ML3-A6_PCA_on_MNIST.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Assignment 6: PCA on MNIST"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code Summary\n",
    "The code aims to implement Principal Component Analysis (PCA) on the MNIST dataset. The primary objective is to reduce the dimensionality of the dataset while maintaining as much variability in the data as possible. Specifically, the PCA basis is computed using only the training dataset, but its quality is then evaluated on the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ------------------------------\n",
    "# Import Required Libraries\n",
    "# ------------------------------\n",
    "\n",
    "# Standard Library\n",
    "import random as rand\n",
    "import math\n",
    "from pathlib import Path\n",
    "import requests\n",
    "import pickle\n",
    "import gzip\n",
    "\n",
    "# Scientific Computing Libraries\n",
    "import numpy as np\n",
    "import scipy.optimize\n",
    "import scipy.linalg as la\n",
    "from scipy.optimize import minimize, LinearConstraint, NonlinearConstraint\n",
    "\n",
    "# Data Visualization Library\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Machine Learning Libraries\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "import torch.nn.functional as F"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# --------------------------------------------------\n",
    "# Install the MNIST Python Package if Necessary\n",
    "# --------------------------------------------------\n",
    "# To install the MNIST Python package, run the following command:\n",
    "# pip install python-mnist\n",
    "\n",
    "try:\n",
    "    import mnist\n",
    "except ImportError:\n",
    "    import subprocess\n",
    "    print(\"Installing the python-mnist package as it is not found...\")\n",
    "    subprocess.run([\"pip\", \"install\", \"python-mnist\"])\n",
    "    import mnist\n",
    "\n",
    "# Now the MNIST package should be available for use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ---------------------------------------------\n",
    "# Load and Preprocess MNIST Dataset\n",
    "# ---------------------------------------------\n",
    "\n",
    "# Import Libraries for Linear Algebra and Optimization\n",
    "import scipy.linalg as la\n",
    "from scipy.optimize import LinearConstraint\n",
    "\n",
    "# Import MNIST Library\n",
    "from mnist import MNIST\n",
    "\n",
    "# Load MNIST Data\n",
    "mndata = MNIST(\"/Users/dadmehr/Codes/Python/Past/data/mnist/raw\")\n",
    "X_train, labels_train = map(np.array, mndata.load_training())\n",
    "X_test, labels_test = map(np.array, mndata.load_testing())\n",
    "\n",
    "# Preprocess Data: Normalize the features to [0, 1] range\n",
    "X_train = X_train / 255.0\n",
    "X_test = X_test / 255.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculating Mean and Covariance Matrix for MNIST Training Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get the dimensions of the training data (n = number of samples, d = number of features)\n",
    "n, d = X_train.shape\n",
    "\n",
    "# ------------------------------\n",
    "# Compute the Mean Vector (mu)\n",
    "# ------------------------------\n",
    "# Create an array of ones of shape (n,)\n",
    "ones_array = np.ones(n)\n",
    "\n",
    "# Calculate the mean of each feature (mu) using matrix multiplication\n",
    "mu = np.matmul(X_train.T, ones_array) / n\n",
    "\n",
    "# --------------------------------------\n",
    "# Compute the Covariance Matrix (sigma)\n",
    "# --------------------------------------\n",
    "# Expand mean vector 'mu' to have the same shape as X_train\n",
    "expanded_mu = np.outer(ones_array, mu)\n",
    "\n",
    "# Calculate the covariance matrix using matrix multiplication\n",
    "Big_Sig = ((X_train - expanded_mu).T @ (X_train - expanded_mu)) / n\n",
    "sigma = Big_Sig\n",
    "\n",
    "# ------------------------------------------------\n",
