Traffic_Sign_Classifier.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Self-Driving Car Engineer Nanodegree\n",
    "\n",
    "## Deep Learning\n",
    "\n",
    "## Project: Build a Traffic Sign Recognition Classifier\n",
    "\n",
    "In this notebook, a template is provided for you to implement your functionality in stages which is required to successfully complete this project. If additional code is required that cannot be included in the notebook, be sure that the Python code is successfully imported and included in your submission, if necessary. Sections that begin with **'Implementation'** in the header indicate where you should begin your implementation for your project. Note that some sections of implementation are optional, and will be marked with **'Optional'** in the header.\n",
    "\n",
    "In addition to implementing code, there will be questions that you must answer which relate to the project and your implementation. Each section where you will answer a question is preceded by a **'Question'** header. Carefully read each question and provide thorough answers in the following text boxes that begin with **'Answer:'**. Your project submission will be evaluated based on your answers to each of the questions and the implementation you provide.\n",
    "\n",
    ">**Note:** Code and Markdown cells can be executed using the **Shift + Enter** keyboard shortcut. In addition, Markdown cells can be edited by typically double-clicking the cell to enter edit mode."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Step 0: Load The Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Load pickled data\n",
    "import pickle\n",
    "\n",
    "training_file ='train.p'\n",
    "testing_file ='test.p'\n",
    "\n",
    "with open(training_file, mode='rb') as f:\n",
    "    train = pickle.load(f)\n",
    "with open(testing_file, mode='rb') as f:\n",
    "    test = pickle.load(f)\n",
    "    \n",
    "X_train, y_train = train['features'], train['labels']\n",
    "X_test, y_test = test['features'], test['labels']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## Step 1: Dataset Summary & Exploration\n",
    "\n",
    "The pickled data is a dictionary with 4 key/value pairs:\n",
    "\n",
    "- `'features'` is a 4D array containing raw pixel data of the traffic sign images, (num examples, width, height, channels).\n",
    "- `'labels'` is a 2D array containing the label/class id of the traffic sign. The file `signnames.csv` contains id -> name mappings for each id.\n",
    "- `'sizes'` is a list containing tuples, (width, height) representing the the original width and height the image.\n",
    "- `'coords'` is a list containing tuples, (x1, y1, x2, y2) representing coordinates of a bounding box around the sign in the image. **THESE COORDINATES ASSUME THE ORIGINAL IMAGE. THE PICKLED DATA CONTAINS RESIZED VERSIONS (32 by 32) OF THESE IMAGES**\n",
    "\n",
    "Complete the basic data summary below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of training examples = 39209\n",
      "Number of testing examples = 12630\n",
      "Image data shape = (32, 32, 3)\n",
      "Number of classes = 43\n"
     ]
    }
   ],
   "source": [
    "### Replace each question mark with the appropriate value.\n",
    "\n",
    "# Number of training examples\n",
    "n_train = len(X_train)\n",
    "\n",
    "# Number of testing examples.\n",
    "n_test = len(X_test)\n",
    "\n",
    "# What's the shape of an traffic sign image?\n",
    "image_shape = X_train[0].shape\n",
    "\n",
    "# How many unique classes/labels there are in the dataset.\n",
    "n_classes = len(set(y_train))\n",
    "\n",
    "print(\"Number of training examples =\", n_train)\n",
    "print(\"Number of testing examples =\", n_test)\n",
    "print(\"Image data shape =\", image_shape)\n",
    "print(\"Number of classes =\", n_classes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualize the German Traffic Signs Dataset using the pickled file(s). This is open ended, suggestions include: plotting traffic sign images, plotting the count of each sign, etc.\n",
    "\n",
    "The [Matplotlib](http://matplotlib.org/) [examples](http://matplotlib.org/examples/index.html) and [gallery](http://matplotlib.org/gallery.html) pages are a great resource for doing visualizations in Python.\n",
    "\n",
    "**NOTE:** It's recommended you start with something simple first. If you wish to do more, come back to it after you've completed the rest of the sections."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Through only a few examples, we can see these data are difficult real-world signs where there might be lighting conditions, motion-blur, sun glare, etc.\n"
     ]
    },
    {
     "data": {
