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   "source": [
    "# Introduction to Neural Networks with tensorflow"
   ],
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   }
  },
  {
   "source": [
    "# what are neural networks?\n",
    "### A neural network is nothing more than a bunch of neurons connected together. Here’s what a simple neural network might look like\n",
    "\n",
    "## Building Blocks: Neurons\n",
    "\n",
    "First, we have to talk about neurons, the basic unit of a neural network. A neuron takes inputs, does some math with them, and produces one output. Here’s what a 2-input neuron looks like:\n",
    "\n",
    "![neuron with 2 inputs](https://victorzhou.com/a74a19dc0599aae11df7493c718abaf9/perceptron.svg)\n",
    "\n",
    "3 things are happening here. First, each input is multiplied by a weight:\n",
    "#### x1→x1∗w1x_1\n",
    "#### x_1 * w_1x1​→x1​∗w1​ x2→x2∗w2x_2\n",
    "#### x_2 * w_2x2​→x2​∗w2​\n",
    "\n",
    "Next, all the weighted inputs are added together with a bias bbb:\n",
    "#### (x1∗w1)+(x2∗w2)+b(x_1 * w_1) + (x_2 * w_2) + b(x1​∗w1​)+(x2​∗w2​)+b\n",
    "\n",
    "Finally, the sum is passed through an activation function:\n",
    "#### y=f(x1∗w1+x2∗w2+b)y = f(x_1 * w_1 + x_2 * w_2 + b)y=f(x1​∗w1​+x2​∗w2​+b)"
   ],
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   "metadata": {}
  },
  {
   "source": [
    "## Combining Neurons into a Neural Network\n",
    "![nn](https://victorzhou.com/77ed172fdef54ca1ffcfb0bba27ba334/network.svg)\n",
    "![nn explaination](https://i.imgur.com/QD4RiMP.jpg)"
   ],
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   "source": [
    "## Backpropagation:\n",
    "\n",
    "### Backpropagation is a supervised learning algorithm, for training Multi-layer Perceptrons (Artificial Neural Networks).\n",
    "Why We Need Backpropagation?\n",
    "\n",
    "While designing a Neural Network, in the beginning, we initialize weights with some random values or any variable for that fact.\n",
    "\n",
    "Now obviously, we are not superhuman. So, it’s not necessary that whatever weight values we have selected will be correct, or it fits our model the best.\n",
    "\n",
    "Okay, fine, we have selected some weight values in the beginning, but our model output is way different than our actual output i.e. the error value is huge.\n",
    "\n",
    "Now, how will you reduce the error?\n",
    "\n",
    "Basically, what we need to do, we need to somehow explain the model to change the parameters (weights), such that error becomes minimum.\n",
    "\n",
    "Let’s put it in an another way, we need to train our model.\n",
    "\n",
    "\n",
    "![example](https://d1jnx9ba8s6j9r.cloudfront.net/blog/wp-content/uploads/2017/09/Training-A-Neural-Network-Backpropagation-Edureka-528x216.png)"
   ],
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   "metadata": {}
  },
  {
   "source": [
    "![nn](https://miro.medium.com/max/1280/1*OIOg3wDym2fzNIgelpOdwQ.gif)"
   ],
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   "metadata": {}
  },
  {
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   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## how many neural network types are there?\n",
    "https://towardsdatascience.com/the-mostly-complete-chart-of-neural-networks-explained-3fb6f2367464"
   ]
  },
  {
   "source": [
    "Steps for building model using TensorFlow\n",
    "\n",
    "* Import required libraries\n",
    "* Load the dataset for training and evaluation\n",
    "* Analyze the dataset\n",
    "* Normalize the dataset for inputting into CNN\n",
    "* Build the CNN model\n",
    "* Create the estimator\n",
    "* Train the model\n",
    "* Evaluate the model\n",
    "* Improve the accuracy of the model"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
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   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# importing our dependencies\n",
    "\n",
    "import tensorflow as tf\n",
    "from tensorflow.keras.datasets import fashion_mnist"
   ]
  },
  {
   "source": [
    "# DataPreprocessing\n",
    "## Loading the dataset\n",
    "\n",
    "## Here we will load the Fashion mnist dataset using the load_data() method."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "(60000, 28, 28)\n(60000,)\n"
    }
   ],
   "source": [
    "(X_train, y_train), (X_test, y_test) = fashion_mnist.load_data()\n",
    "print(X_train.shape)\n",
    "print(y_train.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "labelNames = [\"top\", \"trouser\", \"pullover\", \"dress\", \"coat\",\n",
    "\t\"sandal\", \"shirt\", \"sneaker\", \"bag\", \"ankle boot\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "fig = plt.figure(figsize=(15,3))\n",
    "for i in range(20):\n",
    " ax = fig.add_subplot(2,10, i+1, xticks=[], yticks=[])\n",