    "# Compute Eigenvalues and Eigenvectors of sigma\n",
    "# ------------------------------------------------\n",
    "# Compute eigenvalues and eigenvectors\n",
    "eigvals, eigvecs = np.linalg.eig(Big_Sig)\n",
    "\n",
    "# Remove the imaginary parts if they exist\n",
    "# This is to ensure all numbers are real\n",
    "eigvals = np.real(eigvals)\n",
    "eigvecs = np.real(eigvecs)\n",
    "\n",
    "# Reset mu to its earlier computed value (optional, as mu hasn't changed)\n",
    "muu = mu\n",
    "\n",
    "# The variables 'eigvals' and 'eigvecs' now contain the eigenvalues and eigenvectors of the covariance matrix\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Average = Mu\n",
    "\n",
    "One point to note is that every estimation starts with the mean, often represented as 'mu'. So, when the value of 'k' is low, the image will closely resemble this average, or 'mu.' This means that the best initial guess for representing the image is simply the average of all images in the dataset. This is particularly useful when the goal is to minimize the message size for data transmission."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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V1zhvWC5tWDuNiOgmXVOubKivbw4tS5+N66BjPzSE6pmm9VLLpTvDmwIASSkAkJQCAEkpAJCUAgBJKQCQlAIASSkAkJQCAEkpAJCUAgBJKQCQDOLdVQ0jehER4y2O791p3S2N6LUwHscd5k0BgKQUAEhKAYCkFABISgGApBQASEoBgKQUAEhKAYCkFABISgGApBQASN04WucC4BveFABISgGApBQASEoBgKQUAEhKAYCkFABISgGApBQASP8LyXbzUI3vtYUAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Reshaping the Mean (Mu) to a 2D Array for Visualization\n",
    "# In this case, the original image dimensions are assumed to be 28x28 pixels\n",
    "x_shape = np.reshape(mu, (28, 28))\n",
    "\n",
    "# Displaying the Reshaped Mean as an Image\n",
    "plt.imshow(x_shape)\n",
    "\n",
    "# Removing the Axes for a Cleaner Display\n",
    "plt.axis('off')\n",
    "\n",
    "# Showing the Image\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A6. a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Eigenvalue Analysis of the Sample Covariance Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The 1st largest eigenvalue: 5.11678772834208\n",
      "The 2nd largest eigenvalue: 3.741328478864824\n",
      "The 10th largest eigenvalue: 1.2427293764173368\n",
      "The 30th largest eigenvalue: 0.3642557202788903\n",
      "The 50th largest eigenvalue: 0.16970842700672778\n",
      "The summation of all eigenvalues is: 52.72503549512692\n"
     ]
    }
   ],
   "source": [
    "# Print the 1st largest eigenvalue\n",
    "print('The 1st largest eigenvalue:', eigvals[0])  # Python indexing starts at 0\n",
    "\n",
    "# Print the 2nd largest eigenvalue\n",
    "print('The 2nd largest eigenvalue:', eigvals[1])\n",
    "\n",
    "# Print the 10th largest eigenvalue\n",
    "print('The 10th largest eigenvalue:', eigvals[9])  # 10 - 1 = 9\n",
    "\n",
    "# Print the 30th largest eigenvalue\n",
    "print('The 30th largest eigenvalue:', eigvals[29])  # 30 - 1 = 29\n",
    "\n",
    "# Print the 50th largest eigenvalue\n",
    "print('The 50th largest eigenvalue:', eigvals[49])  # 50 - 1 = 49\n",
    "\n",
    "# Print the summation of all eigenvalues\n",
    "print('The summation of all eigenvalues is:', sum(eigvals))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Title: PCA Projection Using Top-k Eigenvalues and Eigenvectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to get the top-k eigenvectors\n",
    "def k_eigvecs(k):\n",
    "    \"\"\"\n",
    "    Returns the top-k eigenvectors from the global eigenvectors array.\n",
    "    \n",
    "    Parameters:\n",
    "        k (int): The number of top eigenvectors to return.\n",
    "\n",
    "    Returns:\n",
    "        np.ndarray: Top-k eigenvectors.\n",
    "    \"\"\"\n",
    "    return eigvecs[:, :k]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to project a point x using PCA with top-k eigenvalues and eigenvectors\n",
    "def new_PCA_project(x, k):\n",
    "    \"\"\"\n",
