🧠 PCA IMPLEMENTATION

This project demonstrates Principal Component Analysis (PCA) applied on the MNIST dataset to reduce dimensionality while preserving key features of handwritten digit images.

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📁 Dataset

The dataset used is the MNIST handwritten digits dataset, downloaded from Kaggle. It contains:

• 60,000 training images
• 10,000 test images
• Each image is 28x28 pixels (784 features)

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🔧 Tools & Libraries

• Python 🐍
• NumPy & Pandas
• Matplotlib & Seaborn (for visualization)
• Scikit-Learn (for PCA and data preprocessing)

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📊 Project Steps

1. Data Loading & Preprocessing

   • Read the MNIST dataset
   • Normalize pixel values
   • Optional: Visualize a few digit samples

2. PCA Application

   • Apply PCA to reduce from 784 dimensions to N components
   • Plot explained variance ratio vs. number of components
   • Reconstruct digits from reduced dimensions

3. Visualization

   • Compare original and reconstructed images
   • 2D scatter plots of digits after PCA for clustering insight

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📈 Results

• PCA reduced dimensions while retaining ~95% variance with ~150 components
• Reconstructed images were visually close to originals
• 2D PCA plots showed visible clustering of different digits

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💡 Insights

• PCA is effective for compression and visualization of high-dimensional data like MNIST.
• You can balance between compression (fewer components) and reconstruction quality.