16. Demo 2: Dimensionality Reduction with Principal Components Analysis (PCA)

Understanding Principal Components Analysis for Dimensionality Reduction

Principal Components Analysis (PCA) is a technique to reduce datasets' dimensions by identifying core features while preserving data variance. Here's how it's applied:

• Dataset: Analyze six features representing US treasury yields since 1981.
• Correlation: High correlation among features can lead to redundancy and computational inefficiency.
• Scaling: Essential to scale features before applying PCA to avoid errors.
• PCA Application:
  • Utilize PCA class from scikit-learn.
  • Determine components to keep by analyzing the variance explained.
• Variance Explained:
  • 97% of total variance captured by the first principal component.
  • More than 99% covered with the first two components.
• Orthogonality: Principal components are uncorrelated, shown via correlation matrix analysis.
• Interpretation: The first component captures trend levels, while others depict slope and curvature dynamics.
• Model Integration: Ensure transformation applies consistently when training and testing models for reliable results.

PCA helps streamline data preparation by consolidating features without significant information loss, enhancing model efficiency.