Chapter 12 Quiz: Dimensionality Reduction

Chapter 11: Reducing Dimensions — PCA and Beyond

Learning objectives

  • Test your understanding of PCA, t-SNE, explained variance, and dimensionality reduction code

This quiz covers both the lecture material and lab exercises from Chapter 12.

Key Concepts Review

  • PCA: Rotates to max-variance directions. Eigenvalues = variance per component. Standardize first.
  • Explained Variance: Sum eigenvalues. Choose components explaining 90-95% of total.
  • t-SNE: Nonlinear, preserves local structure. Perplexity controls neighborhood size.
  • Linear AE: Equivalent to PCA. Nonlinear AE captures curved manifolds.
  • PCA Limitations: Linear only. Alternatives: Kernel PCA, UMAP, autoencoders.

References

  • Hastie, T., Tibshirani, R., Friedman, J. (2009). The Elements of Statistical Learning (2nd ed.), ch. 14.5. Springer.
  • Bishop, C.M. (2006). Pattern Recognition and Machine Learning, ch. 12. Springer.
  • van der Maaten, L., Hinton, G. (2008). Visualizing data using t-SNE. J. Mach. Learn. Res. 9, 2579–2605.

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