Overview
Principal Component Analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components.
It's commonly used for dimensionality reduction, which helps in visualization and can improve model performance by reducing overfitting.
Key Concepts
- Eigenvalues and eigenvectors
- Variance and covariance matrices
- Principal components and explained variance
- Selecting the number of components
- Applications of PCA in machine learning
Practice Exercise
Exercise: Image Compression and Visualization
Complete two tasks using PCA:
- Apply PCA to compress a set of images
- Use PCA to visualize high-dimensional data (e.g., MNIST) in 2D
- Analyze the explained variance ratio
- Determine the optimal number of components
- Compare the results before and after PCA
Resources
StatQuest
Main resource for today
PCA in Python
Step-by-step implementation with scikit-learn
Mathematical Explanation of PCA
Detailed mathematical foundation
PCA vs. Other Dimensionality Reduction Techniques
Comparison with t-SNE, UMAP, etc.
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