    "    Projects a data point x to a lower-dimensional space using PCA.\n",
    "\n",
    "    Parameters:\n",
    "        x (np.ndarray): Original high-dimensional data point.\n",
    "        k (int): The number of principal components to use for the projection.\n",
    "\n",
    "    Returns:\n",
    "        np.ndarray: Data point projected to the lower-dimensional space.\n",
    "    \"\"\"\n",
    "    # Compute the projection using top-k eigenvectors and adding back the mean (muu)\n",
    "    return muu + (x - muu) @ k_eigvecs(k) @ k_eigvecs(k).T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# e)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Title: Visualizing PCA Reconstruction for Different Values of k\n",
    "Note: The approximation improves as we include more eigenvectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Find the index of the first training example with label 2\n",
    "j = np.where(labels_train == 2)[0][0]\n",
    "\n",
    "# Create a figure to plot the PCA reconstructions\n",
    "plt.figure(figsize=(10, 5), dpi=100)\n",
    "\n",
    "# Initialize subplot counter\n",
    "ii = 0\n",
    "\n",
    "# List of 'k' values to be used for PCA reconstruction\n",
    "k_values = [5, 15, 40, 100, 300, 500, 700, 28*28]\n",
    "\n",
    "# Corresponding titles for each subplot\n",
    "titles = ['k=5', 'k=15', 'k=40', 'k=100', 'k=300', 'k=500', 'k=700', 'k=784']\n",
    "\n",
    "# Loop through each 'k' value to perform PCA reconstruction and plotting\n",
    "for i in range(8):\n",
    "    ii += 1\n",
    "    plt.subplot(3, 3, ii)\n",
    "    plt.title(titles[i])\n",
    "    \n",
    "    # Perform PCA reconstruction for the current 'k' value\n",
    "    reconstructed_img = new_PCA_project(X_train[j], k_values[i])\n",
    "    \n",
    "    # Reshape the reconstructed image to its original shape and plot\n",
    "    reshaped_img = np.reshape(reconstructed_img, (28, 28))\n",
    "    plt.imshow(reshaped_img)\n",
    "    plt.axis('off')\n",
    "\n",
    "# Plot the original image for comparison\n",
    "plt.subplot(3, 3, 9)\n",
    "plt.title('Original Image')\n",
    "original_img = np.reshape(X_train[j], (28, 28))\n",
    "plt.imshow(original_img)\n",
    "plt.axis('off')\n",
    "\n",
    "# Show all plots\n",
    "plt.show()\n",
    "\n",
    "# Note: The approximation improves as we include more eigenvectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Find the index of the first training example with label 6\n",
    "j = np.where(labels_train == 6)[0][0]\n",
    "\n",
    "# Create a figure to plot the PCA reconstructions\n",
    "plt.figure(figsize=(10, 5), dpi=100)\n",
    "\n",
    "# Initialize subplot counter\n",
    "ii = 0\n",
    "\n",
    "# List of 'k' values to be used for PCA reconstruction\n",
    "k_values = [5, 15, 40, 100, 300, 500, 700, 28*28]\n",
    "\n",
    "# Corresponding titles for each subplot\n",
    "titles = ['k=5', 'k=15', 'k=40', 'k=100', 'k=300', 'k=500', 'k=700', 'k=784']\n",
    "\n",
    "# Loop through each 'k' value to perform PCA reconstruction and plotting\n",
    "for i in range(8):\n",
    "    ii += 1\n",
    "    plt.subplot(3, 3, ii)\n",
    "    plt.title(titles[i])\n",
    "    \n",
    "    # Perform PCA reconstruction for the current 'k' value\n",
    "    reconstructed_img = new_PCA_project(X_train[j], k_values[i])\n",
    "    \n",
    "    # Reshape the reconstructed image to its original shape and plot\n",
    "    reshaped_img = np.reshape(reconstructed_img, (28, 28))\n",
    "    plt.imshow(reshaped_img)\n",
    "    plt.axis('off')\n",
    "\n",
    "# Plot the original image for comparison\n",
    "plt.subplot(3, 3, 9)\n",
    "plt.title('Original Image')\n",
    "original_img = np.reshape(X_train[j], (28, 28))\n",
    "plt.imshow(original_img)\n",
    "plt.axis('off')\n",
    "\n",
    "# Show all plots\n",
    "plt.show()\n",
    "\n",
    "# Note: The approximation improves as we include more eigenvectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Find the index of the first training example with label 7\n",
