2. Define the Network Architecture.ipynb

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    "## Define the Convolutional Neural Network\n",
    "\n",
    "After you've looked at the data you're working with and, in this case, know the shapes of the images and of the keypoints, you are ready to define a convolutional neural network that can *learn* from this data.\n",
    "\n",
    "In this notebook and in `models.py`, you will:\n",
    "1. Define a CNN with images as input and keypoints as output\n",
    "2. Construct the transformed FaceKeypointsDataset, just as before\n",
    "3. Train the CNN on the training data, tracking loss\n",
    "4. See how the trained model performs on test data\n",
    "5. If necessary, modify the CNN structure and model hyperparameters, so that it performs *well* **\\***\n",
    "\n",
    "**\\*** What does *well* mean?\n",
    "\n",
    "\"Well\" means that the model's loss decreases during training **and**, when applied to test image data, the model produces keypoints that closely match the true keypoints of each face. And you'll see examples of this later in the notebook.\n",
    "\n",
    "---\n"
   ]
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    "## CNN Architecture\n",
    "\n",
    "Recall that CNN's are defined by a few types of layers:\n",
    "* Convolutional layers\n",
    "* Maxpooling layers\n",
    "* Fully-connected layers\n",
    "\n",
    "You are required to use the above layers and encouraged to add multiple convolutional layers and things like dropout layers that may prevent overfitting. You are also encouraged to look at literature on keypoint detection, such as [this paper](https://arxiv.org/pdf/1710.00977.pdf), to help you determine the structure of your network.\n",
    "\n",
    "\n",
    "### TODO: Define your model in the provided file `models.py` file\n",
    "\n",
    "This file is mostly empty but contains the expected name and some TODO's for creating your model.\n",
    "\n",
    "---"
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    "## PyTorch Neural Nets\n",
    "\n",
    "To define a neural network in PyTorch, you define the layers of a model in the function `__init__` and define the feedforward behavior of a network that employs those initialized layers in the function `forward`, which takes in an input image tensor, `x`. The structure of this Net class is shown below and left for you to fill in.\n",
    "\n",
    "Note: During training, PyTorch will be able to perform backpropagation by keeping track of the network's feedforward behavior and using autograd to calculate the update to the weights in the network.\n",
    "\n",
    "#### Define the Layers in ` __init__`\n",
    "As a reminder, a conv/pool layer may be defined like this (in `__init__`):\n",
    "```\n",
    "# 1 input image channel (for grayscale images), 32 output channels/feature maps, 3x3 square convolution kernel\n",
    "self.conv1 = nn.Conv2d(1, 32, 3)\n",
    "\n",
    "# maxpool that uses a square window of kernel_size=2, stride=2\n",
    "self.pool = nn.MaxPool2d(2, 2)      \n",
    "```\n",
    "\n",
    "#### Refer to Layers in `forward`\n",
    "Then referred to in the `forward` function like this, in which the conv1 layer has a ReLu activation applied to it before maxpooling is applied:\n",
    "```\n",
    "x = self.pool(F.relu(self.conv1(x)))\n",
    "```\n",
    "\n",
    "Best practice is to place any layers whose weights will change during the training process in `__init__` and refer to them in the `forward` function; any layers or functions that always behave in the same way, such as a pre-defined activation function, should appear *only* in the `forward` function."
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    "#### Why models.py\n",
    "\n",
    "You are tasked with defining the network in the `models.py` file so that any models you define can be saved and loaded by name in different notebooks in this project directory. For example, by defining a CNN class called `Net` in `models.py`, you can then create that same architecture in this and other notebooks by simply importing the class and instantiating a model:\n",
    "```\n",
    "    from models import Net\n",
    "    net = Net()\n",
    "```"
   ]
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    }
   ],
   "source": [
    "# load the data if you need to; if you have already loaded the data, you may comment this cell out\n",
    "# -- DO NOT CHANGE THIS CELL -- #\n",
    "!mkdir /data\n",
    "!wget -P /data/ https://s3.amazonaws.com/video.udacity-data.com/topher/2018/May/5aea1b91_train-test-data/train-test-data.zip\n",
    "!unzip -n /data/train-test-data.zip -d /data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\">**Note:** Workspaces automatically close connections after 30 minutes of inactivity (including inactivity while training!). Use the code snippet below to keep your workspace alive during training. (The active_session context manager is imported below.)\n",
    "</div>\n",
    "```\n",
    "from workspace_utils import active_session\n",
    "\n",
    "with active_session():\n",
    "    train_model(num_epochs)\n",
    "```\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import the usual resources\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# import utilities to keep workspaces alive during model training\n",
    "from workspace_utils import active_session\n",
    "\n",
    "# watch for any changes in model.py, if it changes, re-load it automatically\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.4.0\n",
      "Net(\n",
      "  (conv1): Conv2d(1, 32, kernel_size=(5, 5), stride=(1, 1))\n",
      "  (pool1): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False)\n",
      "  (fc_drop1): Dropout(p=0.2)\n",
      "  (conv2): Conv2d(32, 36, kernel_size=(5, 5), stride=(1, 1))\n",
      "  (pool2): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False)\n",
      "  (fc_drop2): Dropout(p=0.2)\n",
      "  (conv3): Conv2d(36, 48, kernel_size=(5, 5), stride=(1, 1))\n",
      "  (pool3): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False)\n",
      "  (fc_drop3): Dropout(p=0.2)\n",
      "  (conv4): Conv2d(48, 64, kernel_size=(3, 3), stride=(1, 1))\n",