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6QkibBYeoaTeppKlB0KSuxcBiseCZZ57N3wfEd7b5zgdvsoC5v7/P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\nIYVLxD+kcIn4hxQuEf+QwiXiH1L4vyGQ8CbKNNQ2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f523428a5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f51fe187470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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U8NF2/eMW7t5BXZB3i6l/x/273p2nyWIsYVntZZlsizU93vR06uhzs5+nWG3oTQgU6zF2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\n4Tnin1F4jvhnFJ4j/hmF54h/RuH/BQy6icVVEyCoAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f51fe1b41d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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LvhbSTVAivmaC89ZTeN96IQvkiNLIIoWiUKiMOXFltIDSlBOh+SQWo6+H9OuS98/VMpNT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\n71N7APx9ag+Av0/t/wPh8pPFR/W74wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f51fe11ea58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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hmnccIGfSNJDWK/L6mGF9ARlmXFLk+q1h8xbcsbmES5AzaZoYUmIaV0DmwlA5zpXj9cSF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\nJZf2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f51fe0f06a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Data exploration visualization\n",
    "import random\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "# show 5 traffic sign pictures for a frist impression\n",
    "for i in range(1,6):\n",
    "    index = random.randint(0, len(X_train))\n",
    "    image = X_train[index].squeeze()\n",
    "    plt.figure(figsize=(1,1))\n",
    "    plt.imshow(image)\n",
    "\n",
    "print('Through only a few examples, we can see these data are difficult real-world signs where there might be lighting conditions, motion-blur, sun glare, etc.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Counts for each sign, from #0 to #42 respectively, obviously they are not evenly distributed: \n",
      "{1410, 390, 780, 270, 2070, 540, 1440, 420, 1320, 2220, 300, 1200, 689, 2100, 1980, 1470, 450, 1860, 2250, 330, 210, 1110, 600, 2010, 1500, 360, 2160, 240, 630, 510}\n"
     ]
    }
   ],
   "source": [
    "### Data exploration visualization (cont'd)\n",
    "# count number of each traffic sign    \n",
    "from collections import Counter\n",
    "counter=Counter(y_train)\n",
    "print('Counts for each sign, from #0 to #42 respectively, obviously they are not evenly distributed: ')\n",
    "print(set(counter.values()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "\n",
    "## Step 2: Design and Test a Model Architecture\n",
    "\n",
    "Design and implement a deep learning model that learns to recognize traffic signs. Train and test your model on the [German Traffic Sign Dataset](http://benchmark.ini.rub.de/?section=gtsrb&subsection=dataset).\n",
    "\n",
    "There are various aspects to consider when thinking about this problem:\n",
    "\n",
    "- Neural network architecture\n",
    "- Play around preprocessing techniques (normalization, rgb to grayscale, etc)\n",
    "- Number of examples per label (some have more than others).\n",
    "- Generate fake data.\n",
    "\n",
    "Here is an example of a [published baseline model on this problem](http://yann.lecun.com/exdb/publis/pdf/sermanet-ijcnn-11.pdf). It's not required to be familiar with the approach used in the paper but, it's good practice to try to read papers like these.\n",
    "\n",
    "**NOTE:** The LeNet-5 implementation shown in the [classroom](https://classroom.udacity.com/nanodegrees/nd013/parts/fbf77062-5703-404e-b60c-95b78b2f3f9e/modules/6df7ae49-c61c-4bb2-a23e-6527e69209ec/lessons/601ae704-1035-4287-8b11-e2c2716217ad/concepts/d4aca031-508f-4e0b-b493-e7b706120f81) at the end of the CNN lesson is a solid starting point. You'll have to change the number of classes and possibly the preprocessing, but aside from that it's plug and play!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation\n",
    "\n",
    "Use the code cell (or multiple code cells, if necessary) to implement the first step of your project. Once you have completed your implementation and are satisfied with the results, be sure to thoroughly answer the questions that follow."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### Preprocess the data.\n",
    "from sklearn.utils import shuffle\n",
    "\n",
    "X_train, y_train = shuffle(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 1 \n",
    "\n",
    "_Describe how you preprocessed the data. Why did you choose that technique?_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer:** I shuffled the data in order to minimize the impact of data ordering on actual training, since I observed the trffaic labels appear in the raw data are unevenly distributed. Also attempts to normalize and grayscale the data didn't improve accuracy, thus abandoned."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### Split the data into training/validation/testing sets.\n",
