Tue/Thu: 1045-1205. WEB L114
- Core Geometric Objects
- (1/11-1/8) Convex Hulls I: Convexity, representation of convex hulls, the gift-wrapping algorithm, divide-and-conquer, Chan's optimal algorithm, linear classification. Notes.
- Assignment 1 due Jan 29.
- (1/18-1/25): Voronoi Diagrams. Notes.
- (1/30-2/6): Delaunay Triangulations (Mount, starting at page 74)
- (2/6-2/20): Arrangements, duality and sweep-line algorithms.
- Data Structures
- (2/27) Range trees & kd-trees (Mount, starting at page 48)
- (3/1) Quad trees (Har-Peled, Chapter 2)
- (3/6) Well-separated pair decompositions (Har-Peled, Chapter 3)
- Sampling and Learning (Har-Peled, Chapter 5)
- VC dimension
- epsilon-nets and epsilon-samples
- discrepancy-based constructions
- High Dimensional Geometry
- SVDs, PCA and MDS
- Random projections (and an application to clustering)
- Near neighbors (see these nice Euclidean LSH notes, and this for the main LSH resource page)
- Core sets and extents (see Chapter 23 from this book)
- The Geometry of Learning
- Kernels and Hilbert spaces
- Support Vector Machines
- The graph Laplacian
- Bregman Divergences.
- Polyhedra and Optimization
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