      "  (pool4): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False)\n",
      "  (fc_drop4): Dropout(p=0.2)\n",
      "  (conv5): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1))\n",
      "  (pool5): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False)\n",
      "  (fc6): Linear(in_features=1024, out_features=136, bias=True)\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "## TODO: Define the Net in models.py\n",
    "\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "print(torch.__version__)\n",
    "\n",
    "## TODO: Once you've define the network, you can instantiate it\n",
    "# one example conv layer has been provided for you\n",
    "from models import Net\n",
    "\n",
    "            \n",
    "\n",
    "net = Net()\n",
    "print(net)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Transform the dataset \n",
    "\n",
    "To prepare for training, create a transformed dataset of images and keypoints.\n",
    "\n",
    "### TODO: Define a data transform\n",
    "\n",
    "In PyTorch, a convolutional neural network expects a torch image of a consistent size as input. For efficient training, and so your model's loss does not blow up during training, it is also suggested that you normalize the input images and keypoints. The necessary transforms have been defined in `data_load.py` and you **do not** need to modify these; take a look at this file (you'll see the same transforms that were defined and applied in Notebook 1).\n",
    "\n",
    "To define the data transform below, use a [composition](http://pytorch.org/tutorials/beginner/data_loading_tutorial.html#compose-transforms) of:\n",
    "1. Rescaling and/or cropping the data, such that you are left with a square image (the suggested size is 224x224px)\n",
    "2. Normalizing the images and keypoints; turning each RGB image into a grayscale image with a color range of [0, 1] and transforming the given keypoints into a range of [-1, 1]\n",
    "3. Turning these images and keypoints into Tensors\n",
    "\n",
    "These transformations have been defined in `data_load.py`, but it's up to you to call them and create a `data_transform` below. **This transform will be applied to the training data and, later, the test data**. It will change how you go about displaying these images and keypoints, but these steps are essential for efficient training.\n",
    "\n",
    "As a note, should you want to perform data augmentation (which is optional in this project), and randomly rotate or shift these images, a square image size will be useful; rotating a 224x224 image by 90 degrees will result in the same shape of output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "from torch.utils.data import Dataset, DataLoader\n",
    "from torchvision import transforms, utils\n",
    "import multiprocessing\n",
    "\n",
    "# the dataset we created in Notebook 1 is copied in the helper file `data_load.py`\n",
    "from data_load import FacialKeypointsDataset\n",
    "# the transforms we defined in Notebook 1 are in the helper file `data_load.py`\n",
    "from data_load import Rescale, RandomCrop, Normalize, ToTensor\n",
    "\n",
    "\n",
    "## TODO: define the data_transform using transforms.Compose([all tx's, . , .])\n",
    "# order matters! i.e. rescaling should come before a smaller crop\n",
    "data_transform = transforms.Compose([ Rescale(256), RandomCrop(224), Normalize(), ToTensor() ])\n",
    "\n",
    "# testing that you've defined a transform\n",
    "assert(data_transform is not None), 'Define a data_transform'\n",
    "num_workers = multiprocessing.cpu_count()\n",
    "print(num_workers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of images:  3462\n",
      "0 torch.Size([1, 224, 224]) torch.Size([68, 2])\n",
      "1 torch.Size([1, 224, 224]) torch.Size([68, 2])\n",
      "2 torch.Size([1, 224, 224]) torch.Size([68, 2])\n",
      "3 torch.Size([1, 224, 224]) torch.Size([68, 2])\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n"
     ]
    }
   ],
   "source": [
    "# create the transformed dataset\n",
    "transformed_dataset = FacialKeypointsDataset(csv_file='/data/training_frames_keypoints.csv',\n",
    "                                             root_dir='/data/training/',\n",
    "                                             transform=data_transform)\n",
    "\n",
    "\n",
    "print('Number of images: ', len(transformed_dataset))\n",
    "\n",
    "# iterate through the transformed dataset and print some stats about the first few samples\n",
    "for i in range(4):\n",
    "    sample = transformed_dataset[i]\n",
    "    print(i, sample['image'].size(), sample['keypoints'].size())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Batching and loading data\n",
    "\n",
    "Next, having defined the transformed dataset, we can use PyTorch's DataLoader class to load the training data in batches of whatever size as well as to shuffle the data for training the model. You can read more about the parameters of the DataLoader, in [this documentation](http://pytorch.org/docs/master/data.html).\n",
    "\n",
    "#### Batch size\n",
    "Decide on a good batch size for training your model. Try both small and large batch sizes and note how the loss decreases as the model trains. Too large a batch size may cause your model to crash and/or run out of memory while training.\n",
    "\n",
    "**Note for Windows users**: Please change the `num_workers` to 0 or you may face some issues with your DataLoader failing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# load training data in batches\n",
    "batch_size = 10\n",
    "\n",
    "train_loader = DataLoader(transformed_dataset, \n",
    "                          batch_size=batch_size,\n",
    "                          shuffle=True, \n",
    "                          num_workers=4)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Before training\n",
    "\n",
    "Take a look at how this model performs before it trains. You should see that the keypoints it predicts start off in one spot and don't match the keypoints on a face at all! It's interesting to visualize this behavior so that you can compare it to the model after training and see how the model has improved.\n",
    "\n",
    "#### Load in the test dataset\n",
    "\n",
