Principal Component Analysis (PCA) is a dimensionality reduction technique used to simplify complex datasets while preserving as much variance as possible. It transforms data into a new coordinate system where the greatest variance by default lies on the first coordinate (called the first principal component), the second greatest on the second, and so on.
✅ Key Steps in PCA
Standardize the Data
Ensure all features have a mean of 0 and standard deviation of 1 to avoid bias toward larger scales.Compute the Covariance Matrix
Understand relationships between variables using their covariance.Calculate Eigenvalues and Eigenvectors
Identify principal components by finding the eigenvectors of the covariance matrix and sorting them by eigenvalues.Select Top K Eigenvectors
Choose the top K eigenvectors corresponding to the largest eigenvalues to form a feature transformation matrix.Transform the Data
Project the original dataset onto the new coordinate system using the selected eigenvectors.
📌 Applications
- Data Visualization: Reduce high-dimensional data to 2D/3D for plotting.
- Noise Reduction: Remove less significant features to focus on key patterns.
- Machine Learning: Improve model performance by reducing redundant features.
Explore more about Machine Learning
⚠️ Important Notes
- PCA is sensitive to the scale of features, so standardization is critical.
- The number of components (K) depends on the desired balance between simplicity and information retention.
- Always validate PCA results with domain knowledge to ensure meaningful interpretation.
For deeper insights, check our guide on Linear Algebra Fundamentals to understand eigenvectors and eigenvalues better. 📚