    "\n",
    "# use the last 1/20 of shuffled training data as validation set\n",
    "cut=round(len(X_train)/20)\n",
    "X_validation, y_validation = X_train[cut:][cut:][cut:][cut:], y_train[cut:][cut:][cut:][cut:]\n",
    "X_train, y_train           = X_train[:cut][:cut][:cut][:cut], y_train[:cut][:cut][:cut][:cut]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 2\n",
    "\n",
    "_Describe how you set up the training, validation and testing data for your model. **Optional**: If you generated additional data, how did you generate the data? Why did you generate the data? What are the differences in the new dataset (with generated data) from the original dataset?_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer:** \n",
    "\n",
    "- Training set: the first 19/20 of shuffled data from training file\n",
    "\n",
    "- Validation set: the last 1/20 of shuffled data from training file \n",
    "\n",
    "- Test set: all data from testing file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "### EPOCH and BATCH_SIZE values, affecting the training speed and model accuracy\n",
    "import tensorflow as tf\n",
    "\n",
    "EPOCHS = 40\n",
    "BATCH_SIZE = 128"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### Network architecture.\n",
    "from tensorflow.contrib.layers import flatten\n",
    "\n",
    "def Mynet(x):    \n",
    "    # Hyperparameters\n",
    "    mu = 0\n",
    "    sigma = 0.01\n",
    "    \n",
    "    # Layer 1: Convolutional. Input = 32x32x3. Output = 28x28x108.\n",
    "    conv1_W = tf.Variable(tf.truncated_normal(shape=(5, 5, 3, 108), mean = mu, stddev = sigma))\n",
    "    conv1_b = tf.Variable(tf.zeros(108))\n",
    "    conv1   = tf.nn.conv2d(x, conv1_W, strides=[1, 1, 1, 1], padding='VALID') + conv1_b\n",
    "\n",
    "    # Activation.\n",
    "    conv1 = tf.nn.tanh(conv1)\n",
    "\n",
    "    # Pooling. Input = 28x28x108. Output = 14x14x108.\n",
    "    conv1 = tf.nn.max_pool(conv1, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='VALID')\n",
    "\n",
    "    # Layer 2: Convolutional. Output = 10x10x108.\n",
    "    conv2_W = tf.Variable(tf.truncated_normal(shape=(5, 5, 108, 108), mean = mu, stddev = sigma))\n",
    "    conv2_b = tf.Variable(tf.zeros(108))\n",
    "    conv2   = tf.nn.conv2d(conv1, conv2_W, strides=[1, 1, 1, 1], padding='VALID') + conv2_b\n",
    "    \n",
    "    # Activation.\n",
    "    conv2 = tf.nn.tanh(conv2)\n",
    "\n",
    "    # Pooling. Input = 10x10x108. Output = 5x5x108.\n",
    "    conv2 = tf.nn.max_pool(conv2, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='VALID')\n",
    "\n",
    "    # Flatten. Input = 5x5x108. Output = 2700.\n",
    "    fc0   = flatten(conv2)\n",
    "    \n",
    "    # Layer 3: Fully Connected. Input = 2700. Output = 500.\n",
    "    fc1_W = tf.Variable(tf.truncated_normal(shape=(2700, 500), mean = mu, stddev = sigma))\n",
    "    fc1_b = tf.Variable(tf.zeros(500))\n",
    "    fc1   = tf.matmul(fc0, fc1_W) + fc1_b\n",
    "    \n",
    "    # Activation.\n",
    "    fc1    = tf.nn.tanh(fc1)\n",
    "\n",
    "    # Layer 5: Fully Connected. Input = 500. Output = 43.\n",
    "    fc2_W  = tf.Variable(tf.truncated_normal(shape=(500, 43), mean = mu, stddev = sigma))\n",
    "    fc2_b  = tf.Variable(tf.zeros(43))\n",
    "    logits = tf.matmul(fc1, fc2_W) + fc2_b\n",
    "    \n",
    "    return logits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "###Features and Labels\n",
    "x = tf.placeholder(tf.float32, (None, 32, 32, 3))\n",
    "y = tf.placeholder(tf.int32, (None))\n",
    "one_hot_y = tf.one_hot(y, 43)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "###Training Pipeline\n",
    "rate = 0.0005\n",
    "\n",
    "logits = Mynet(x)\n",
    "\n",
    "cross_entropy = tf.nn.softmax_cross_entropy_with_logits(logits, one_hot_y)\n",
    "loss_operation = tf.reduce_mean(cross_entropy)\n",
    "optimizer = tf.train.AdamOptimizer(learning_rate = rate)\n",
    "training_operation = optimizer.minimize(loss_operation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "###Model Evaluation definition\n",
    "correct_prediction = tf.equal(tf.argmax(logits, 1), tf.argmax(one_hot_y, 1))\n",
    "accuracy_operation = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))\n",
    "saver = tf.train.Saver()\n",
    "\n",
    "def evaluate(X_data, y_data):\n",
    "    num_examples = len(X_data)\n",
    "    total_accuracy = 0\n",
    "    sess = tf.get_default_session()\n",
    "    for offset in range(0, num_examples, BATCH_SIZE):\n",
    "        batch_x, batch_y = X_data[offset:offset+BATCH_SIZE], y_data[offset:offset+BATCH_SIZE]\n",