    "The test dataset is one that this model has *not* seen before, meaning it has not trained with these images. We'll load in this test data and before and after training, see how your model performs on this set!\n",
    "\n",
    "To visualize this test data, we have to go through some un-transformation steps to turn our images into python images from tensors and to turn our keypoints back into a recognizable range. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# load in the test data, using the dataset class\n",
    "# AND apply the data_transform you defined above\n",
    "\n",
    "# create the test dataset\n",
    "test_dataset = FacialKeypointsDataset(csv_file='/data/test_frames_keypoints.csv',\n",
    "                                             root_dir='/data/test/',\n",
    "                                             transform=data_transform)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# load test data in batches\n",
    "batch_size = 10\n",
    "\n",
    "test_loader = DataLoader(test_dataset, \n",
    "                          batch_size=batch_size,\n",
    "                          shuffle=True, \n",
    "                          num_workers=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Apply the model on a test sample\n",
    "\n",
    "To test the model on a test sample of data, you have to follow these steps:\n",
    "1. Extract the image and ground truth keypoints from a sample\n",
    "2. Wrap the image in a Variable, so that the net can process it as input and track how it changes as the image moves through the network.\n",
    "3. Make sure the image is a FloatTensor, which the model expects.\n",
    "4. Forward pass the image through the net to get the predicted, output keypoints.\n",
    "\n",
    "This function test how the network performs on the first batch of test data. It returns the images, the transformed images, the predicted keypoints (produced by the model), and the ground truth keypoints."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# test the model on a batch of test images\n",
    "\n",
    "def net_sample_output():\n",
    "    \n",
    "    # iterate through the test dataset\n",
    "    for i, sample in enumerate(test_loader):\n",
    "        \n",
    "        # get sample data: images and ground truth keypoints\n",
    "        images = sample['image']\n",
    "        key_pts = sample['keypoints']\n",
    "\n",
    "        # convert images to FloatTensors\n",
    "        images = images.type(torch.FloatTensor)\n",
    "\n",
    "        # forward pass to get net output\n",
    "        output_pts = net(images)\n",
    "        \n",
    "        # reshape to batch_size x 68 x 2 pts\n",
    "        output_pts = output_pts.view(output_pts.size()[0], 68, -1)\n",
    "        \n",
    "        # break after first image is tested\n",
    "        if i == 0:\n",
    "            return images, output_pts, key_pts\n",
    "            "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Debugging tips\n",
    "\n",
    "If you get a size or dimension error here, make sure that your network outputs the expected number of keypoints! Or if you get a Tensor type error, look into changing the above code that casts the data into float types: `images = images.type(torch.FloatTensor)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([10, 1, 224, 224])\n",
      "torch.Size([10, 68, 2])\n",
      "torch.Size([10, 68, 2])\n"
     ]
    }
   ],
   "source": [
    "# call the above function\n",
    "# returns: test images, test predicted keypoints, test ground truth keypoints\n",
    "test_images, test_outputs, gt_pts = net_sample_output()\n",
    "\n",
    "# print out the dimensions of the data to see if they make sense\n",
    "print(test_images.data.size())\n",
    "print(test_outputs.data.size())\n",
    "print(gt_pts.size())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize the predicted keypoints\n",
    "\n",
    "Once we've had the model produce some predicted output keypoints, we can visualize these points in a way that's similar to how we've displayed this data before, only this time, we have to \"un-transform\" the image/keypoint data to display it.\n",
    "\n",
    "Note that I've defined a *new* function, `show_all_keypoints` that displays a grayscale image, its predicted keypoints and its ground truth keypoints (if provided)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_all_keypoints(image, predicted_key_pts, gt_pts=None):\n",
    "    \"\"\"Show image with predicted keypoints\"\"\"\n",
    "    # image is grayscale\n",
    "    plt.imshow(image, cmap='gray')\n",
    "    plt.scatter(predicted_key_pts[:, 0], predicted_key_pts[:, 1], s=20, marker='.', c='m')\n",
    "    # plot ground truth points as green pts\n",
    "    if gt_pts is not None:\n",
    "        plt.scatter(gt_pts[:, 0], gt_pts[:, 1], s=20, marker='.', c='g')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Un-transformation\n",
    "\n",
    "Next, you'll see a helper function. `visualize_output` that takes in a batch of images, predicted keypoints, and ground truth keypoints and displays a set of those images and their true/predicted keypoints.\n",
    "\n",
    "This function's main role is to take batches of image and keypoint data (the input and output of your CNN), and transform them into numpy images and un-normalized keypoints (x, y) for normal display. The un-transformation process turns keypoints and images into numpy arrays from Tensors *and* it undoes the keypoint normalization done in the Normalize() transform; it's assumed that you applied these transformations when you loaded your test data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3de5013c8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3de471390>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3de438c18>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3de403080>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3de3484e0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3de30a278>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3de33be48>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3de2893c8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3de24a908>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3de20d9e8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualize the output\n",
