Week 09 — Dimensionality Reduction

Pearson 1901: find the hyperplane minimizing orthogonal distances. The result surfaces the eigenvectors of the covariance matrix.

Lecture

PCA as SVD · probabilistic PCA · factor analysis · t-SNE (van der Maaten 2008) · UMAP (McInnes 2018) · autoencoders for nonlinear dimensionality reduction.

Read before the lecture

• Pearson, *On Lines and Planes of Closest Fit to Systems of Points in Space* (Phil. Mag. 1901)

Code lab

Lab 4 — Visualizing genomic data

Apply PCA, t-SNE, and UMAP to a public single-cell RNA-seq dataset. Compare what each method preserves. Discuss the cost of nonlinear methods for downstream interpretation.

Notebook: lab04-genomic.ipynb  ·  Dataset: 10x Genomics single-cell PBMC (public).

Reference text for this week: chapter 09 of the bilingual notes — EN PDF · FR PDF.