    "j = np.where(labels_train == 7)[0][0]\n",
    "\n",
    "# Create a figure to plot the PCA reconstructions\n",
    "plt.figure(figsize=(10, 5), dpi=100)\n",
    "\n",
    "# Initialize subplot counter\n",
    "ii = 0\n",
    "\n",
    "# List of 'k' values to be used for PCA reconstruction\n",
    "k_values = [5, 15, 40, 100, 300, 500, 700, 28*28]\n",
    "\n",
    "# Corresponding titles for each subplot\n",
    "titles = ['k=5', 'k=15', 'k=40', 'k=100', 'k=300', 'k=500', 'k=700', 'k=784']\n",
    "\n",
    "# Loop through each 'k' value to perform PCA reconstruction and plotting\n",
    "for i in range(8):\n",
    "    ii += 1\n",
    "    plt.subplot(3, 3, ii)\n",
    "    plt.title(titles[i])\n",
    "    \n",
    "    # Perform PCA reconstruction for the current 'k' value\n",
    "    reconstructed_img = new_PCA_project(X_train[j], k_values[i])\n",
    "    \n",
    "    # Reshape the reconstructed image to its original shape and plot\n",
    "    reshaped_img = np.reshape(reconstructed_img, (28, 28))\n",
    "    plt.imshow(reshaped_img)\n",
    "    plt.axis('off')\n",
    "\n",
    "# Plot the original image for comparison\n",
    "plt.subplot(3, 3, 9)\n",
    "plt.title('Original Image')\n",
    "original_img = np.reshape(X_train[j], (28, 28))\n",
    "plt.imshow(original_img)\n",
    "plt.axis('off')\n",
    "\n",
    "# Show all plots\n",
    "plt.show()\n",
    "\n",
    "# Note: The approximation improves as we include more eigenvectors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Title: Function to Calculate Reconstruction Error for PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "def reconstruction_error(k):\n",
    "    \"\"\"\n",
    "    Calculate the mean squared error in the PCA reconstruction \n",
    "    of training and testing data for a given 'k' eigenvectors.\n",
    "    \n",
    "    Parameters:\n",
    "        k (int): The number of eigenvectors to use for PCA.\n",
    "        \n",
    "    Returns:\n",
    "        tuple: Mean squared error for training and testing data.\n",
    "    \"\"\"\n",
    "    \n",
    "    # Initialize counter and error variables for training data\n",
    "    n = 1\n",
    "    train_error = 0\n",
    "    \n",
    "    # Calculate the number of training samples to process\n",
    "    n1 = int(np.shape(X_train)[0] / n)\n",
    "    \n",
    "    # Loop through training samples to accumulate the squared error\n",
    "    for i in range(n1):\n",
    "        train_error += np.linalg.norm(new_PCA_project(X_train[i], k) - X_train[i])**2\n",
    "    \n",
    "    # Initialize error variable for testing data\n",
    "    test_error = 0\n",
    "    \n",
    "    # Calculate the number of testing samples to process\n",
    "    n2 = int(np.shape(X_test)[0] / n)\n",
    "    \n",
    "    # Loop through testing samples to accumulate the squared error\n",
    "    for i in range(n2):\n",
    "        test_error += np.linalg.norm(new_PCA_project(X_test[i], k) - X_test[i])**2\n",
    "    \n",
    "    # Return the mean squared errors for training and testing data\n",
    "    return train_error / n1, test_error / n2\n",
    "\n",
    "# Note: The function can be used to evaluate the quality of PCA basis by calculating the reconstruction error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(52.66800352142155, 52.84524106822601)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reconstruction_error(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(52.70193547889742, 52.87343386035088)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reconstruction_error(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The reconstruction_error function calculates the mean squared error (MSE) for PCA reconstructions on both the training and test datasets. It takes the number of eigenvectors k to be used in the PCA approximation as an argument. The function returns two values: the MSE for the training dataset and the MSE for the test dataset. Lower MSE values indicate better approximations of the original data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A6. c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Title: Analyzing PCA Variance and Reconstruction Error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize the number of different 'k' values to consider\n",