    "# by default this shows a batch of 10 images\n",
    "def visualize_output(test_images, test_outputs, gt_pts=None, batch_size=10):\n",
    "\n",
    "    for i in range(batch_size):\n",
    "        plt.figure(figsize=(20,10))\n",
    "        ax = plt.subplot(1, batch_size, i+1)\n",
    "\n",
    "        # un-transform the image data\n",
    "        image = test_images[i].data   # get the image from it's Variable wrapper\n",
    "        image = image.numpy()   # convert to numpy array from a Tensor\n",
    "        image = np.transpose(image, (1, 2, 0))   # transpose to go from torch to numpy image\n",
    "\n",
    "        # un-transform the predicted key_pts data\n",
    "        predicted_key_pts = test_outputs[i].data\n",
    "        predicted_key_pts = predicted_key_pts.numpy()\n",
    "        # undo normalization of keypoints  \n",
    "        predicted_key_pts = predicted_key_pts*50.0+100\n",
    "        \n",
    "        # plot ground truth points for comparison, if they exist\n",
    "        ground_truth_pts = None\n",
    "        if gt_pts is not None:\n",
    "            ground_truth_pts = gt_pts[i]         \n",
    "            ground_truth_pts = ground_truth_pts*50.0+100\n",
    "        \n",
    "        # call show_all_keypoints\n",
    "        show_all_keypoints(np.squeeze(image), predicted_key_pts, ground_truth_pts)\n",
    "            \n",
    "        plt.axis('off')\n",
    "\n",
    "    plt.show()\n",
    "    \n",
    "# call it\n",
    "visualize_output(test_images, test_outputs, gt_pts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training\n",
    "\n",
    "#### Loss function\n",
    "Training a network to predict keypoints is different than training a network to predict a class; instead of outputting a distribution of classes and using cross entropy loss, you may want to choose a loss function that is suited for regression, which directly compares a predicted value and target value. Read about the various kinds of loss functions (like MSE or L1/SmoothL1 loss) in [this documentation](http://pytorch.org/docs/master/_modules/torch/nn/modules/loss.html).\n",
    "\n",
    "### TODO: Define the loss and optimization\n",
    "\n",
    "Next, you'll define how the model will train by deciding on the loss function and optimizer.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "## TODO: Define the loss and optimization\n",
    "import torch.optim as optim\n",
    "\n",
    "\n",
    "#criterion = nn.L1Loss()\n",
    "criterion = nn.MSELoss()\n",
    "\n",
    "#optimizer = optim.SGD(net.parameters(), lr=0.01, momentum=0.9)\n",
    "optimizer = optim.Adam(net.parameters(), lr= 1e-4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training and Initial Observation\n",
    "\n",
    "Now, you'll train on your batched training data from `train_loader` for a number of epochs. \n",
    "\n",
    "To quickly observe how your model is training and decide on whether or not you should modify it's structure or hyperparameters, you're encouraged to start off with just one or two epochs at first. As you train, note how your the model's loss behaves over time: does it decrease quickly at first and then slow down? Does it take a while to decrease in the first place? What happens if you change the batch size of your training data or modify your loss function? etc. \n",
    "\n",
    "Use these initial observations to make changes to your model and decide on the best architecture before you train for many epochs and create a final model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_net(n_epochs):\n",
    "\n",
    "    # prepare the net for training\n",
    "    net.train()\n",
    "\n",
    "    for epoch in range(n_epochs):  # loop over the dataset multiple times\n",
    "        \n",
    "        running_loss = 0.0\n",
    "\n",
    "        # train on batches of data, assumes you already have train_loader\n",
    "        for batch_i, data in enumerate(train_loader):\n",
    "            # get the input images and their corresponding labels\n",
    "            images = data['image']\n",
    "            key_pts = data['keypoints']\n",
    "\n",
    "            # flatten pts\n",
    "            key_pts = key_pts.view(key_pts.size(0), -1)\n",
    "\n",
    "            # convert variables to floats for regression loss\n",
    "            key_pts = key_pts.type(torch.FloatTensor)\n",
    "            images = images.type(torch.FloatTensor)\n",
    "\n",
    "            # forward pass to get outputs\n",
    "            output_pts = net(images)\n",
    "\n",
    "            # calculate the loss between predicted and target keypoints\n",
    "            loss = criterion(output_pts, key_pts)\n",
    "\n",
    "            # zero the parameter (weight) gradients\n",
    "            optimizer.zero_grad()\n",
    "            \n",
    "            # backward pass to calculate the weight gradients\n",
    "            loss.backward()\n",
    "\n",
    "            # update the weights\n",
    "            optimizer.step()\n",
    "\n",
    "            # print loss statistics\n",
    "            running_loss += loss.item()\n",
    "            if batch_i % 10 == 9:    # print every 10 batches\n",
    "                print('Epoch: {}, Batch: {}, Avg. Loss: {}'.format(epoch + 1, batch_i+1, running_loss/10))\n",
    "                running_loss = 0.0\n",
    "\n",
    "    print('Finished Training')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 1, Batch: 10, Avg. Loss: 0.429077610373497\n",
      "Epoch: 1, Batch: 20, Avg. Loss: 0.3595661401748657\n",
      "Epoch: 1, Batch: 30, Avg. Loss: 0.28457565158605574\n",
      "Epoch: 1, Batch: 40, Avg. Loss: 0.3088138893246651\n",
      "Epoch: 1, Batch: 50, Avg. Loss: 0.34053459018468857\n",
      "Epoch: 1, Batch: 60, Avg. Loss: 0.3138849601149559\n",
      "Epoch: 1, Batch: 70, Avg. Loss: 0.3062646046280861\n",
      "Epoch: 1, Batch: 80, Avg. Loss: 0.28877975344657897\n",
      "Epoch: 1, Batch: 90, Avg. Loss: 0.27392940521240233\n",
      "Epoch: 1, Batch: 100, Avg. Loss: 0.2836073532700539\n",
      "Epoch: 1, Batch: 110, Avg. Loss: 0.2722312182188034\n",
      "Epoch: 1, Batch: 120, Avg. Loss: 0.2882743313908577\n",
