MNIST_using_PyTorch.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "MNIST - using PyTorch.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/subhadeep-123/MNIST-Handwritten-Character-Detection/blob/master/MNIST_using_PyTorch.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k_wQRHxZT6pM",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Importing The Packages\n",
        "import torch\n",
        "from torch import optim\n",
        "from torch import nn\n",
        "import torch.nn.functional as F\n",
        "import torchvision.datasets as dataset\n",
        "import torchvision.transforms as transforms\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import helper\n",
        "import warnings\n",
        "\n",
        "warnings.filterwarnings('ignore')\n",
        "%matplotlib inline\n",
        "%config InlineBackend.figure_format = 'retina'"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EjevNReyUKSP",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 255
        },
        "outputId": "9725f876-a579-4a06-9677-35e1dbf82e11"
      },
      "source": [
        "#Normalizing The Dataset\n",
        "transformed = transforms.Compose([transforms.ToTensor(),\n",
        "                                 transforms.Normalize((0.5,), (0.5,)),\n",
        "                                 ])\n",
        "\n",
        "#Downloading The Dataset\n",
        "trainset = dataset.MNIST('MNIST_NEW',\n",
        "                        download = True,\n",
        "                        train = True,\n",
        "                        transform = transformed)\n",
        "\n",
        "#Setting up the batch size\n",
        "trainloader = torch.utils.data.DataLoader(trainset,\n",
        "                                          batch_size = 64,\n",
        "                                          shuffle = True)"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\r0it [00:00, ?it/s]"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz to MNIST_NEW/MNIST/raw/train-images-idx3-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "9920512it [00:02, 3862315.77it/s]                             \n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Extracting MNIST_NEW/MNIST/raw/train-images-idx3-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "\r0it [00:00, ?it/s]"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz to MNIST_NEW/MNIST/raw/train-labels-idx1-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "32768it [00:00, 56696.62it/s]                           \n",
            "0it [00:00, ?it/s]"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Extracting MNIST_NEW/MNIST/raw/train-labels-idx1-ubyte.gz\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz to MNIST_NEW/MNIST/raw/t10k-images-idx3-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "1654784it [00:01, 951007.82it/s]                             \n",
            "0it [00:00, ?it/s]"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Extracting MNIST_NEW/MNIST/raw/t10k-images-idx3-ubyte.gz\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz to MNIST_NEW/MNIST/raw/t10k-labels-idx1-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "8192it [00:00, 21312.91it/s]            "
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Extracting MNIST_NEW/MNIST/raw/t10k-labels-idx1-ubyte.gz\n",
            "Processing...\n",
            "Done!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZmaWhahZajze",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "outputId": "4739302f-97f2-4add-a4f9-ff6ebd377c03"
      },
      "source": [
        "#Spliting The Dataset\n",
        "dataiter = iter(trainloader)\n",
        "images, labels = dataiter.next()\n",
        "print(type(images))\n",
        "print(images.shape)\n",
        "print(labels.shape)"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "<class 'torch.Tensor'>\n",
            "torch.Size([64, 1, 28, 28])\n",
            "torch.Size([64])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "68KKqa0Va8GU",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 284
        },
        "outputId": "0a0cbf08-ddaf-4529-a184-30becdb4b054"
      },
      "source": [
        "#Plotting a Visualization\n",
        "plt.imshow(images[0].numpy().squeeze(), cmap='Greys_r')"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7fd99a3c1ba8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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OmLp2zK1a5+29733vqPpTTz116tqXvvSlo8a+9tprR9Wz5rhNLQCwNEEPAB0T9ADQMUEP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\nY/8Pn0byAPOFKd4AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 253,
              "height": 250
            }
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3MaRdfJnbuRP",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Defining The Networks Architecture\n",
        "class Neural_Network(nn.Module):\n",
        "  \n",
        "  def __init__(self):\n",
        "    super().__init__()\n",
        "    \n",
        "    self.fc1 = nn.Linear(784, 256)\n",
        "    self.fc2 = nn.Linear(256, 128)\n",