    "        accuracy = sess.run(accuracy_operation, feed_dict={x: batch_x, y: batch_y})\n",
    "        total_accuracy += (accuracy * len(batch_x))\n",
    "    return total_accuracy / num_examples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 3\n",
    "\n",
    "_What does your final architecture look like? (Type of model, layers, sizes, connectivity, etc.)  For reference on how to build a deep neural network using TensorFlow, see [Deep Neural Network in TensorFlow\n",
    "](https://classroom.udacity.com/nanodegrees/nd013/parts/fbf77062-5703-404e-b60c-95b78b2f3f9e/modules/6df7ae49-c61c-4bb2-a23e-6527e69209ec/lessons/b516a270-8600-4f93-a0a3-20dfeabe5da6/concepts/83a3a2a2-a9bd-4b7b-95b0-eb924ab14432) from the classroom._\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer:** The final network architecture consists of: \n",
    "- 1st conv layer with 108 features\n",
    "- 2nd conv layer with 108 features\n",
    "- one full connected layer to the output, with one flattened input, from 2700 to 500\n",
    "- tanh activation functions after each layer\n",
    "- two max pooling after each conv layer\n",
    "- filter size of 5x5 with stride 1x1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training...\n",
      "\n",
      "EPOCH 1 ...\n",
      "Validation Accuracy = 0.129\n",
      "\n",
      "EPOCH 2 ...\n",
      "Validation Accuracy = 0.164\n",
      "\n",
      "EPOCH 3 ...\n",
      "Validation Accuracy = 0.275\n",
      "\n",
      "EPOCH 4 ...\n",
      "Validation Accuracy = 0.346\n",
      "\n",
      "EPOCH 5 ...\n",
      "Validation Accuracy = 0.467\n",
      "\n",
      "EPOCH 6 ...\n",
      "Validation Accuracy = 0.575\n",
      "\n",
      "EPOCH 7 ...\n",
      "Validation Accuracy = 0.682\n",
      "\n",
      "EPOCH 8 ...\n",
      "Validation Accuracy = 0.791\n",
      "\n",
      "EPOCH 9 ...\n",
      "Validation Accuracy = 0.848\n",
      "\n",
      "EPOCH 10 ...\n",
      "Validation Accuracy = 0.877\n",
      "\n",
      "EPOCH 11 ...\n",
      "Validation Accuracy = 0.907\n",
      "\n",
      "EPOCH 12 ...\n",
      "Validation Accuracy = 0.913\n",
      "\n",
      "EPOCH 13 ...\n",
      "Validation Accuracy = 0.927\n",
      "\n",
      "EPOCH 14 ...\n",
      "Validation Accuracy = 0.929\n",
      "\n",
      "EPOCH 15 ...\n",
      "Validation Accuracy = 0.937\n",
      "\n",
      "EPOCH 16 ...\n",
      "Validation Accuracy = 0.943\n",
      "\n",
      "EPOCH 17 ...\n",
      "Validation Accuracy = 0.944\n",
      "\n",
      "EPOCH 18 ...\n",
      "Validation Accuracy = 0.944\n",
      "\n",
      "EPOCH 19 ...\n",
      "Validation Accuracy = 0.949\n",
      "\n",
      "EPOCH 20 ...\n",
      "Validation Accuracy = 0.950\n",
      "\n",
      "EPOCH 21 ...\n",
      "Validation Accuracy = 0.949\n",
      "\n",
      "EPOCH 22 ...\n",
      "Validation Accuracy = 0.949\n",
      "\n",
      "EPOCH 23 ...\n",
      "Validation Accuracy = 0.951\n",
      "\n",
      "EPOCH 24 ...\n",
      "Validation Accuracy = 0.953\n",
      "\n",
      "EPOCH 25 ...\n",
      "Validation Accuracy = 0.953\n",
      "\n",
      "EPOCH 26 ...\n",
      "Validation Accuracy = 0.954\n",
      "\n",
      "EPOCH 27 ...\n",
      "Validation Accuracy = 0.951\n",
      "\n",
      "EPOCH 28 ...\n",
      "Validation Accuracy = 0.954\n",
      "\n",
      "EPOCH 29 ...\n",
      "Validation Accuracy = 0.955\n",
      "\n",
      "EPOCH 30 ...\n",
      "Validation Accuracy = 0.955\n",
      "\n",
      "EPOCH 31 ...\n",
      "Validation Accuracy = 0.955\n",
      "\n",
      "EPOCH 32 ...\n",
      "Validation Accuracy = 0.955\n",
      "\n",
      "EPOCH 33 ...\n",
      "Validation Accuracy = 0.955\n",
      "\n",
      "EPOCH 34 ...\n",
      "Validation Accuracy = 0.955\n",
      "\n",
      "EPOCH 35 ...\n",
      "Validation Accuracy = 0.956\n",
      "\n",
      "EPOCH 36 ...\n",
      "Validation Accuracy = 0.955\n",
      "\n",
      "EPOCH 37 ...\n",
      "Validation Accuracy = 0.956\n",
      "\n",
      "EPOCH 38 ...\n",
      "Validation Accuracy = 0.956\n",
      "\n",
      "EPOCH 39 ...\n",
      "Validation Accuracy = 0.956\n",
      "\n",
      "EPOCH 40 ...\n",
      "Validation Accuracy = 0.957\n",
      "\n",
      "Model saved\n"
     ]
    }
   ],
   "source": [
    "### Train the model\n",
    "with tf.Session() as sess:\n",
    "    sess.run(tf.global_variables_initializer())\n",
    "    num_examples = len(X_train)\n",
    "    \n",
    "    print(\"Training...\")\n",
    "    print()\n",
    "    for i in range(EPOCHS):\n",
    "        X_train, y_train = shuffle(X_train, y_train)\n",
    "        for offset in range(0, num_examples, BATCH_SIZE):\n",
    "            end = offset + BATCH_SIZE\n",
    "            batch_x, batch_y = X_train[offset:end], y_train[offset:end]\n",