      "Epoch: 1, Batch: 130, Avg. Loss: 0.2757502183318138\n",
      "Epoch: 1, Batch: 140, Avg. Loss: 0.235450279712677\n",
      "Epoch: 1, Batch: 150, Avg. Loss: 0.23590002506971358\n",
      "Epoch: 1, Batch: 160, Avg. Loss: 0.23106693625450134\n",
      "Epoch: 1, Batch: 170, Avg. Loss: 0.25025791525840757\n",
      "Epoch: 1, Batch: 180, Avg. Loss: 0.24328759908676148\n",
      "Epoch: 1, Batch: 190, Avg. Loss: 0.2737410545349121\n",
      "Epoch: 1, Batch: 200, Avg. Loss: 0.2651865392923355\n",
      "Epoch: 1, Batch: 210, Avg. Loss: 0.21935042142868041\n",
      "Epoch: 1, Batch: 220, Avg. Loss: 0.24802300482988357\n",
      "Epoch: 1, Batch: 230, Avg. Loss: 0.2831435680389404\n",
      "Epoch: 1, Batch: 240, Avg. Loss: 0.23541404008865358\n",
      "Epoch: 1, Batch: 250, Avg. Loss: 0.22444071024656295\n",
      "Epoch: 1, Batch: 260, Avg. Loss: 0.2524387210607529\n",
      "Epoch: 1, Batch: 270, Avg. Loss: 0.2748199224472046\n",
      "Epoch: 1, Batch: 280, Avg. Loss: 0.30137585997581484\n",
      "Epoch: 1, Batch: 290, Avg. Loss: 0.26660059541463854\n",
      "Epoch: 1, Batch: 300, Avg. Loss: 0.21146298497915267\n",
      "Epoch: 1, Batch: 310, Avg. Loss: 0.2570319131016731\n",
      "Epoch: 1, Batch: 320, Avg. Loss: 0.23704853802919387\n",
      "Epoch: 1, Batch: 330, Avg. Loss: 0.23481266647577287\n",
      "Epoch: 1, Batch: 340, Avg. Loss: 0.24618016704916953\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 2, Batch: 10, Avg. Loss: 0.2320678487420082\n",
      "Epoch: 2, Batch: 20, Avg. Loss: 0.21022069007158278\n",
      "Epoch: 2, Batch: 30, Avg. Loss: 0.26889698803424833\n",
      "Epoch: 2, Batch: 40, Avg. Loss: 0.25249484926462173\n",
      "Epoch: 2, Batch: 50, Avg. Loss: 0.20795214921236038\n",
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     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n"
     ]
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 3, Batch: 10, Avg. Loss: 0.2579158179461956\n",
      "Epoch: 3, Batch: 20, Avg. Loss: 0.20479376167058944\n",
      "Epoch: 3, Batch: 30, Avg. Loss: 0.25750264823436736\n",
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     ]
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    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n"
     ]
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 4, Batch: 10, Avg. Loss: 0.17667145580053328\n",
      "Epoch: 4, Batch: 20, Avg. Loss: 0.169380272179842\n",
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      "Epoch: 4, Batch: 340, Avg. Loss: 0.1911061093211174\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 5, Batch: 10, Avg. Loss: 0.18948309496045113\n",
      "Epoch: 5, Batch: 20, Avg. Loss: 0.20567480921745301\n",
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      "Epoch: 5, Batch: 60, Avg. Loss: 0.16025734841823577\n",
      "Epoch: 5, Batch: 70, Avg. Loss: 0.1892789237201214\n",
      "Epoch: 5, Batch: 80, Avg. Loss: 0.17216198816895484\n",
      "Epoch: 5, Batch: 90, Avg. Loss: 0.19196643382310868\n",
      "Epoch: 5, Batch: 100, Avg. Loss: 0.17088673412799835\n",
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      "Epoch: 5, Batch: 120, Avg. Loss: 0.4216479420661926\n",
      "Epoch: 5, Batch: 130, Avg. Loss: 0.18556149452924728\n",
      "Epoch: 5, Batch: 140, Avg. Loss: 0.14829537346959115\n",
      "Epoch: 5, Batch: 150, Avg. Loss: 0.16510800793766975\n",
      "Epoch: 5, Batch: 160, Avg. Loss: 0.1780644379556179\n",
      "Epoch: 5, Batch: 170, Avg. Loss: 0.13922992572188378\n",
      "Epoch: 5, Batch: 180, Avg. Loss: 0.24086174219846726\n",
      "Epoch: 5, Batch: 190, Avg. Loss: 0.27800378799438474\n",
      "Epoch: 5, Batch: 200, Avg. Loss: 0.1733022466301918\n",
      "Epoch: 5, Batch: 210, Avg. Loss: 0.1594754457473755\n",
      "Epoch: 5, Batch: 220, Avg. Loss: 0.15112803280353546\n",
      "Epoch: 5, Batch: 230, Avg. Loss: 0.19852418527007104\n",
      "Epoch: 5, Batch: 240, Avg. Loss: 0.19102140069007872\n",
      "Epoch: 5, Batch: 250, Avg. Loss: 0.16690797060728074\n",
      "Epoch: 5, Batch: 260, Avg. Loss: 0.18845268413424493\n",
      "Epoch: 5, Batch: 270, Avg. Loss: 0.15238164067268373\n",
      "Epoch: 5, Batch: 280, Avg. Loss: 0.1465403862297535\n",
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      "Epoch: 5, Batch: 300, Avg. Loss: 0.17891534939408302\n",
      "Epoch: 5, Batch: 310, Avg. Loss: 0.1786491721868515\n",
      "Epoch: 5, Batch: 320, Avg. Loss: 0.16311827152967454\n",
      "Epoch: 5, Batch: 330, Avg. Loss: 0.19341946616768838\n",
      "Epoch: 5, Batch: 340, Avg. Loss: 0.2042226679623127\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 6, Batch: 10, Avg. Loss: 0.14272939637303353\n",
      "Epoch: 6, Batch: 20, Avg. Loss: 0.18394259363412857\n",
      "Epoch: 6, Batch: 30, Avg. Loss: 0.37104969173669816\n",
      "Epoch: 6, Batch: 40, Avg. Loss: 0.16001007407903672\n",
      "Epoch: 6, Batch: 50, Avg. Loss: 0.1864407889544964\n",
      "Epoch: 6, Batch: 60, Avg. Loss: 0.2882182031869888\n",
      "Epoch: 6, Batch: 70, Avg. Loss: 0.20326186269521712\n",
      "Epoch: 6, Batch: 80, Avg. Loss: 0.1384461112320423\n",
      "Epoch: 6, Batch: 90, Avg. Loss: 0.16399977430701257\n",
      "Epoch: 6, Batch: 100, Avg. Loss: 0.18303826302289963\n",
      "Epoch: 6, Batch: 110, Avg. Loss: 0.16454447954893112\n",
      "Epoch: 6, Batch: 120, Avg. Loss: 0.18391164317727088\n",
      "Epoch: 6, Batch: 130, Avg. Loss: 0.17245626524090768\n",
      "Epoch: 6, Batch: 140, Avg. Loss: 0.1740809813141823\n",
      "Epoch: 6, Batch: 150, Avg. Loss: 0.16950005516409875\n",
      "Epoch: 6, Batch: 160, Avg. Loss: 0.15168614089488983\n",
      "Epoch: 6, Batch: 170, Avg. Loss: 0.18782462552189827\n",
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      "Epoch: 6, Batch: 200, Avg. Loss: 0.18004702478647233\n",
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      "Epoch: 6, Batch: 270, Avg. Loss: 0.1502125732600689\n",
      "Epoch: 6, Batch: 280, Avg. Loss: 0.17661684975028039\n",
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      "Epoch: 6, Batch: 300, Avg. Loss: 0.15519784837961198\n",
      "Epoch: 6, Batch: 310, Avg. Loss: 0.25558438450098037\n",
      "Epoch: 6, Batch: 320, Avg. Loss: 0.16965629085898398\n",
      "Epoch: 6, Batch: 330, Avg. Loss: 0.16865389794111252\n",
