SVD_ON_MNIST_DATASET.ipynb

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  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# **IMPORT NECESSARY MODELS**"
      ],
      "metadata": {
        "id": "5m2ZCfHC1nZG"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "4jTGgAbP4KGb"
      },
      "outputs": [],
      "source": [
        "import tensorflow as tf\n",
        "from tensorflow.keras.datasets import mnist\n",
        "import numpy as np\n",
        "from matplotlib import pyplot as plt\n",
        "from sklearn.decomposition import TruncatedSVD\n",
        "import random\n",
        "import seaborn as sns\n",
        "from sklearn.metrics import confusion_matrix, accuracy_score"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#**LOAD MNIST DATASET**"
      ],
      "metadata": {
        "id": "hWZ8xX2j1xez"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#loading the data into train and test set\n",
        "(train_images, train_labels), (test_images, test_labels) = mnist.load_data()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Wxxl0fyx4W24",
        "outputId": "a37d91c6-c3c9-4773-a202-f47d81a24d3d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz\n",
            "11490434/11490434 [==============================] - 0s 0us/step\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **DATA PREPROCESSING**\n",
        "\n",
        "- Reshaping data"
      ],
      "metadata": {
        "id": "6rArN4tv2FAb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Reshaping data\n",
        "num_pixels = 784\n",
        "train_images_flat = train_images.reshape(train_images.shape[0], num_pixels)\n",
        "test_images_flat = test_images.reshape(test_images.shape[0], num_pixels)"
      ],
      "metadata": {
        "id": "7SSGuci94Zq0"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# The following code forms a matrix for each digit 'i' whose columns are images of that digit."
      ],
      "metadata": {
        "id": "r0mYUB3F3jQA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Define a dictionary to store digit image matrices\n",
        "digit_images = {}\n",
        "\n",
        "# Loop through each digit class (0-9)\n",
        "for digit in range(10):\n",
        "  # Select all images belonging to the current digit\n",
        "  digit_images[digit] = train_images_flat[train_labels == digit][:4000, :]\n",
        "for digit in range(10):\n",
        "  digit_images[digit] = digit_images[digit].T\n",
        "# Each value in `digit_images` will be a matrix with dimensions (784, 4000)\n",
        "# where 4000 represents all images of that digit in the training set."
      ],
      "metadata": {
        "id": "rt6fqL-b4ftg"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Extract the top n left singular vectors from a matrix."
      ],
      "metadata": {
        "id": "EtDWHWyf36oL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def get_top_singular_vectors(matrix, num_components=4):\n",
        "  \"\"\"\n",
        "  Extracts the top `num_components` left singular vectors from a matrix.\n",
        "\n",
        "  Args:\n",
        "      matrix: The input matrix.\n",
        "      num_components: The number of singular vectors to extract (default: 4).\n",
        "\n",
        "  Returns:\n",
        "      A NumPy array containing the top `num_components` left singular vectors.\n",
        "  \"\"\"\n",
        "  u, s, vh = np.linalg.svd(matrix, full_matrices=False)\n",
        "  return u[:, :num_components]"
      ],
      "metadata": {
        "id": "cfS9DQOc4jUE"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Extract top 4 principal components for each digit matrix."
      ],
      "metadata": {
        "id": "aCKHyN_g4IXJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Extract top 4 principal components for each digit matrix\n",
        "digit_components = {}\n",
        "for digit, matrix in digit_images.items():\n",
        "  components = get_top_singular_vectors(matrix)\n",
        "  digit_components[digit] = components"
      ],
      "metadata": {
        "id": "ClQQlO7c4qi1"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Visualization of images obtained using left singular vectors\n",
        "\n",
        "- The following function prints 50 images, 5 for each of the labels ----- one original image and\n",
        "4 images corresponding to the left singular vectors."