    "            sess.run(training_operation, feed_dict={x: batch_x, y: batch_y})\n",
    "            \n",
    "        validation_accuracy = evaluate(X_validation, y_validation)\n",
    "        print(\"EPOCH {} ...\".format(i+1))\n",
    "        print(\"Validation Accuracy = {:.3f}\".format(validation_accuracy))\n",
    "        print()\n",
    "        \n",
    "    saver.save(sess, 'p1')\n",
    "    print(\"Model saved\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test Accuracy = 0.915\n"
     ]
    }
   ],
   "source": [
    "### Show test accuracy\n",
    "with tf.Session() as sess:\n",
    "    saver.restore(sess, tf.train.latest_checkpoint('.'))\n",
    "    \n",
    "    # accuracy on test set\n",
    "    test_accuracy = evaluate(X_test, y_test)\n",
    "    print(\"Test Accuracy = {:.3f}\".format(test_accuracy))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 4\n",
    "\n",
    "_How did you train your model? (Type of optimizer, batch size, epochs, hyperparameters, etc.)_\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer:** \n",
    "- optimizer: AdamOptimizer\n",
    "- batch size: 128\n",
    "- epochs: 40\n",
    "- mean and stddev for prior weights generation: 0 and 0.01\n",
    "- learning rate: 0.0005"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 5\n",
    "\n",
    "\n",
    "_What approach did you take in coming up with a solution to this problem? It may have been a process of trial and error, in which case, outline the steps you took to get to the final solution and why you chose those steps. Perhaps your solution involved an already well known implementation or architecture. In this case, discuss why you think this is suitable for the current problem._"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer:** Generally, I started off from LeNet-5 lab, tried all sorts of alterations of hypterparameters, otpimizer, structures, etc, but only acheived 0.77 accuracy, so I simply gave it up. Then I started to read a couple of published paper of on this specific task, and got inspariations from Pierre Sermanet and Yann LeCun's \"Traffic Sign Recognition with Multi-Scale Convolutional Networks\". However, there are tons of parameters and configurations they hide in this paper, so I took some time to figure out a best result of my capability. \n",
    "\n",
    "Concisesly, the attemps I tried are as follows:\n",
    "- LeNet-5 + AdamOptimizer\t40 epochs\t0.77    sigma=0.1     rate=0.001    \n",
    "- LeNet-5 + AdamOptimizer\t40 epochs\t0.71\tsigma=0.1     rate=0.0005         \n",
    "- LeNet-5 + SGD\t\t\t    40 epochs \t0.055   sigma=0.1     rate=0.001\n",
    "- LeNet-5 + Momentum\t\t40 epochs\t0.11    sigma=0.1     rate=0.001\n",
    "\n",
    "Then I'm done with LeNet, began my own designs:\n",
    "\n",
    "- Mynet + AdamOptimizer\t\t40 epochs\t0.81\tsigma=0.05    rate=0.001    38,64         activation:ReLU\n",
    "- Mynet + AdamOptimizer\t\t40 epochs\t0.88\tsigma=0.01    rate=0.001    38,64         activation:ReLU\n",
    "- Mynet + AdamOptimizer\t\t40 epochs\t0.87\tsigma=0.01\t  rate=0.001    38,64         activation:ReLU       batchsize=256\n",
    "- Mynet + AdamOptimizer\t\t40 epochs\t0.91\tsigma=0.01\t  rate=0.0005\t38,64\t      activation:ReLU\n",
    "- Mynet + AdamOptimizer\t\t40 epochs\t0.92\tsigma=0.01\t  rate=0.0005\t108,108       activation:ReLU\n",
    "- Mynet + AdamOptimizer\t\t40 epochs\t0.95\tsigma=0.01\t  rate=0.0005\t108,108\t\t  activation:tanh\n",
    "- Mynet + AdamOptimizer\t\t40 epochs\t0.86\tsigma=0.01\t  rate=0.0005\t108,108\t\t  activation:tanh\t\t2 x dropout 0.5\n",
    "\n",
    "After a few experiments, I figured out the best configuration, and adding dropout between any layers does not increase accuracy. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## Step 3: Test a Model on New Images\n",
    "\n",
    "Take several pictures of traffic signs that you find on the web or around you (at least five), and run them through your classifier on your computer to produce example results. The classifier might not recognize some local signs but it could prove interesting nonetheless.\n",
    "\n",
    "You may find `signnames.csv` useful as it contains mappings from the class id (integer) to the actual sign name."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation\n",
    "\n",