      "Epoch: 6, Batch: 340, Avg. Loss: 0.14833207428455353\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 7, Batch: 10, Avg. Loss: 0.1588280387222767\n",
      "Epoch: 7, Batch: 20, Avg. Loss: 0.2991710714995861\n",
      "Epoch: 7, Batch: 30, Avg. Loss: 0.17083312720060348\n",
      "Epoch: 7, Batch: 40, Avg. Loss: 0.12166350483894348\n",
      "Epoch: 7, Batch: 50, Avg. Loss: 0.14485077932476997\n",
      "Epoch: 7, Batch: 60, Avg. Loss: 0.18978022262454033\n",
      "Epoch: 7, Batch: 70, Avg. Loss: 0.1726635918021202\n",
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      "Epoch: 7, Batch: 90, Avg. Loss: 0.18254344388842583\n",
      "Epoch: 7, Batch: 100, Avg. Loss: 0.18279920667409896\n",
      "Epoch: 7, Batch: 110, Avg. Loss: 0.15130367800593375\n",
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      "Epoch: 7, Batch: 320, Avg. Loss: 0.14335911870002746\n",
      "Epoch: 7, Batch: 330, Avg. Loss: 0.143263977766037\n",
      "Epoch: 7, Batch: 340, Avg. Loss: 0.14385680332779885\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 8, Batch: 10, Avg. Loss: 0.1280115246772766\n",
      "Epoch: 8, Batch: 20, Avg. Loss: 0.14242251813411713\n",
      "Epoch: 8, Batch: 30, Avg. Loss: 0.16789032369852067\n",
      "Epoch: 8, Batch: 40, Avg. Loss: 0.14728230386972427\n",
      "Epoch: 8, Batch: 50, Avg. Loss: 0.17816970720887185\n",
      "Epoch: 8, Batch: 60, Avg. Loss: 0.14521745666861535\n",
      "Epoch: 8, Batch: 70, Avg. Loss: 0.1719675898551941\n",
      "Epoch: 8, Batch: 80, Avg. Loss: 0.19012758880853653\n",
      "Epoch: 8, Batch: 90, Avg. Loss: 0.14799971953034402\n",
      "Epoch: 8, Batch: 100, Avg. Loss: 0.1561215952038765\n",
      "Epoch: 8, Batch: 110, Avg. Loss: 0.13362896591424941\n",
      "Epoch: 8, Batch: 120, Avg. Loss: 0.16685092598199844\n",
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      "Epoch: 8, Batch: 320, Avg. Loss: 0.14865378215909003\n",
      "Epoch: 8, Batch: 330, Avg. Loss: 0.1404437780380249\n",
      "Epoch: 8, Batch: 340, Avg. Loss: 0.16699240058660508\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 9, Batch: 10, Avg. Loss: 0.14179441183805466\n",
      "Epoch: 9, Batch: 20, Avg. Loss: 0.1467851832509041\n",
      "Epoch: 9, Batch: 30, Avg. Loss: 0.16965631693601607\n",
      "Epoch: 9, Batch: 40, Avg. Loss: 0.1722601681947708\n",
      "Epoch: 9, Batch: 50, Avg. Loss: 0.1508489206433296\n",
      "Epoch: 9, Batch: 60, Avg. Loss: 0.14785073548555375\n",
      "Epoch: 9, Batch: 70, Avg. Loss: 0.18087462931871415\n",
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      "Epoch: 9, Batch: 200, Avg. Loss: 0.1691995643079281\n",
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      "Epoch: 9, Batch: 220, Avg. Loss: 0.18205377981066703\n",
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      "Epoch: 9, Batch: 340, Avg. Loss: 0.15266387015581132\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 10, Batch: 10, Avg. Loss: 0.1385280206799507\n",
      "Epoch: 10, Batch: 20, Avg. Loss: 0.14044036567211152\n",
      "Epoch: 10, Batch: 30, Avg. Loss: 0.16917830854654312\n",
      "Epoch: 10, Batch: 40, Avg. Loss: 0.17593248263001443\n",
      "Epoch: 10, Batch: 50, Avg. Loss: 0.1676836684346199\n",
      "Epoch: 10, Batch: 60, Avg. Loss: 0.191153684258461\n",
      "Epoch: 10, Batch: 70, Avg. Loss: 0.13946541175246238\n",
      "Epoch: 10, Batch: 80, Avg. Loss: 0.20533570200204848\n",
      "Epoch: 10, Batch: 90, Avg. Loss: 0.14772598892450334\n",
      "Epoch: 10, Batch: 100, Avg. Loss: 0.14904977902770042\n",
      "Epoch: 10, Batch: 110, Avg. Loss: 0.16736584901809692\n",
      "Epoch: 10, Batch: 120, Avg. Loss: 0.17996074706315995\n",
      "Epoch: 10, Batch: 130, Avg. Loss: 0.16012193262577057\n",
      "Epoch: 10, Batch: 140, Avg. Loss: 0.14094884395599366\n",
      "Epoch: 10, Batch: 150, Avg. Loss: 0.16864350959658622\n",
      "Epoch: 10, Batch: 160, Avg. Loss: 0.18389898985624314\n",
      "Epoch: 10, Batch: 170, Avg. Loss: 0.1367723174393177\n",
      "Epoch: 10, Batch: 180, Avg. Loss: 0.198594781011343\n",
      "Epoch: 10, Batch: 190, Avg. Loss: 0.16746994256973266\n",
      "Epoch: 10, Batch: 200, Avg. Loss: 0.20010739862918853\n",
      "Epoch: 10, Batch: 210, Avg. Loss: 0.17139464542269706\n",
      "Epoch: 10, Batch: 220, Avg. Loss: 0.162195985019207\n",
      "Epoch: 10, Batch: 230, Avg. Loss: 0.1437486670911312\n",
      "Epoch: 10, Batch: 240, Avg. Loss: 0.18631556406617164\n",
      "Epoch: 10, Batch: 250, Avg. Loss: 0.2021394543349743\n",
      "Epoch: 10, Batch: 260, Avg. Loss: 0.14902517721056938\n",
      "Epoch: 10, Batch: 270, Avg. Loss: 0.16318371891975403\n",
      "Epoch: 10, Batch: 280, Avg. Loss: 0.15038680508732796\n",
      "Epoch: 10, Batch: 290, Avg. Loss: 0.16551948785781861\n",
      "Epoch: 10, Batch: 300, Avg. Loss: 0.14866113662719727\n",
      "Epoch: 10, Batch: 310, Avg. Loss: 0.19109792560338973\n",
      "Epoch: 10, Batch: 320, Avg. Loss: 0.13906548842787742\n",
      "Epoch: 10, Batch: 330, Avg. Loss: 0.17366836369037628\n",
      "Epoch: 10, Batch: 340, Avg. Loss: 0.17944004908204078\n",
      "Finished Training\n"
     ]
    }
   ],
   "source": [
    "# train your network\n",
    "n_epochs = 10 # start small, and increase when you've decided on your model structure and hyperparams\n",
    "\n",
    "# this is a Workspaces-specific context manager to keep the connection\n",
    "# alive while training your model, not part of pytorch\n",
    "with active_session():\n",
    "    train_net(n_epochs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test data\n",
    "\n",
    "See how your model performs on previously unseen, test data. We've already loaded and transformed this data, similar to the training data. Next, run your trained model on these images to see what kind of keypoints are produced. You should be able to see if your model is fitting each new face it sees, if the points are distributed randomly, or if the points have actually overfitted the training data and do not generalize."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n",
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([10, 1, 224, 224])\n",
      "torch.Size([10, 68, 2])\n",
      "torch.Size([10, 68, 2])\n"
     ]
    }
   ],
