Chapter 12 Quiz: Dimensionality Reduction
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.