    " ax.imshow(np.squeeze(X_train[i]), cmap='gray')\n",
    " ax.set_title(labelNames[y_train[i]])"
   ]
  },
  {
   "source": [
    "## Normalization\n",
    "\n",
    "Here, we divide each image by the maximum number of pixels(255) so that the image range will be between 0 and 1. We normalize images so that our models train faster."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = X_train/255.0\n",
    "X_test = X_test/255.0\n",
    "\n",
    "X_train = X_train.reshape(-1, 28*28)\n",
    "X_test = X_test.reshape(-1, 28*28)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(10000, 784)"
     },
     "metadata": {},
     "execution_count": 67
    }
   ],
   "source": [
    "X_train = X_train.reshape(-1, 28*28)\n",
    "X_test = X_test.reshape(-1, 28*28)\n",
    "X_test.shape"
   ]
  },
  {
   "source": [
    "## Building our model\n",
    "\n",
    "The first thing we need to do before building a model is to create a model object itself, this object will be an instance of the class called Sequential."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = tf.keras.models.Sequential([\n",
    "   tf.keras.layers.Dense(units = 128, activation = 'relu', input_shape = (784,)),\n",
    "    tf.keras.layers.Dropout(0.2),\n",
    "   tf.keras.layers.Dense(units = 10, activation = 'softmax')\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "# compile the model\n",
    "model.compile(optimizer = 'adam', loss = 'sparse_categorical_crossentropy', metrics = ['sparse_categorical_accuracy'])\n",
    "# model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Model: &quot;sequential_10&quot;\n_________________________________________________________________\nLayer (type)                 Output Shape              Param #   \n=================================================================\ndense_20 (Dense)             (None, 128)               100480    \n_________________________________________________________________\ndropout_10 (Dropout)         (None, 128)               0         \n_________________________________________________________________\ndense_21 (Dense)             (None, 10)                1290      \n=================================================================\nTotal params: 101,770\nTrainable params: 101,770\nNon-trainable params: 0\n_________________________________________________________________\n"
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Epoch 1/5\n1875/1875 [==============================] - 6s 3ms/step - loss: 0.5305 - sparse_categorical_accuracy: 0.8108\nEpoch 2/5\n1875/1875 [==============================] - 6s 3ms/step - loss: 0.3974 - sparse_categorical_accuracy: 0.8565\nEpoch 3/5\n1875/1875 [==============================] - 6s 3ms/step - loss: 0.3667 - sparse_categorical_accuracy: 0.8663\nEpoch 4/5\n1875/1875 [==============================] - 6s 3ms/step - loss: 0.3483 - sparse_categorical_accuracy: 0.8719\nEpoch 5/5\n1875/1875 [==============================] - 7s 4ms/step - loss: 0.3297 - sparse_categorical_accuracy: 0.8782\n"
    }
   ],
   "source": [
    "# train\n",
    "history = model.fit(X_train, y_train, epochs =5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Accuracy: 87.07000017166138\n"
    }
   ],
   "source": [
    "# evaluate the model\n",
    "loss, accuracy = model.evaluate(X_test, y_test, verbose=0)\n",
    "print(f'Accuracy: {accuracy*100}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "\n",
    "# ploting the learning curves\n",
    "plt.title('Learning Curves')\n",
    "plt.xlabel('Epochs')\n",
    "plt.ylabel('Cross Entropy')\n",
    "plt.plot(history.history['loss'], label='train')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "## Prediction"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Predicted: dress\n"
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "&lt;Figure size 432x288 with 1 Axes&gt;",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "image = X_train[3].reshape(-1,28,28)\n",
    "# lets display the image which we want to predict\n",
    "plt.imshow(np.squeeze(image), cmap='gray')\n",
    "\n",
    "\n",
    "# make a prediction\n",
    "# reshaping the image for model input\n",
    "image= image.reshape(-1,28*28)\n",
    "# predicting the label of image\n",
    "yhat = model.predict([image])\n",
    "print('Predicted: {}'.format(labelNames[np.argmax(yhat)]))"
   ]
  },
  {
   "source": [
    "## resources:\n",
    "* https://towardsdatascience.com/the-mostly-complete-chart-of-neural-networks-explained-3fb6f2367464\n",
    "* https://www.edureka.co/blog/backpropagation/\n",
    "* https://towardsdatascience.com/simple-introduction-to-neural-networks-ac1d7c3d7a2c\n",
    "* https://victorzhou.com/blog/intro-to-neural-networks/\n",
    "* https://www.pyimagesearch.com/2019/02/11/fashion-mnist-with-keras-and-deep-learning/\n"
   ],
   "cell_type": "markdown",
   "metadata": {}
  }
 ]
}