   "source": [
    "# get a sample of test data again\n",
    "\n",
    "\n",
    "net.load_state_dict(torch.load('saved_models/keypoints_model_1.pt'))\n",
    "\n",
    "## print out your net and prepare it for testing (uncomment the line below)\n",
    "net.eval()\n",
    "\n",
    "test_images, test_outputs, gt_pts = net_sample_output()\n",
    "\n",
    "print(test_images.data.size())\n",
    "print(test_outputs.data.size())\n",
    "print(gt_pts.size())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3de4d9160>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3de0b6e48>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3de0843c8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3de0453c8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3de0e4cc0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3ddfbf908>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3ddf82e48>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3dded03c8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3ddf01b38>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3dde46c18>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## TODO: visualize your test output\n",
    "# you can use the same function as before, by un-commenting the line below:\n",
    "\n",
    "visualize_output(test_images, test_outputs, gt_pts)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once you've found a good model (or two), save your model so you can load it and use it later!\n",
    "\n",
    "Save your models but please **delete any checkpoints and saved models before you submit your project** otherwise your workspace may be too large to submit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "## TODO: change the name to something uniqe for each new model\n",
    "model_dir = 'saved_models/'\n",
    "model_name = 'keypoints_model_1.pt'\n",
    "\n",
    "# after training, save your model parameters in the dir 'saved_models'\n",
    "torch.save(net.state_dict(), model_dir+model_name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After you've trained a well-performing model, answer the following questions so that we have some insight into your training and architecture selection process. Answering all questions is required to pass this project."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 1: What optimization and loss functions did you choose and why?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer**: write your answer here (double click to edit this cell)\n",
    "\n",
    "I choose MSE loss as we are working with regression task and showed better results than L1 loss and Adam as optimizer as it is very efficient for training batches of data and it showed better results as compared to SGD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 2: What kind of network architecture did you start with and how did it change as you tried different architectures? Did you decide to add more convolutional layers or any layers to avoid overfitting the data?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer**: write your answer here\n",
    "\n",
    "I created the architechture like the one provided \"NaimishNet\" but made some required changes. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 3: How did you decide on the number of epochs and batch_size to train your model?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer**: I choose number of epochs by trial and error to see when it gives better results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature Visualization\n",
    "\n",
    "Sometimes, neural networks are thought of as a black box, given some input, they learn to produce some output. CNN's are actually learning to recognize a variety of spatial patterns and you can visualize what each convolutional layer has been trained to recognize by looking at the weights that make up each convolutional kernel and applying those one at a time to a sample image. This technique is called feature visualization and it's useful for understanding the inner workings of a CNN."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the cell below, you can see how to extract a single filter (by index) from your first convolutional layer. The filter should appear as a grayscale grid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.01959764 -0.03422438 -0.07674434 -0.04049142 -0.15274519]\n",
      " [-0.10863382  0.05976049 -0.0255484  -0.01487105  0.10329093]\n",
      " [-0.17247283  0.10131419  0.1756852  -0.1870909   0.14421536]\n",
      " [-0.07251019  0.16281481 -0.06297833 -0.00324896  0.15906127]\n",
      " [-0.0680932  -0.09515241 -0.04064824  0.17043236  0.11739366]]\n",
      "(5, 5)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7ff3ddf82278>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPgAAAD8CAYAAABaQGkdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4wLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvpW3flQAACbpJREFUeJzt3c9r3HUex/HXq9O0sWRFyvZgm7L1IGXbwrYQitBLKSK1ih68VLAnIZcVKlj8QU/9B8SLl6DFBUURFJTiIgXrL3DVqFFso6WIW4titkjRHJrQ9r2HmUNXk853Mt9vPpn3Ph8QyLRfvn1R8sx3ZhJmHBECkNOq0gMANIfAgcQIHEiMwIHECBxIjMCBxAgcSIzAgcQIHEhsdRMnHRkZifXr1zdx6tpdvny59ISezM/Pl57Qk6GhodITKrt06VLpCZVdvXpV165dc7fjGgl8/fr1OnLkSBOnrt3Zs2dLT+jJ+fPnS0/oycaNG0tPqOyNN94oPaGyixcvVjqOu+hAYgQOJEbgQGIEDiRG4EBiBA4kRuBAYgQOJEbgQGIEDiRG4EBiBA4kRuBAYgQOJEbgQGIEDiRWKXDb+21/a/uc7SebHgWgHl0Dt92S9KykuyVtk/Sg7W1NDwPQvypX8N2SzkXEdxExL+kVSfc3OwtAHaoEvknSD9fdvtD5MwArXJXAF3rlxj+8qbjtcduTtidnZ2f7Xwagb1UCvyBp83W3RyX9+PuDImIiIsYiYmxkZKSufQD6UCXwTyXdbvs222skHZT0ZrOzANSh6+uiR8QV249IeltSS9LxiDjd+DIAfav0xgcR8ZaktxreAqBm/CYbkBiBA4kROJAYgQOJETiQGIEDiRE4kBiBA4kROJAYgQOJETiQGIEDiRE4kBiBA4kROJAYgQOJETiQmCP+8AKpfRsZGYkdO3bUft4mPPHEE6Un9OSDDz4oPaEnw8PDpSdU9sADD5SeUNmhQ4d05syZhV7x+H9wBQcSI3AgMQIHEiNwIDECBxIjcCAxAgcSI3AgMQIHEiNwIDECBxIjcCAxAgcSI3AgMQIHEiNwIDECBxLrGrjt47ZnbH+9HIMA1KfKFfwFSfsb3gGgAV0Dj4j3Jf2yDFsA1IzH4EBiq+s6ke1xSeOStGbNmrpOC6APtV3BI2IiIsYiYmxoaKiu0wLoA3fRgcSq/JjsZUkfSdpq+4Lth5ufBaAOXR+DR8SDyzEEQP24iw4kRuBAYgQOJEbgQGIEDiRG4EBiBA4kRuBAYgQOJEbgQGIEDiRG4EBiBA4kRuBAYgQOJEbgQGKOiNpP2mq1Ynh4uPbzNuG9994rPaEnY2NjpSf0xHbpCZX9/PPPpSdUdtddd2lqaqrrfy5XcCAxAgcSI3AgMQIHEiNwIDECBxIjcCAxAgcSI3AgMQIHEiNwIDECBxIjcCAxAgcSI3AgMQIHEiNwILGugdvebPuU7Wnbp20fXo5hAPq3usIxVyQ9FhGf2/6TpM9sn4yIMw1vA9CnrlfwiPgpIj7vfP6bpGlJm5