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Added code for Principal Component Analysis #97

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Added code for Principal Component Analysis #97

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198 changes: 198 additions & 0 deletions PCA_Code.ipynb
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"provenance": []
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "markdown",
"source": [
"### **1. Installing Packages**"
],
"metadata": {
"id": "pSXJVwyF2Ed8"
}
},
{
"cell_type": "code",
"source": [
"!pip install -U scikit-learn"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "WMc2NjhLzTk_",
"outputId": "baf5c845-5778-4adf-cecd-340b49845107"
},
"execution_count": 29,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Requirement already satisfied: scikit-learn in /usr/local/lib/python3.10/dist-packages (1.3.1)\n",
"Requirement already satisfied: numpy<2.0,>=1.17.3 in /usr/local/lib/python3.10/dist-packages (from scikit-learn) (1.23.5)\n",
"Requirement already satisfied: scipy>=1.5.0 in /usr/local/lib/python3.10/dist-packages (from scikit-learn) (1.11.3)\n",
"Requirement already satisfied: joblib>=1.1.1 in /usr/local/lib/python3.10/dist-packages (from scikit-learn) (1.3.2)\n",
"Requirement already satisfied: threadpoolctl>=2.0.0 in /usr/local/lib/python3.10/dist-packages (from scikit-learn) (3.2.0)\n"
]
}
]
},
{
"cell_type": "markdown",
"source": [
"### **2. Importing Necessary Modules**"
],
"metadata": {
"id": "VqbC4ieK13sm"
}
},
{
"cell_type": "code",
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from sklearn.decomposition import PCA\n",
"from sklearn.datasets import load_digits"
],
"metadata": {
"id": "emxbvfX5yRU1"
},
"execution_count": 30,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"### **3. Loading the datatset**"
],
"metadata": {
"id": "bT4CTPVm19aZ"
}
},
{
"cell_type": "code",
"source": [
"# Load the Digits dataset\n",
"digits = load_digits()\n",
"X = digits.data\n",
"y = digits.target"
],
"metadata": {
"id": "j4-ZKuDcyZEU"
},
"execution_count": 31,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"### **4. Applying PCA and reducing the image**"
],
"metadata": {
"id": "-n5etZJf2FJ1"
}
},
{
"cell_type": "code",
"source": [
"# Randomly select an image for demonstration\n",
"random_image_index = np.random.randint(0, X.shape[0])\n",
"\n",
"# Define the number of principal components you want to keep\n",
"n_components = int(input(\"Enter the number of components you want to keep (in the range of 0 to 64): \"))\n",
"\n",
"# Apply PCA to the image data\n",
"pca = PCA(n_components=n_components)\n",
"X_pca = pca.fit_transform(X)\n",
"\n",
"# Inverse transform to get the reduced-dimension image\n",
"X_inverse = pca.inverse_transform(X_pca)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "1TsSSFR3yi7x",
"outputId": "ea8a130e-06e6-4998-daaf-bb430a7d1e2e"
},
"execution_count": 52,
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Enter the number of components you want to keep (in the range of 0 to 64): 0\n"
]
}
]
},
{
"cell_type": "markdown",
"source": [
"### **5. Displaying the reduced image**"
],
"metadata": {
"id": "MhJN70II2Tyb"
}
},
{
"cell_type": "code",
"source": [
"# Original image\n",
"original_image = X[random_image_index].reshape(8, 8)\n",
"\n",
"# Reduced-dimension image\n",
"reduced_image = X_inverse[random_image_index].reshape(8, 8)\n",
"\n",
"# Plot the original and reduced images\n",
"plt.figure(figsize=(8, 4))\n",
"plt.subplot(1, 2, 1)\n",
"plt.imshow(original_image, cmap='gray')\n",
"plt.title('Original Image')\n",
"plt.axis('off')\n",
"\n",
"plt.subplot(1, 2, 2)\n",
"plt.imshow(reduced_image, cmap='gray')\n",
"plt.title(f'Reduced to {n_components} Components')\n",
"plt.axis('off')\n",
"\n",
"plt.show()\n",
"\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 341
},
"id": "UlbzCCVFynKk",
"outputId": "512b3526-2745-45f1-e67c-53c05aacec5c"
},
"execution_count": 53,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 800x400 with 2 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
}
]
}