    "n = 100\n",
    "\n",
    "# Create arrays to store the k values, the proportion of unexplained variance,\n",
    "# and the reconstruction errors for training and test sets\n",
    "pca_k_range = list(range(0, n))\n",
    "pca_y = np.zeros(n)\n",
    "train_e = np.zeros(n)\n",
    "test_e = np.zeros(n)\n",
    "\n",
    "# Loop over each 'k' value from 0 to n-1\n",
    "for i in range(n):\n",
    "    # Calculate and store the proportion of total variance not explained\n",
    "    # by the first 'i' principal components\n",
    "    pca_y[i] = 1 - sum(eigvals[:i]) / sum(eigvals)\n",
    "    \n",
    "    # Calculate and store the reconstruction error (Mean Squared Error)\n",
    "    # for both the training and test datasets using 'i' principal components\n",
    "    train_e[i], test_e[i] = reconstruction_error(pca_k_range[i])\n",
    "\n",
    "# pca_y now contains the proportion of unexplained variance for each 'k'\n",
    "# train_e and test_e contain the reconstruction errors for training and test sets\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting Reconstruction Error for Training and Test Sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a plot to visualize the reconstruction error\n",
    "plt.figure(figsize=(8, 6), dpi=100)\n",
    "\n",
    "# Uncomment the following line to plot the proportion of unexplained variance\n",
    "# plt.plot(pca_k_range, pca_y)\n",
    "\n",
    "# Plot the reconstruction error (Mean Squared Error) for the training set\n",
    "plt.plot(pca_k_range, train_e, label='Train Error')\n",
    "\n",
    "# Plot the reconstruction error (Mean Squared Error) for the test set\n",
    "plt.plot(pca_k_range, test_e, label='Test Error')\n",
    "\n",
    "# Add a legend to differentiate the curves\n",
    "plt.legend(loc=\"best\")\n",
    "\n",
    "# Display the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Title: Plotting Proportion of Unexplained Variance Over PCA Components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a plot to visualize the proportion of unexplained variance\n",
    "plt.figure(figsize=(7, 5), dpi=100)\n",
    "\n",
    "# Plot the proportion of unexplained variance for different numbers of PCA components (k)\n",
    "plt.plot(pca_k_range, pca_y)\n",
    "\n",
    "# Uncomment the following line to add a legend if necessary\n",
    "# plt.legend(loc=\"best\")\n",
    "\n",
    "# Display the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A6. d) Displaying the First 10 Eigenvectors as Images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a figure to display the first 10 eigenvectors\n",
    "plt.figure(figsize=(10, 5), dpi=100)\n",
    "\n",
    "# Initialize an index counter\n",
    "ii = 0\n",
    "\n",
    "# Define the text labels for each subplot\n",
    "text_labels = ['1st', '2nd', '3rd', '4th', '5th', '6th', '7th', '8th', '9th', '10th']\n",
    "\n",
    "# Loop through the first 10 eigenvectors to display them\n",
    "for i in range(10):\n",
    "    ii += 1\n",
    "    \n",
    "    # Create a subplot for each eigenvector\n",
    "    plt.subplot(2, 5, ii)\n",
    "    \n",
    "    # Add a title to each subplot\n",
    "    plt.title(text_labels[i])\n",
    "    \n",
    "    # Reshape the eigenvector to 28x28 for visualization\n",
    "    eigenvector_image = np.reshape(eigvecs[ii - 1], (28, 28))\n",
    "    \n",
    "    # Display the eigenvector as an image\n",
    "    plt.imshow(eigenvector_image)\n",
    "    \n",
    "    # Hide axis labels and ticks\n",
    "    plt.axis('off')\n",
    "\n",
    "# Show the figure\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}