    "  plt.xlabel(\"{} {:2.0f}% ({})\".format(str(predicted_label),\n",
    "                                100*np.max(predictions_array),\n",
    "                                true_label),\n",
    "                                color=color)\n",
    "\n",
    "def plot_value_array(i, predictions_array, true_label):\n",
    "  predictions_array, true_label = predictions_array, true_label[i]\n",
    "  plt.xticks(range(10))\n",
    "  plt.yticks([])\n",
    "  thisplot = plt.bar(range(10), predictions_array, color=\"#777777\")\n",
    "  plt.ylim([0, 1])\n",
    "  predicted_label = np.argmax(predictions_array)\n",
    "\n",
    "  thisplot[predicted_label].set_color('red')\n",
    "  thisplot[true_label].set_color('green')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1200x1800 with 54 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the first X test images, their predicted labels, and the true labels.\n",
    "# Color correct predictions in blue and incorrect predictions in red.\n",
    "num_rows = 9\n",
    "num_cols = 3\n",
    "num_images = num_rows*num_cols\n",
    "plt.figure(figsize=(2*2*num_cols, 2*num_rows))\n",
    "for i in range(num_images):\n",
    "  plt.subplot(num_rows, 2*num_cols, 2*i+1)\n",
    "  plot_image(i, predictions[i], y_test, x_test)\n",
    "  plt.subplot(num_rows, 2*num_cols, 2*i+2)\n",
    "  plot_value_array(i, predictions[i], y_test)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "@webio": {
   "lastCommId": null,
   "lastKernelId": null
  },
  "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": "3.9.17"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}