Linear_algebra_for_DL.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "Linear algebra plays a fundamental role in deep learning, enabling us to perform various operations on data to extract meaningful patterns and make accurate predictions. In this code example, we explore the application of linear transformations with a focus on non-linear activation using the Rectified Linear Unit (ReLU). By understanding and implementing these concepts, we can gain insights into how deep learning models learn and process data.\n",
        "\n",
        "The Code:\n",
        "The code begins by defining an input shape as a set of points in a two-dimensional space. These points represent the initial object that we aim to transform using linear operations. We then visualize the initial shape to provide a clear reference.\n",
        "\n",
        "The first transformation applied is scaling, which involves multiplying each coordinate of the object by scaling factors. By specifying appropriate scaling factors, we can stretch or shrink the object along different dimensions. The scaled shape is plotted to visualize the transformation.\n",
        "\n",
        "Next, we introduce rotation as a linear transformation. We rotate the original shape by a specified angle using a rotation matrix. The rotated shape is then displayed, showcasing the effect of rotation on the object.\n",
        "\n",
        "Finally, we explore the concept of shearing, a linear transformation that skews the shape along different axes. By applying a shearing matrix to the initial shape, we observe how the object is distorted. The sheared shape is plotted for visualization.\n",
        "\n",
        "To incorporate non-linearity into the transformations, we apply the ReLU activation function. The ReLU function sets negative values to zero while leaving positive values unchanged. We visualize both the transformed shapes before and after applying the ReLU activation, providing a clear understanding of how non-linearity impacts the final outcome.\n"
      ],
      "metadata": {
        "id": "HHytmHXJomXc"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "lfL4wkwIlEfD",
        "outputId": "8c611b59-fa7b-488c-e7d0-a6f8ca3bbc0c"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Linear Algebra in Deep Learning: Linear Transformations\n",
        "\n",
        "# Define the input shape\n",
        "points = np.array([[1, 1],\n",
        "                   [1, 3],\n",
        "                   [3, 3],\n",
        "                   [3, 1]])\n",
        "\n",
        "# Plot the input shape\n",
        "plt.figure(figsize=(5, 5))\n",
        "plt.plot(points[:, 0], points[:, 1], '-o', color='b')\n",
        "plt.xlim(-10, 10)\n",
        "plt.ylim(-10, 10)\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.title('Input Shape')\n",
        "plt.grid(True)\n",
        "plt.show()\n",
        "\n",
        "\n",
        "# Linear Transformation: Scaling\n",
        "\n",
        "# Define the scaling factor\n",
        "scale_x = 2\n",
        "scale_y = 0.5\n",
        "\n",
        "# Create the scaling matrix\n",
        "scaling_matrix = np.array([[scale_x, 0],\n",
        "                           [0, scale_y]])\n",
        "\n",
        "# Apply the scaling transformation\n",
        "scaled_points = np.dot(points, scaling_matrix)\n",
        "\n",
        "# Plot the scaled shape\n",
        "plt.figure(figsize=(5, 5))\n",
        "plt.plot(scaled_points[:, 0], scaled_points[:, 1], '-o', color='r')\n",
        "plt.xlim(-10, 10)\n",
        "plt.ylim(-10, 10)\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.title('Scaled Shape')\n",
        "plt.grid(True)\n",
        "plt.show()\n",
        "\n",
        "\n",
        "# Linear Transformation: Rotation\n",
        "\n",
        "# Define the rotation angle (in radians)\n",
        "angle = np.pi / 4\n",
        "\n",
        "# Create the rotation matrix\n",
        "rotation_matrix = np.array([[np.cos(angle), -np.sin(angle)],\n",
        "                            [np.sin(angle), np.cos(angle)]])\n",
        "\n",
        "# Apply the rotation transformation\n",
        "rotated_points = np.dot(points, rotation_matrix)\n",
        "\n",
        "# Plot the rotated shape\n",
        "plt.figure(figsize=(5, 5))\n",
        "plt.plot(rotated_points[:, 0], rotated_points[:, 1], '-o', color='g')\n",
        "plt.xlim(-10, 10)\n",
        "plt.ylim(-10, 10)\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.title('Rotated Shape')\n",
        "plt.grid(True)\n",
        "plt.show()\n",
        "\n",
        "\n",
        "# Linear Transformation: Shearing\n",
        "\n",
        "# Define the shearing factors\n",
        "shear_x = 1.5\n",
        "shear_y = 0.5\n",
        "\n",
        "# Create the shearing matrix\n",
        "shearing_matrix = np.array([[1, shear_x],\n",
        "                            [shear_y, 1]])\n",
        "\n",
        "# Apply the shearing transformation\n",
        "sheared_points = np.dot(points, shearing_matrix)\n",
        "\n",
        "# Plot the sheared shape\n",
        "plt.figure(figsize=(5, 5))\n",
        "plt.plot(sheared_points[:, 0], sheared_points[:, 1], '-o', color='m')\n",
        "plt.xlim(-10, 10)\n",
        "plt.ylim(-10, 10)\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.title('Sheared Shape')\n",
        "plt.grid(True)\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In this example:\n",
        "\n",
        "* The input shape is defined as a set of points in 2D space.\n",
        "\n",
        "* The input shape is plotted to visualize the original shape.\n",
        "\n",
        "* Linear transformations such as scaling, rotation, and shearing are applied to the input shape using matrix multiplication.\n",
        "\n",
        "* Each transformed shape is plotted individually to visualize how the linear transformation changes the geometry of the input shape.\n",
        "\n",
        "* Detailed comments are provided throughout the code to explain the linear algebra concepts and the effect of each transformation.\n",
        "\n",
        "*  By visualizing the input shape and the transformed shapes using matplotlib, you can observe how linear transformations such as scaling, rotation, and shearing alter the size, orientation, and shape of the original input."
