Dimension reduction and manifold learning

Agenda

Course material

• General presentation (slides)

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, Metric learning, Manifold estimation, Noise (slides)

Deep embeddings, clustering, and label information

• Auto-encoders, Variational Auto-encoders, Clustering, Supervised dimension reduction (slides)

Exam

Instructions, Reading report, Article choice