    "Use the code cell (or multiple code cells, if necessary) to implement the first step of your project. Once you have completed your implementation and are satisfied with the results, be sure to thoroughly answer the questions that follow."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NyKP4/rj3kyS2g5GjHB8WWQ6nT6ecPptRThOmk5SNjZa2Cezv1UxLR1k5XKtzS4MFxDAp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\nPafopVRVg7WWLI0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nhM6VMF3U4Qm0Glk86r+6DQ5flaQ5Jg9dUDFrUmCtxaYJNkuwaUrb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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f51bc5e2128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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F5G8D85hjyr9hb28rrn4jpG9E+oa9LyJ4rskyzefSjI7lKZZGyOXSuJ7QC74I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\nCUGQol6rUCuXuX79Gm+/+Sb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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f51b84b56d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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5VNMu164zl3vZ7/1oXVdgs0UL74uLbaGNkYcjJUu0953b7Kg/l/B/4ErBExh2\nLTcYZzCqWBoK6xkOFLRkc/Mkxx99mPHGOr5xXWatMv9D9wnnPEgTYc8FFeVsRlmWFMUSiKfxHltO\nKKsprg7KzSALwZmmhhnhHTTAlgfdt73nZX/vXDzRK2UjmdILJW3zfbaYbB0v6ISF9E7Ha5HXdyLJ\nItjoonUY8eRZ2PNm1swYb5xi7cQjDPMBw6wIXMEnkXZwxf58BGlgHwUVJZ6xa5CmIs8KrM0oioKi\nyBnklsHAInlG5Wy7TXkT3yzltKtukejY2f7BBMTMJ84ETLfKVQ/p/c+d5SAL4y2ei99bpPcXBqRU\nqpBAqlgDuQ3eOeNmlOMZ4/WTbJw+xfraOmb1MEvFCGttGNb78HIGfzDUn9MgTQ9eHUXBl0TkPSJy\n6ZkGKoGxb1ivKyqUbDBgaWmZpdGQ0bBgeVSwslywspwzGhoGuSe3Dis1RmqM+FAPR5xRy3bTu+e2\nkcPpY5sP1zvS3nJz+XJno0lvcQbQD8GGfGEbHDQKuSijAlaGQDNlfPo4ayeOs3HqNOONMU3jsHke\n3tIhgk/v23uiNj/aIUgD+yyo8JmhNoJRzxJCZjMGeUGR5xSR4u0ww6phuXSUpWBLTymKNOGVdSny\nlTJ0dY50+6y+I+U5tr7A4rteO/HWaA30ri1aWe1iW5ACRpSMsHPlaCAMBzBZm7Bx+jhrJ4+zubFB\nOS1RVfIiJytyxIS9+rdkEe8DznmQZr8FFcePn2R9bQMjlswYcmN50XXX85IXPT++1jGkW2VGWF7J\nEGOYTGom44bpzDOrlFnpgj3eas2tMdfzlrVnuusJL7IVv/3QUL9n94Pnv+iWS9r71unyWW4Y5YbR\nUBgOlUEOtZtw+vQJ1tZOUZYliGDznD/+73fyx3d+hizPsFlA2fr6+k6P8qzgXAdptsDZFlR827XX\ncsmRyxiYghWTsyoZTzl6GTRN0ITxYMJbnJaNYTQSilywErY79E4pCTHtbgvQOAeY07eS1T6H/NQu\nWYTRJaw9hC1675nvmX7vnG+oux4sEY3bM2Z5znDZsDQURkPIjVI3HeLBUBQDbJ5x00038SM//iMs\nHVpiuDwAhc9//m5ufrx89cCuQZod2p9VQYUxGYeWVzmyeoSRCkXjGYyG2DxHMaiYVtSKBWOUYmRY\n1jxseZ0p2PCeuapqaJySctRB2ldKtInO0nPItBo3bXZOUvaS6ZSyc5LL1mvaaSPY4Z1/KObZ9Sjd\nxLQta4RFou0eAAANeUlEQVQ8t+SZZTQ0DAdQFBreQinhVaXSu7eIYK2JlG7DO3RTUufj6bk7U5Am\nFlvczj4KKgyW1ZVDXH3FVeTeo9Mpg6URtigC0hEQE2LzsfQ0HxlMlmMKi8kc1nrGY4/XJr5PPqfN\nj08eshaB3Yt/kpclZeRAT9y3NnPMfkF6SIeE8bSMggxOb40M6d+WsAV5YYXRwLK0ZMnyEIjJs6DV\nW4TMGDITEBwcOnH7kyxVEQspjezxjsefKUjj2GdBxSWXXsYVV1zFFVddidQV1eYmwyIjGw5Q0711\nquctAVfj6xqtGrRqoG6wGAaZwUh4iYHzKW1ZI6XSVqS2SI9eHScpCCQx8TVZBorDoy6kBfRVRenl\nBGis3k3WhYn772cm7OMzLGB5CMsjwWYpwYLgn1Ahtxm5zclthgLWZuR5RjEIfxPVh13PH0fEnylI\nE0Oz+yqouPba63jms5/NoUMruNmU2TBnYCAbDSAlUcYyKon5adXamI0TpxivjYOiN6nIlw6ztHwI\nHQ4pnVL5hqqCqoz+fbFoKMEMVOs0vBDGpXi/ASuYLFQsJrnvncPVM1Q9eZ6RZVnM9tVWOVSN25KZ\n8E7ZPBeKTAPiTVDgRoVjmEGex/fMZpY8vp1hUBQUWUGRFyiQFwXDQcFoOGA4LEIZubWoHDz96knj\nq3/Oc67lGc/+NsTAbLxBXhisevLhAI1+afUeSa+k8Ep5eoP1Bx9l7fgpJrOS6azksmuewujQALuU\nk6VXfCLgBNeEfXC9ZOH9tEooy6oc1C5uLCSYLCR2Snp/OEJV18ymJd7VjEZDlozESFmnyasqJgvJ\nE3kOw0IZDiAzSmaUIvMMC8/Aeoo8Z1Bk5LnFmgz1MMgKBnnBICtQEfKiYDAsGI4KBoMck4V30nv0\n8d38SER+GvgZ4Jnx1D3Au+P2KKnNnospAIbDguXhINi3bog0Sxg82WiIDArEWqwY6smMkw8/Go5H\nj3Hy0WNMpzNMkSODgspPcX6KdYLUjqz2LGlBURS4QvBi8SK4RvG1xh2wJWArcgOshLd7myCvvTqy\nTBmNLKgwGGQMhhYT9Q2J1T0GxUiDoUbrKetrp3hsfBptStRVGOMpMktRWJZXlllaXWE0WmI4GGFN\nzskTJ5hOpzjvsZGrWJu1Sh0QlNDFotB9wF4p/gHgF4CvEsTYTwLvF5EXquoX91tMATAYDFgeDoIi\npA71NYgGxBcFkmUYMZSTKY994z7u/Yu7OXXyFGtr6ziBlSsuZfnyS6l0htcJOMVUNbasyfMVTGHA\n5ngrOBHqEmrjwxuijaCZDe+gVYM3grfh7dHqHGiDtRrkrIEiz8nzDGMUie+OscaTWY+4Epopk8kJ\n1h+7j0cf/CbldEw1G6PeYbPghTt8ySUcvvQSVg8dYWX5EMPhMidPnGA2m+G8JxMhy3Kste0LmaBT\ncQ7ov9mzjP+9hVO/KCI/A3w38EX2/ZICaKopH/3wh/i+17wWX9dBIzYGayzWGsrpjMl0zKlvPcJD\n9z/Ag/ffz51f/gpPO3oZZlAg1YhCK06vnwJxFDbHVQ2udgyGqxSjVT5153/ne193MyYfIWWNzhrE\nG6wU2KxAbQ62wAlU6vnDT36QG2+8Ce8bDB4jihUQrdBaaHyNd4GaRSs+9emPc+NLXkxTTRivneTR\nRx7ksYcfoiyn1OWMxrnW/Xv5VVfxp5+/m1f/5Zcznc4YDJZZ31ijrMvwdmxj4rYwFhGLYHjf+36H\nt/zAm3tUv384iMvWEF4bugT8yU7FFCKSiil2Rfz6qdPccceHeekLX4iqw6mnGBSYuPpPnTrJI/fd\nx8P33cfDDz7A8c0NPv/g/Ry98lLyQqit4rThsWOP8vCDD6KNx3jBqGG0vMxoaYUP//7v8ZLnP5el\n5WWqsqGc1VhbMByukA1XKAYrFMtC7ZVJVfInn/4gr3v194C6+EpwhzbhJQGVc5TjDWYba8zGG1ST\nDT7ye7/LkXKDcjZhWk6YzCZMymks+oCmaainJc2sYri8zGfv/hLf89IX43WTyaxkc7pJ1VQYmyFW\nsC2rD5tB/dZvvZ+3vOXNpFeXHQT248C5nvCG6CGwAXy/qn5ZRF5OEDx7f0kBsLl2mrqqOX3qJNYa\njDVYAVeV+LLk1PHjfPPee7nv61/n9KnTrI03cKqUGUguNDiqpubEsWMcf+QY1aSksDkDU7C0MmJ5\nZYnZZMzxh77K4cOrVGVDVdYUgxFm9RIG5gj5csPy0FI1jrqeIFqR6anoGWzwVY2rKsqqoqpKNk+e\nZP34MTZOHGd8+hSbp0/xpc9+hvF0SuUdMiyQQYEZDLCDAa5xTMdTZmubHDk6wXulrCrKpkERpmVJ\n7WuKzMZ3z0WK7xXFt5W9B4T9UPyXgO8CDgM/CPxbEXnlQSfyX973X3j0sUf51X/xz6JnDV7+spfx\nmlfeyLGHH+LYI49w7OTJkKBRzdioSxSlGA7Ji4LZrOT4Y8dZO73O5iyw1cYYauPCThszZVZVfPFr\nXycz4OtQjz8oBqysrHL40BGuvOYpXHHNUygbx4nTa0w3N7jvy18CaCt566qicQ2Nr9lcX2f91Gk2\n19eZbo6ZNY5HxhVV7fCEvLnMNAzzgswIWZaR5wWuGOCcp3EN48mE5dUVRqMRdaOYWR1EXJaRFwUi\nht/6nffzoQ9/mM997s/5sR97G6pPgK9eVRvg6/Hrn4vIywiy/VcIy3LPxRQAt73pNu644w7e9r/9\nFIbg7aJpuP+b36AcbzKZjBlPxmyWMzaqko16hhcYDAcUec50MuH0ZMJ4OmM8K/EodW7IjaFyymRW