        "    self.fc3 = nn.Linear(128, 64)\n",
        "    self.fc4 = nn.Linear(64, 10)\n",
        "    \n",
        "  def forward(self, x):\n",
        "    \n",
        "    x = F.relu(self.fc1(x))\n",
        "    x = F.relu(self.fc2(x))\n",
        "    x = F.relu(self.fc3(x))\n",
        "    x = F.log_softmax(self.fc4(x), dim = 1)\n",
        "    \n",
        "    return x"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eO4Z2chieIQu",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 119
        },
        "outputId": "146e8cf3-4007-4064-ff31-f78b6f9d5a4f"
      },
      "source": [
        "#Printing the Architecture of the Network\n",
        "model = Neural_Network()\n",
        "model"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Neural_Network(\n",
              "  (fc1): Linear(in_features=784, out_features=256, bias=True)\n",
              "  (fc2): Linear(in_features=256, out_features=128, bias=True)\n",
              "  (fc3): Linear(in_features=128, out_features=64, bias=True)\n",
              "  (fc4): Linear(in_features=64, out_features=10, bias=True)\n",
              ")"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "73tdM0V6eTC0",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Defining the Criterion\n",
        "criterion = nn.NLLLoss()\n",
        "\n",
        "#Defining the Optimizer\n",
        "optimizer = optim.SGD(model.parameters(), lr=0.003)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KI5yUEvJe8zv",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "outputId": "c70b6cde-23e2-4331-9401-36d00485f2c5"
      },
      "source": [
        "#Training the Network\n",
        "epoch = 5\n",
        "\n",
        "for x in range(epoch):\n",
        "  running_loss = 0\n",
        "  \n",
        "  #looping through the dataset\n",
        "  for images, labels in trainloader:\n",
        "    \n",
        "    #Flattening The Image\n",
        "    images = images.view(images.shape[0], -1)\n",
        "    \n",
        "    #Clearing Previous Gradients\n",
        "    optimizer.zero_grad()\n",
        "    \n",
        "    #-> Forward Pass \n",
        "    #-> Calculating Loss \n",
        "    #-> Calculating Gradients Through Backward Pass\n",
        "    #-> Updating the Weights, using optimizer.step()\n",
        "    \n",
        "    output = model.forward(images)\n",
        "    loss = criterion(output, labels)\n",
        "    loss.backward()\n",
        "    optimizer.step()\n",
        "    \n",
        "    #Appending the new loss\n",
        "    running_loss += loss.item()\n",
        "    \n",
        "  else:\n",
        "    print(f\"Training Loss: {running_loss/len(trainloader)}\")\n",
        "    "
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Training Loss: 2.2044236544352858\n",
            "Training Loss: 1.4961222967486392\n",
            "Training Loss: 0.7811902038324108\n",
            "Training Loss: 0.5425858480780363\n",
            "Training Loss: 0.44764498217718435\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FsSeySVziWQf",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def view_classify(img, ps, version=\"MNIST\"):\n",
        "    ''' Function for viewing an image and it's predicted classes.\n",
        "    '''\n",
        "    ps = ps.data.numpy().squeeze()\n",
        "\n",
        "    fig, (ax1, ax2) = plt.subplots(figsize=(6,9), ncols=2)\n",
        "    ax1.imshow(img.resize_(1, 28, 28).numpy().squeeze())\n",
        "    ax1.axis('off')\n",
        "    ax2.barh(np.arange(10), ps)\n",
        "    ax2.set_aspect(0.1)\n",
        "    ax2.set_yticks(np.arange(10))\n",
        "    if version == \"MNIST\":\n",
        "        ax2.set_yticklabels(np.arange(10))\n",
        "    ax2.set_title('Class Probability')\n",
        "    ax2.set_xlim(0, 1.1)\n",
        "\n",
        "    plt.tight_layout()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XPQR00mQj9K8",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 243
        },
        "outputId": "6c54dc89-6f44-4e27-f9d7-6ea4a77f99c8"
      },
      "source": [
        "#Checking our model\n",
        "\n",
        "images, labels = next(iter(trainloader))\n",
        "\n",
        "img = images[0].view(1, 784)\n",
        "\n",
        "# Turn off gradients to speed up this part\n",
        "with torch.no_grad():\n",
        "    logps = model.forward(img)\n",
        "\n",
        "# Output of the network are logits, need to take softmax for probabilities\n",
        "ps = torch.exp(logps)\n",
        "view_classify(img.view(1, 28, 28), ps)"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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QnAAAAAYITgAAAAMEJwAAgAGCEwAAwADBCQAAYIDgBAAAMEBwAgAAGCA4AQAADBCcAAAA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\n",
            "text/plain": [
              "<Figure size 432x648 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 423,
              "height": 226
            }
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lWMoka0JkOGY",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}