      ],
      "metadata": {
        "id": "v1uj6q5G5dFR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "fig, axes = plt.subplots(10, 5, figsize=(12, 20))\n",
        "\n",
        "for digit in range(10):\n",
        "    #sample_image = train_images[np.where(train_labels == digit)[0][0]]\n",
        "     # Choose a random training image for this digit\n",
        "    random_idx = np.random.randint(4000)\n",
        "    sample_image = digit_images[digit][:, random_idx].reshape(28, 28)\n",
        "    axes[digit, 0].imshow(sample_image, cmap='gray')\n",
        "    axes[digit, 0].set_title(f\"Sample: {digit}\")\n",
        "    axes[digit, 0].axis('off')\n",
        "    left_singular_vectors = digit_components[digit]\n",
        "    for i in range(4):\n",
        "        singular_vector_image = left_singular_vectors[:, i].reshape(28, 28)\n",
        "        axes[digit, i + 1].imshow(singular_vector_image, cmap='gray')\n",
        "        axes[digit, i + 1].set_title(f\"Left Singular Vector {i+1}\")\n",
        "        axes[digit, i + 1].axis('off')\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "SagM6h2y5VJy",
        "outputId": "24ab2cdd-23c5-4867-e6fb-7e69ad58ee4a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x2000 with 50 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Predict the label for an image"
      ],
      "metadata": {
        "id": "rHCZds1N4hwv"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Classification function\n",
        "def classify(image):\n",
        "  \"\"\"the classification function predict the label for an image passed to the function\n",
        "   on the basis of the norm mentioned in the function\"\"\"\n",
        "  min_distance = float('inf')\n",
        "  predicted_digit = -1\n",
        "  for i, U in digit_projections.items():\n",
        "    distance = np.linalg.norm(image - U @ U.T @ image)\n",
        "    if distance < min_distance:\n",
        "      min_distance = distance\n",
        "      predicted_digit = i\n",
        "  return predicted_digit"
      ],
      "metadata": {
        "id": "757xwWqY-3_J"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **TRAINING, TESTING AND CONFUSION MATRIX**\n",
        "\n",
        "In the following code, we perform SVD on the dataset, obtain the confusion matrix and the accuracy score"
      ],
      "metadata": {
        "id": "quomo5J_65sc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# using between 2500 − −3000 images of each digit in the training set to form the matrices and use the remaining as (labeled) test images\n",
        "\n",
        "train_images = train_images.reshape(-1, 28 * 28).astype('float32') / 255\n",
        "test_images = test_images.reshape(-1, 28 * 28).astype('float32') / 255\n",
        "np.random.seed(0)\n",
        "n_images_per_digit = random.randint(2500, 3000)\n",
        "digit_projections = {}\n",
        "for digit in range(10):\n",
        "    indices = np.where(train_labels == digit)[0]\n",
        "    selected_indices = np.random.choice(indices, size=n_images_per_digit, replace=False)\n",
        "    images = train_images[selected_indices]\n",
        "    svd = TruncatedSVD(n_components=4)\n",
        "    svd.fit(images)\n",
        "    U = svd.components_.T\n",
        "    digit_projections[digit] = U\n",
        "remaining_indices = np.setdiff1d(np.arange(len(train_images)), selected_indices)\n",
        "remaining_test_images = train_images[remaining_indices]\n",
        "remaining_test_labels = train_labels[remaining_indices]\n",
        "predicted_labels = []\n",
        "for i in range(len(remaining_test_images)):\n",
        "    test_image = remaining_test_images[i]\n",
        "    predicted_label = classify(test_image)\n",
        "    predicted_labels.append(predicted_label)\n",
        "confusion = confusion_matrix(remaining_test_labels, predicted_labels)\n",
        "accuracy = accuracy_score(remaining_test_labels, predicted_labels) * 100\n",
        "plt.figure(figsize=(10, 8))\n",
        "sns.heatmap(confusion, annot=True, fmt='d', cmap='Blues', xticklabels=range(10), yticklabels=range(10))\n",
        "plt.title('Confusion Matrix')\n",
        "plt.xlabel('Predicted Digit')\n",
        "plt.ylabel('Actual Digit')\n",
        "plt.show()\n",
        "print(f\"Accuracy: {accuracy:.2f}%\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 735
        },
        "id": "OtQlW-buAUs8",
        "outputId": "3c053362-1413-4d54-992c-d06c8387d39d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x800 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy: 91.40%\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# REPORT\n",
        "\n",
        "For **classification**, I adopted a model based on low-rank approximations of the SVD factorization. Instead of using the full matrix representation of each digit, I utilized a reduced-rank approximation by considering only the first four columns of the left singular vectors. The classification of a test image z was performed by computing the minimum norm ρ_n(z) for each digit n between 0 to 9, where the label of z is determined by the digit with the least norm.\n",
        "\n",
        "The norm here is defined as ρ_n(z) = min||D(n)x-z||\n",
        "\n",
        "The function calculates the projection of the test image ono the left singular vectors (U.T @ image) and then reconstruct the test image using this projection (U @ U.T @ image). It then calculates the difference between the original test image and the reconstructed image for each digit.\n",
        "\n",
        "The function classify finds the digit which minimizes the norm and returns the corresponding digit as the predicted label for the image.\n",
        "\n",
        "**Justification--**\n",
        "\n",
        "By using the minimum the left singular vectors of each digit matrix the function reduces the dimentionality of the problem , thus making the classification process more effective.\n",
        "\n",
        "The norm used for classification serves as a measure of similarity. A lower norm indicates a closer match between the test image and the digit's subspace, indicating a better match.\n",
        "\n",
        "Using the left singular vectors of each digit matrix helps capture the most significant features of the images, making the classification more robust to variations in the test images.\n",
        "\n",
        "**Conclusion--**\n",
        "We obtain an accuracy score of 91.40% by performing this experiment on MNIST dataset."
      ],
      "metadata": {
        "id": "a15FB33WbhQP"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "lhrAsvNxc1Ly"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}