oeBqB/PT0Gt71F0i5JHzcxBkC9qtxFlyTZHpH0mqRHI+LXBf5+XNJ45/PaBgJYukqB2x5SO+6XIuL1hY6JiAlJE1L7ZZNrWwhgyao8i25Jz0uajoinm58EoC5VHoPvkXRI0j7bU52PAw3vAlCDrnfRI+JDSTyoBgYQv8kGJEbgQGIEDiRG4EBiBA4kRuBAYgQOJEbgQGIEDiRG4EBiBA4kRuBAYgQOJEbgQGIEDiRG4EBiBA4kVvlVVXtx8803a+/evU2cunbbt28vPaEnBw8eLD2hJ8eOHSs9obJ169aVnlDZqlXVrs1cwYHECBxIjMCBxAgcSIzAgcQIHEiMwIHECBxIjMCBxAgcSIzAgcQIHEiMwIHECBxIjMCBxAgcSIzAgcS6Bm572PYntr+0fdr24LxEB/B/rspLNs1J2hcRs7aHJH1o+58R8a+GtwHoU9fAIyIkzXZuDnU+oslRAOpR6TG47ZbtKUkzkk5GxMfNzgJQh0qBR8TViNgpaVTSbts7fn+M7XHbk7Yn5+bm6t4JYAl6ehY9Ii5JelfS/gX+biIixiJibO3atTXNA9CPKs+ib7B9S+fzmyTdKembpocB6F+VZ9FvlfQP2y21vyG8GhEnmp0FoA5VnkX/StKuZdgCoGb8JhuQGIEDiRE4kBiBA4kROJAYgQOJETiQGIEDiRE4kBiBA4kROJAYgQOJETiQGIEDiRE4kBiBA4lVeUWXJWm1Wk2dulYHDhwoPaEnW7duLT2hJ0ePHi09obKzZ8+WnlDZ/Px8peO4ggOJETiQGIEDiRE4kBiBA4kROJAYgQOJETiQGIEDiRE4kBiBA4kROJAYgQOJETiQGIEDiRE4kBiBA4lVDtx2y/YXtk80OQhAfXq5gh+WNN3UEAD1qxS47VFJ90h6rtk5AOpU9Qr+jKTHJV1rcAuAmnUN3Pa9kmYi4rMux43bnrQ9OTc3V9tAAEtX5Qq+R9J9tr+X9IqkfbZf/P1BETEREWMRMbZ27dqaZwJYiq6BR8RTETEaEVskHZT0TkQ81PgyAH3j5+BAYj29s0lEvCvp3UaWAKgdV3AgMQIHEiNwIDECBxIjcCAxAgcSI3AgMQIHEiNwIDECBxIjcCAxAgcSI3AgMQIHEiNwIDECBxIjcCAxR0T9J7X/I+nfNZ/2z5Iu1nzOJg3S3kHaKg3W3qa2/iUiNnQ7qJHAm2B7MiLGSu+oapD2DtJWabD2lt7KXXQgMQIHEhukwCdKD+jRIO0dpK3SYO0tunVgHoMD6N0gXcEB9GggAre93/a3ts/ZfrL0nhuxfdz2jO2vS2/pxvZm26dsT9s+bftw6U2LsT1s+xPbX3a2Hiu9qQrbLdtf2D5R4t9f8YHbbkl6VtLdkrZJetD2trKrbugFSftLj6joiqTHIuKvku6Q9PcV/H87J2lfRPxN0k5J+23fUXhTFYclTZf6x1d84JJ2SzoXEd9FxLza73B6f+FNi4qI9yX9UnpHFRHxU0R83vn8N7W/EDeVXbWwaJvt3BzqfKzoJ5Bsj0q6R9JzpTYMQuCbJP1w3e0LWqFfhIPM9hZJuyR9XHbJ4jp3d6ckzUg6GRErdmvHM5Iel3St1IBBCNwL/NmK/s49aGyPSHpN0qMR8WvpPYuJiKsRsVPSqKTdtneU3rQY2/dKmomIz0ruGITAL0jafN3tUUk/FtqSju0hteN+KSJeL72nioi4pPa73K7k5zr2SLrP9vdqP6zcZ/vF5R4xCIF/Kul227fZXiPpoKQ3C29KwbYlPS9pOiKeLr3nRmxvsH1L5/ObJN0p6ZuyqxYXEU9FxGhEbFH7a/adiHhouXes+MAj4oqkRyS9rfaTQK9GxOmyqxZn+2VJH0naavuC7YdLb7qBPZIOqX11mep8HCg9ahG3Sjpl+yu1v+mfjIgiP3oaJPwmG5DYir+CA1g6AgcSI3AgMQIHEiNwIDECBxIjcCAxAgcS+y/ZrQCSFl7fTAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3ddd86470>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get the weights in the first conv layer, \"conv1\"\n",
    "# if necessary, change this to reflect the name of your first conv layer\n",
    "weights1 = net.conv1.weight.data\n",
    "\n",
    "w = weights1.numpy()\n",
    "\n",
    "filter_index = 0\n",
    "\n",
    "print(w[filter_index][0])\n",
    "print(w[filter_index][0].shape)\n",
    "\n",
    "# display the filter weights\n",
    "plt.imshow(w[filter_index][0], cmap='gray')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature maps\n",
    "\n",
    "Each CNN has at least one convolutional layer that is composed of stacked filters (also known as convolutional kernels). As a CNN trains, it learns what weights to include in it's convolutional kernels and when these kernels are applied to some input image, they produce a set of **feature maps**. So, feature maps are just sets of filtered images; they are the images produced by applying a convolutional kernel to an input image. These maps show us the features that the different layers of the neural network learn to extract. For example, you might imagine a convolutional kernel that detects the vertical edges of a face or another one that detects the corners of eyes. You can see what kind of features each of these kernels detects by applying them to an image. One such example is shown below; from the way it brings out the lines in an the image, you might characterize this as an edge detection filter.\n",
    "\n",
    "<img src='images/feature_map_ex.png' width=50% height=50%/>\n",
    "\n",
    "\n",
    "Next, choose a test image and filter it with one of the convolutional kernels in your trained CNN; look at the filtered output to get an idea what that particular kernel detects.\n",
    "\n",
    "### TODO: Filter an image to see the effect of a convolutional kernel\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3de2e79b0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "##TODO: load in and display any image from the transformed test dataset\n",
    "import cv2\n",
    "\n",
    "fig=plt.figure(figsize=(8, 10))\n",
    "\n",
    "# un-transform the image data\n",
    "image = test_images[3].data   # get the image from it's wrapper\n",
    "image = image.numpy()   # convert to numpy array from a Tensor\n",
    "image = np.transpose(image, (1, 2, 0))   # transpose to go from torch to numpy image\n",
    "\n",
    "# show image\n",
    "imgs = fig.add_subplot(1, 2, 1)\n",
    "imgs.imshow(np.squeeze(image), cmap='gray')\n",
    "imgs.set_title(\"Original\")\n",
    "\n",
    "## TODO: Using cv's filter2D function,\n",
    "## apply a specific set of filter weights (like the one displayed above) to the test image\n",
    "\n",
    "\n",
    "# first conv layer\n",
    "weights = net.conv1.weight.data\n",
    "w = weights.numpy()\n",
    "\n",
    "# filter image\n",
    "filtered_img = cv2.filter2D(image, -1, w[0][0])\n",
    "\n",
    "# show filtered image\n",
    "imgs = fig.add_subplot(1, 2, 2)\n",
    "imgs.imshow(filtered_img, cmap='gray')\n",
    "imgs.set_title(\"Filtered\")\n",
    "\n",
    "plt.show()\n",
    "\n",
    "\n",
    "     \n",
    "## apply a specific set of filter weights (like the one displayed above) to the test image\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 4: Choose one filter from your trained CNN and apply it to a test image; what purpose do you think it plays? What kind of feature do you think it detects?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer**:  The filter here is detecting the vertical edges(like applying sobel operator in x direction) , trying to recognize the structure of Picture. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Moving on!\n",
    "\n",
    "Now that you've defined and trained your model (and saved the best model), you are ready to move on to the last notebook, which combines a face detector with your saved model to create a facial keypoint detection system that can predict the keypoints on *any* face in an image!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "display_name": "Python 3",
   "language": "python",
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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