Dimensionality Reduction

2.6

Dimensionality Reduction

Summary
  • This chapter covers core dimensionality-reduction methods for compressing high-dimensional data while preserving useful structure.
  • You will compare linear methods (PCA, SVD, LDA) with nonlinear methods (t-SNE, Isomap, Kernel PCA).
  • After this chapter, you should be able to choose methods for visualization, denoising, and downstream modeling.

Intuition #

Dimensionality reduction is about preserving the right geometry for your objective: global variance for compression, class separation for supervised projection, or local neighborhoods for visualization.

Detailed Explanation #

What This Chapter Covers #

  • linear reduction methods such as PCA and SVD
  • supervised projection with LDA and nonlinear manifold methods
  • practical criteria for choosing target dimension and validating information retention

What You Can Do After This Chapter #

  • reduce feature space while preserving useful predictive structure
  • compare linear vs nonlinear projections based on analysis goals
  • integrate dimensionality reduction into model training and evaluation workflows