Dimension reduction
and manifold learning (M2 MASH)

Agenda

Course material

• Manifold learning in context

•   - High-dimensional geometry, estimation, and hope (notes)
•   - Linear algebra refresher (notes)

• Multidimensional scaling

•   - Classical scaling and stress minimization (slides)
•   - Classical scaling (practice, solution)
•   - Stress minimization for graph drawing (practice)

• From MDS to dimension reduction

•   - Principal Component Analysis, ISOMAP, LLE (slides)
•   - Basic spectral dimension reduction (practice, solution)

• A non-exhaustive tour into nonlinear dimension reduction

•   - Laplacian Eigenmaps, Kernel PCA, MVU, Diffusion maps, t-SNE, UMAP (slides)

• Geometric inference

•   - Dimension estimation, Manifold estimation, Local PCA, optimality (slides)

• Supervised dimension reduction

•   - TBA (slides)
•   - TBA (practice, solution)

Exam

Instructions, Reading report, Article choice