Spectral Algorithms (CS 8803, Fall 2010)

TR 9:30-11am, Room: CCB 52
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)

Aug 24. Intro/overview.
Aug 26. SVD basics, a geometric characterization; App 1: k-median.
Aug 31, Sep 2. App 2: Mixture Models

Sep 7,9: Algo 1: Cut decomposition; App 3: Constraint Satisfaction Problems (CSPs).
Note: Rademacher talk Sep 7th at 11am in Klaus 1116W
Sep 14,16. Algo 2: Tensor decomposition; App 3: CSPs (contd.)

Sep 17. CSE seminar, 2pm, "The Joy of PCA".
Sep 21. App 4: Learning intersections of halfspaces.

[Sampling based algorithms]
Sep 23. Algo 3: Matrix multiplication; Algo 4: Linear-time low-rank approximation
Sep 28,30. App 5: Matrix reconstruction; Algo 5: Constant-time low-rank approximation; Algo 6: The CUR decomposition.

[Adaptive Sampling]
Oct 5. Algo 7: Adaptive Sampling.
Oct 7. Algo 7 (cont.): Volume Sampling.
Oct 12. Algo 8: Isotropic Random Projection.

[Random inputs]
Oct 19. Fall break
Oct 21. Spectral of random graphs; App 6: planted partitions.

[Cuts and clustering]
Oct 26. Midterm.
Oct 28. Project review.
Nov 2,4. App 7, 8: Sparsest cut.
Nov 9. Spectral clustering.
Nov 11. Spectra of random matrices.

[Current topics]
Nov 16. Spectral partitioning and unique games (Anand).
Nov 18. Random tensors and planted cliques (Andreas).

[Topology]
Nov 23. Null space embeddings.
Nov 25. Thanksgiving

[Extensions of PCA]
Nov 30. Algo 9: Affine-invariant PCA.
Dec 2. Algo 10: Robust PCA; App 2: Mixtures (contd.)

Dec 7. Project reviews/posters
Dec 9. Future directions