TR 9:30-11am, Room: Klaus 1447
Instructor: Santosh Vempala

Spectral methods have transcended their origins in linear algebra and numerical analysis and are now used in almost every domain with large data sets from web search (e.g., pagerank) and information retrieval (e.g., LSI) to medical diagnosis and prediction. This course is about the mathematics and the algorithmic insights driving these applications.

Tentative schedule

Notes (in progress; updated frequently)

Jan 8. Intro/overview.
Jan 10. SVD basics, a geometric characterization; P1: k-means.
Jan 15. P2: Clustering random models; planted clique/partitions
Jan 17. P2 (contd.). Clustering under deterministic assumptions. K-means revisited.
Jan 22, 24. P3: Unraveling Mixture Models via PCA
Jan 29, 31. Learning Mixture models and topic models via higher moments
Feb 5, 7. P4: Independent Component Analysis using moments
Feb 12, 14. Algo 1: Matrix approximation by random sampling.
Feb 19,21. Guest Lectures by Ravi Kannan
A2: Cut decompositions, Weak regularity; P5: Constraint Satisfaction Problems A3: Tensor decompositions via sampling
Feb 26,28. A4: Combinatorial Optimization via Low-rank Approximation.
Mar 5, 7. P6: Cheeger cuts; P7: Clustering with worst-case guarantees
Mar 12, 14. Mar 7. A5: Constant-time approximate SVD Adaptive sampling A6: Volume sampling, A7: Isotropic Random Projection
Mar 19, 21. Spring break
Mar 26, 28. A8: CUR decomposition, P8: Recommendation systems.
Apr 2, 4. P3 (revisited): Mixture models, A9: Affine-invariant PCA.
Apr 9,11. A10: Noise-tolerant PCA
Apr 16, 18. A11: Sparsification via length-squared sampling. P9: Solving linear equations.
Apr 23, 25. P10: Learning convex sets, TBD.