      ],
      "metadata": {
        "id": "0gMZ3kmUl5g3"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Introduction of non-linearity "
      ],
      "metadata": {
        "id": "pz_f8dkqmfF2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Linear Algebra in Deep Learning: Linear Transformations with Non-Linearity\n",
        "\n",
        "# Define the input shape\n",
        "points = np.array([[1, 1],\n",
        "                   [1, 3],\n",
        "                   [3, 3],\n",
        "                   [3, 1]])\n",
        "\n",
        "# Plot the input shape\n",
        "plt.figure(figsize=(10, 5))\n",
        "plt.subplot(121)\n",
        "plt.plot(points[:, 0], points[:, 1], '-o', color='b')\n",
        "plt.xlim(-10, 10)\n",
        "plt.ylim(-10, 10)\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.title('Input Shape')\n",
        "plt.grid(True)\n",
        "\n",
        "\n",
        "# Linear Transformation: Scaling\n",
        "\n",
        "# Define the scaling factors\n",
        "scale_x = 2\n",
        "scale_y = -1\n",
        "\n",
        "# Create the scaling matrix\n",
        "scaling_matrix = np.array([[scale_x, 0],\n",
        "                           [0, scale_y]])\n",
        "\n",
        "# Apply the scaling transformation\n",
        "scaled_points = np.dot(points, scaling_matrix)\n",
        "\n",
        "# Plot the scaled shape\n",
        "plt.subplot(122)\n",
        "plt.plot(scaled_points[:, 0], scaled_points[:, 1], '-o', color='r')\n",
        "plt.xlim(-10, 10)\n",
        "plt.ylim(-10, 10)\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.title('Scaled Shape')\n",
        "plt.grid(True)\n",
        "plt.tight_layout()\n",
        "plt.show()\n",
        "\n",
        "\n",
        "# Apply the ReLU activation to the scaled shape\n",
        "scaled_points_relu = np.maximum(scaled_points, 0)\n",
        "\n",
        "# Plot the scaled shape with ReLU\n",
        "plt.figure(figsize=(10, 5))\n",
        "plt.subplot(121)\n",
        "plt.plot(scaled_points[:, 0], scaled_points[:, 1], '-o', color='r')\n",
        "plt.xlim(-10, 10)\n",
        "plt.ylim(-10, 10)\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.title('Scaled Shape')\n",
        "plt.grid(True)\n",
        "\n",
        "plt.subplot(122)\n",
        "plt.plot(scaled_points_relu[:, 0], scaled_points_relu[:, 1], '-o', color='g')\n",
        "plt.xlim(-10, 10)\n",
        "plt.ylim(-10, 10)\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.title('Scaled Shape with ReLU')\n",
        "plt.grid(True)\n",
        "plt.tight_layout()\n",
        "plt.show()\n",
        "\n",
        "\n",
        "# Linear Transformation: Rotation\n",
        "\n",
        "# Define the rotation angle (in radians)\n",
        "angle = np.pi / 4\n",
        "\n",
        "# Create the rotation matrix\n",
        "rotation_matrix = np.array([[np.cos(angle), -np.sin(angle)],\n",
        "                            [np.sin(angle), np.cos(angle)]])\n",
        "\n",
        "# Apply the rotation transformation\n",
        "rotated_points = np.dot(points, rotation_matrix)\n",
        "\n",
        "# Plot the rotated shape\n",
        "plt.figure(figsize=(10, 5))\n",
        "plt.subplot(121)\n",
        "plt.plot(rotated_points[:, 0], rotated_points[:, 1], '-o', color='g')\n",
        "plt.xlim(-10, 10)\n",
        "plt.ylim(-10, 10)\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.title('Rotated Shape')\n",
        "plt.grid(True)\n",
        "\n",
        "\n",
        "# Apply the ReLU activation to the rotated shape\n",
        "rotated_points_relu = np.maximum(rotated_points, 0)\n",
        "\n",
        "# Plot the rotated shape with ReLU\n",
        "plt.subplot(122)\n",
        "plt.plot(rotated_points_relu[:, 0], rotated_points_relu[:, 1], '-o', color='m')\n",
        "plt.xlim(-10, 10)\n",
        "plt.ylim(-10, 10)\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.title('Rotated Shape with ReLU')\n",
        "plt.grid(True)\n",
        "plt.tight_layout()\n",
        "plt.show()\n",
        "\n",
        "\n",
        "# Linear Transformation\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "bQ4WqgNPlFIW",
        "outputId": "4491c858-e205-46f5-8b83-7f8c2ce690eb"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "Xs9iIMZWmaNN"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "P4uhgUxWoj9U"
      }
    }
  ]
}