\nM6tLvvS1rzEbb2K8YrxnlBcsL404cugQ0/Ea4ivKquGRY8eZjje5/ytfQhGqWcV0OqMqy7Y2bzyZ\nsL4xZjyeUpYV09rx6LjEq8dYKCpPLg12qCzFV4a6PMcVAxrnaRrHZDpl6dAqw+UR07JGIrfL8oy8\nyEEMt95yCz/4Qz/IT/zE2/g3/+5fISrc9fm7eN333rJX9LVwLux4AwwOUEwxBHj0kUeZTqfcd/8D\nbZWc1jXTjQ2mGxtUdUXd1MzKGeubm6yPN6nrhhOn1sizjPF4k+l4wqyuKKsaL5BVFVlRYBAyhLKq\nefj4SWYbGxhVjCrDLGM4HHJ6c4zPCioVqqbh2MlTTKZTvvnAAyhCXdXMZiV1VYcNGkSZliWbkxmz\nWUVdOxrvWJvNAMUYIfcNeWNRE3bltGKoJjOqWYlf36SqKh565DFmzrM5K1lb22Tt9AZ5PmBS1WzO\nSjbLKSfX1yiGBevr63z+83chwL33fm3u+e0ZVPWsD+AfENKvngFcT4i1N8Br4vW/A5wA3gi8APhd\ngulX7DLmj5LCVxeP/Rw/uhccpmOvFH8FYZOjq4E1AmV/n6p+AthvMcUdwI8R7P7ZLu0uwjwMCY60\nXYNfO4Ec1B68CP9zwjl94eBF+J8HLiL+AoWLiL9A4SLiL1C4iPgLFJ4UiBeRnxWRb4jIVEQ+IyIv\n3aHd7dvU5X2hd/0VIvIBEXkoXrttmzHeLSLfEpGJiPyBiPzwbn22qQVUEal3qh1cuEclImsisrGH\nWsM0/pqI/ImIvH6HsdP8n7P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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f51b8584f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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sx7z82m7KlCjKWV4ZsroeM3dqivPNKdTMgOFWn6Xh0GXfsAYrgikmkrYKseI8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\nnlXLvhbHTmMslozv7ik/fq4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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f51b8087128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Fji2hH/z1vwD/kar+mohUgN8EJoF/A/y7J6nD76VhYEPfx9XttVleXuTlV17ilRcDLjwf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\n+4y/R+k+4+9Rus/4e5T+fwJ3L/03UhDzAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f51a85f1fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Load the new images and plot them.\n",
    "import cv2\n",
    "\n",
    "new_images=[]\n",
    "# manually add 5 new labels\n",
    "new_labels=[9,13,17,18,22]\n",
    "    \n",
    "# manually add 5 new images\n",
    "new_image=cv2.imread('9.jpg')\n",
    "new_image=cv2.resize(new_image, (32, 32)) \n",
    "new_images.append(new_image)\n",
    "\n",
    "new_image=cv2.imread('13.jpg')\n",
    "new_image=cv2.resize(new_image, (32, 32)) \n",
    "new_images.append(new_image)\n",
    "    \n",
    "new_image=cv2.imread('17.jpg')\n",
    "new_image=cv2.resize(new_image, (32, 32)) \n",
    "new_images.append(new_image)\n",
    "    \n",
    "new_image=cv2.imread('18.jpg')\n",
    "new_image=cv2.resize(new_image, (32, 32)) \n",
    "new_images.append(new_image)\n",
    "    \n",
    "new_image=cv2.imread('22.jpg')\n",
    "new_image=cv2.resize(new_image, (32, 32)) \n",
    "new_images.append(new_image)\n",
    "    \n",
    "    # plot new images\n",
    "for im in new_images:\n",
    "    plt.figure(figsize=(1,1))\n",
    "    plt.imshow(im)    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 6\n",
    "\n",
    "_Choose five candidate images of traffic signs and provide them in the report. Are there any particular qualities of the image(s) that might make classification difficult? It could be helpful to plot the images in the notebook._\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer:** Images are acquired from screenshots of virtually walking in German streets in Google earth. The first image has relatively complicated patterns, which could potentially be a touch one for the CNN, and the third is a bit worn out and the color is shollow. Otherwise, should't be a problem for the classifier.\n",
    "\n",
    "P.S. due to the color space problem of my snapping/cutting tool, the images displayed out are blue. I really lack of enough knowledge of color space, but apparently it doesn't affect classification."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "New Accuracy = 0.600\n"
     ]
    }
   ],
   "source": [
    "### Run the predictions here.\n",
    "### Feel free to use as many code cells as needed.\n",
    "    \n",
    "#print(predictions[:43])\n",
    "with tf.Session() as sess:\n",
    "    saver.restore(sess, tf.train.latest_checkpoint('.'))\n",
    "    \n",
    "    new_accuracy = evaluate(new_images, new_labels)\n",
    "    print(\"New Accuracy = {:.3f}\".format(new_accuracy))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 7\n",
    "\n",
    "_Is your model able to perform equally well on captured pictures when compared to testing on the dataset? The simplest way to do this check the accuracy of the predictions. For example, if the model predicted 1 out of 5 signs correctly, it's 20% accurate._\n",
    "\n",
    "_**NOTE:** You could check the accuracy manually by using `signnames.csv` (same directory). This file has a mapping from the class id (0-42) to the corresponding sign name. So, you could take the class id the model outputs, lookup the name in `signnames.csv` and see if it matches the sign from the image._\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer:** My model achieved 60% accuracy, namely got 3 correct predictions out of 5 for such a mini test set. As expected, the 1st and 3rd sign are mis-classified. The first one has compilicated patterns while the third is worn out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TopKV2(values=array([[  4.31237340e-01,   2.45777830e-01,   6.80081472e-02],\n",
