Session III: Principal Component Analysis & Clustering Methods

Topics

• Principal Component Analysis (PCA)

Workbook about PCA for visualization and dimension reduction: pca_biplots_ex.ipynb, pca_biplots_ex.py
Workbook with detailed solution: pca_biplots_sol.ipynb, pca_biplots_sol.py

• Clustering:
  • K-Means Clustering
  • Spectral Clustering (if time permits)

Workbook about dimension reduction via PCA and clustering on image data: workshop_pca.ipynb, workshop_pca.py
Workbook with detailed solution: workshop_pca_sol.ipynb, workshop_pca_sol.py

Notes of session

• PDF

Recording of session

• Zoom Recording (Session III)

References

Principal Component Analysis

• Chapter 10.2 of James, Gareth, Daniela Witten, Trevor Hastie, and Robert Tibshirani. “An Introduction to Statistical Learning”, Vol. 112. Springer, 2013 (PDF available),
• Chapter 10 of Marc P. Deisenroth and A. Aldo Faisal and Cheng Soon Ong, “Mathematics for Machine Learning”, Cambridge University Press, 2020 (PDF available),
• Genetics application: Paschou, P., Ziv, E., Burchard, E. G., Choudhry, S., Rodriguez-Cintron, W., Mahoney, M. W., & Drineas, P., “PCA-correlated SNPs for structure identification in worldwide human populations”, PLoS Genet, 3(9), e160.

Clustering: K-Means and Spectal

• Chapter 21 of Kevin P. Murphy, “Probabilistic Machine Learning: An introduction”, MIT Press, 2021 (PDF available),
• Chapter 22 of Shai Shalev-Shwartz and Shai Ben-David. “Understanding machine learning: From theory to algorithms”, Cambridge University Press, 2014 (PDF available),
• Chapter 14 of Trevor Hastie, Robert Tibshirani, and Jerome Friedman, “The Elements of Statistical Learning: Data Mining, Inference, and Prediction”, Springer, 2009 (PDF available)