08. Convolutional Neural Networks/02. Convolution with Strides - MXNet.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Convolutional with Strides - MXNet(From Scratch).ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1YN4PT_Idstj",
        "colab_type": "text"
      },
      "source": [
        "#MXNet (From Scratch)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CLGHa8i6WEaA",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import mxnet as mx\n",
        "from mxnet import nd\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "ctx = mx.gpu()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u5Lekr1xNl3o",
        "colab_type": "text"
      },
      "source": [
        "##Getting the data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SOMvJE7t2j-E",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "mnist = mx.gluon.data.vision.MNIST()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z_t0Blm529jz",
        "colab_type": "code",
        "outputId": "41127546-42a1-4ffe-b541-ebf612e534b8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        }
      },
      "source": [
        "image, _ = mnist[2]\n",
        "\n",
        "image = image.flatten().astype('float32').as_in_context(ctx)\n",
        "\n",
        "print(image.shape)\n",
        "\n",
        "plt.imshow(image.asnumpy(), cmap = 'gray')\n",
        "plt.show()"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(28, 28)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "L2cs16xWIuKK",
        "colab": {}
      },
      "source": [
        "def convolution_with_strides(inputs, kernal, strides):\n",
        "    filter_hight, filter_width = kernal.shape\n",
        "    hight, width = ((inputs.shape[0] - filter_hight)/strides[0]) + 1, ((inputs.shape[1] - filter_width)/strides[1]) + 1\n",
        "    \n",
        "    layer = nd.zeros((int(hight), int(width)))\n",
        "    \n",
        "    row = 0\n",
        "    for i in range(0, inputs.shape[0], strides[0]):\n",
        "        col = 0\n",
        "        for j in range(0, inputs.shape[1], strides[1]):\n",
        "            if (i + filter_hight <= inputs.shape[0]) and (j + filter_width <= inputs.shape[1]):\n",
        "                layer[row, col] = (inputs[i:i + filter_hight, j:j + filter_width] * kernal).sum()\n",
        "            col += 1\n",
        "        row += 1\n",
        "    return layer"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "outputId": "55f4887f-65e9-4e0f-f259-13195baacabf",
        "id": "bAPxZNzwIuKQ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        }
      },
      "source": [
        "kernal = nd.random.normal(0, 1, (3, 3)).as_in_context(ctx)\n",
        "\n",
        "output = convolution_with_strides(image, kernal, strides = (1, 1))\n",
        "\n",
        "plt.imshow(output.asnumpy(), cmap = 'gray')\n",
        "plt.show()\n",
        "\n",
        "output.shape"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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eWpK7vy/p61sWb5a0q3i8S+N/GA0zSY9Nx91Pufu+4vFFSTdPW2+253OyPqekUeHvlnR8\nws8n1LzXCHBJfzazvWa2rdHNZCwurr8gSac1fvWlZtS0p4Lfctp60z6fZZxezwd+eU+4+99I2iTp\nR8VL2abn4+/nmnFXTkWngjfCbU5b/z/N9HxO9fT6WzUq/AOSlk34eWmxrOm4+0DxfUjSm5rk1OUm\nMXjzbMvi+1CD+/mGSk8Fr7fbnbauJnw+qzm9/laNCv8eSavMbLmZtUv6nqTdDeplUmbWWXywIjPr\nlPQdNfepy7slbS0eb5WUvrVtAzTjqeCTnbauJns+Sz+93t0b8iXpWY1/4v+5pJ81qo9MjyskfVh8\nfdxMfUp6Q+Mv8UY0/pnJC5LulfSepCOS/ktSVxP2+G+SPpJ0QOPhWtIEz+UTGn9Jf0DS/uLr2SZ8\nPifrc0rPKUf4AUHxgR8QFOEHgiL8QFCEHwiK8ANBEX4gKMIPBEX4gaD+F+dHumBeIKrdAAAAAElF\nTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(26, 26)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DaZdXucpJQrQ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "af51633a-3cf7-4a5b-b0c6-abd4a2b8b7b3"
      },
      "source": [
        "kernal = nd.random.normal(0, 1, (4, 4)).as_in_context(ctx)\n",
        "\n",
        "output = convolution_with_strides(image, kernal, strides = (2, 2))\n",
        "\n",
        "plt.imshow(output.asnumpy(), cmap = 'gray')\n",
        "plt.show()\n",
        "\n",
        "output.shape"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nFOUHkqL8QFKUH0iK8gNJUX4gqf8DUMvWRqzBOEoAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(13, 13)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HSU98mKgJwW5",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "4fc9d012-f8a3-4237-e904-b182d7bb4c3d"
      },
      "source": [
        "kernal = nd.random.normal(0, 1, (7, 7)).as_in_context(ctx)\n",
        "\n",
        "output = convolution_with_strides(image, kernal, strides = (2, 2))\n",
        "\n",
        "plt.imshow(output.asnumpy(), cmap = 'gray')\n",
        "plt.show()\n",
        "\n",
        "output.shape"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP4AAAD8CAYAAABXXhlaAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDxT0v7wsJ8eTGSdhAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(11, 11)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    }
  ]
}