      "       [  9.99144554e-01,   2.73745594e-04,   1.48749037e-04],\n",
      "       [  7.19420493e-01,   5.32744601e-02,   4.93838042e-02],\n",
      "       [  4.23976004e-01,   1.40563533e-01,   1.35089964e-01],\n",
      "       [  7.41104007e-01,   1.71638414e-01,   2.36951951e-02]], dtype=float32), indices=array([[12, 42, 11],\n",
      "       [13, 38,  3],\n",
      "       [12, 33, 35],\n",
      "       [18, 26, 11],\n",
      "       [22, 15, 25]], dtype=int32))\n"
     ]
    }
   ],
   "source": [
    "### Visualize the softmax probabilities here.\n",
    "### Feel free to use as many code cells as needed.\n",
    "with tf.Session() as sess:\n",
    "    saver.restore(sess, tf.train.latest_checkpoint('.'))\n",
    "    \n",
    "    # get softmax probablity \n",
    "    prediction=tf.nn.softmax(logits) \n",
    "    predictions = sess.run(prediction, feed_dict={x: new_images})\n",
    "    \n",
    "    # visualize the certainty of predictions\n",
    "    print(sess.run(tf.nn.top_k(tf.constant(np.array(predictions)), k=3)) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 8\n",
    "\n",
    "*Use the model's softmax probabilities to visualize the **certainty** of its predictions, [`tf.nn.top_k`](https://www.tensorflow.org/versions/r0.12/api_docs/python/nn.html#top_k) could prove helpful here. Which predictions is the model certain of? Uncertain? If the model was incorrect in its initial prediction, does the correct prediction appear in the top k? (k should be 5 at most)*\n",
    "\n",
    "`tf.nn.top_k` will return the values and indices (class ids) of the top k predictions. So if k=3, for each sign, it'll return the 3 largest probabilities (out of a possible 43) and the correspoding class ids.\n",
    "\n",
    "Take this numpy array as an example:\n",
    "\n",
    "```\n",
    "# (5, 6) array\n",
    "a = np.array([[ 0.24879643,  0.07032244,  0.12641572,  0.34763842,  0.07893497,\n",
    "         0.12789202],\n",
    "       [ 0.28086119,  0.27569815,  0.08594638,  0.0178669 ,  0.18063401,\n",
    "         0.15899337],\n",
    "       [ 0.26076848,  0.23664738,  0.08020603,  0.07001922,  0.1134371 ,\n",
    "         0.23892179],\n",
    "       [ 0.11943333,  0.29198961,  0.02605103,  0.26234032,  0.1351348 ,\n",
    "         0.16505091],\n",
    "       [ 0.09561176,  0.34396535,  0.0643941 ,  0.16240774,  0.24206137,\n",
    "         0.09155967]])\n",
    "```\n",
    "\n",
    "Running it through `sess.run(tf.nn.top_k(tf.constant(a), k=3))` produces:\n",
    "\n",
    "```\n",
    "TopKV2(values=array([[ 0.34763842,  0.24879643,  0.12789202],\n",
    "       [ 0.28086119,  0.27569815,  0.18063401],\n",
    "       [ 0.26076848,  0.23892179,  0.23664738],\n",
    "       [ 0.29198961,  0.26234032,  0.16505091],\n",
    "       [ 0.34396535,  0.24206137,  0.16240774]]), indices=array([[3, 0, 5],\n",
    "       [0, 1, 4],\n",
    "       [0, 5, 1],\n",
    "       [1, 3, 5],\n",
    "       [1, 4, 3]], dtype=int32))\n",
    "```\n",
    "\n",
    "Looking just at the first row we get `[ 0.34763842,  0.24879643,  0.12789202]`, you can confirm these are the 3 largest probabilities in `a`. You'll also notice `[3, 0, 5]` are the corresponding indices."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer:** The top three possible labels and probabilities for each image are, as shown in the last code cell:\n",
    "- image 1: [12, 42, 11] with probability [0.43, 0.25,   0.06].   Actual label is 9. Wrong prediction. \n",
    "- image 2: [13, 38, 3] with probability [0.99, 0.0003, 0.0002]. Actual label is 13. Correct prediction. \n",
    "- image 3: [12, 33, 35] with probability [0.72, 0.05, 0.05].     Actual label is 17. Wrong prediction. \n",
    "- image 4: [18, 26, 11] with probability [0.42, 0.14, 0.13].     Actual label is 18. Correct prediction. \n",
    "- image 5: [22, 15, 25] with probability [0.74, 0.17, 0.02].     Actual label is 22. Correct prediction. "
   ]
  },
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   "metadata": {},
   "source": [
    "> **Note**: Once you have completed all of the code implementations and successfully answered each question above, you may finalize your work by exporting the iPython Notebook as an HTML document. You can do this by using the menu above and navigating to  \\n\",\n",
    "    \"**File -> Download as -> HTML (.html)**. Include the finished document along with this notebook as your submission."
   ]
  }
 ],
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