| Week 1 / Monday, September 14 |
Introduction: Syllabus, motivation, history & basics of geometry |
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Tolga |
| Week 1 / Wednesday, September 16 |
Basics of geometry of curves and surfaces |
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Tolga |
| Week 2 / Monday, September 21 |
Review of differential geometry (topological manifold, smooth manifold, coordinates, charts and atlases) |
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Tolga |
| Week 2 / Wednesday, September 23 |
Review of Riemannian geometry (riemannian metric, geodesics, examples of constant curvature spaces) |
Elements of General Relativity, MA430 Notes by Lia Vas |
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Tolga |
| Week 2 / Friday, September 25 |
Office Hour |
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HW1 Out |
Anthea, Tolga, Ines |
| Week 3 / Monday, September 28 |
Optimization on Riemannian manifolds I (RSGD, riemannian line search) |
Chapters 3 & 4 in Optimization on Smooth Manifolds |
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Tolga |
| Week 3 / Wednesday, September 30 |
Algorithms on Riemannian manifolds (PCA, Karcher mean, PGA, MDS and etc.) |
Karcher Mean, Sphere and Hyperboloid Example, PGA, h-MDS |
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Guest Lecture: Frederic Sala |
| Week 3 / Friday, October 2 |
Office Hour |
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Anthea, Tolga, Ines |
| Week 4 / Monday, October 5 |
Matrix Manifolds and Applications in Computer Vision I |
Edelman et al. 1998,
Optimization Algorithms on Matrix Manifolds (Ch. 1-4)
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Tolga |
| Week 4 / Wednesday, October 7 |
Probability on Riemannian manifolds & Sampling |
Intrinsic Statistics on Riemannian Manifolds |
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Guest Lecture: Nina Miolane |
| Week 4 / Friday, October 9 |
Office Hour |
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HW2 Out, iPython Notebook |
Anthea, Tolga, Ines |
| Week 5 / Monday, October 12 |
Riemannian Bayesian Inference |
[Recipe for SG-MCMC], [SG-GMC], [Birdal & Simsekli'19], [Birdal & et al.'18], [HMC] |
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Tolga |
| Week 5 / Wednesday, October 14 [9am PDT] |
Second Order Methods in Riemannian Optimization |
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Guest Lecture (9am PDT): Nicolas Boumal |
| Week 5 / Friday, October 16 |
Office Hour |
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Anthea, Tolga, Ines |
| Week 6 / Monday, October 19 [9am PDT] |
From Manifolds to Graphs: Geodesics |
Convergence of Geodesics, IsoMap paper |
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Ines |
| Week 6 / Wednesday, October 21 [9am PDT] |
From Manifolds to Graphs: Laplacian |
Convergence of the Laplacian, SSL, Laplacian Eigenmaps, Section IV in GDL Survey, Spectral Clustering |
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Ines |
Week 6 / Friday, October 23 |
Office Hour |
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HW2 Due, Project Proposal Out |
Anthea, Tolga, Ines |
| Week 7 / Monday, October 26 [9am PDT] |
From Graphs to Manifolds: Shallow Graph Embeddings |
Deep Walk, Sections 1-4 in Graph Survey, Poincare embeddings, Product-space embeddings |
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Ines |
| Week 7 / Wednesday, October 28 [9am PDT] |
From Graphs to Manifolds: Graph Neural Networks |
Spectral Graph CNN, Section III, V and VI in GDL Survey, ChebyNet, GCN, Sections 5-7 in Graph Survey, Hyperbolic GCN |
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Ines |
| Week 7 / Friday, October 30 |
Office Hour |
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Anthea, Tolga, Ines |
| Week 8 / Monday, November 2 |
Computer Vision Applications: Shape Modeling |
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Guest Lecture: Emanuele Rodola |
| Week 8 / Wednesday, November 4 |
Computer Vision Applications: Point Clouds |
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Tolga |
Week 8 / Friday, November 6 |
Office Hour |
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Anthea, Tolga, Ines |
| Week 9 / Monday, November 9 |
Laplace-Beltrami Operators and Intrinsic Descriptors on Manifolds |
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Guest Lecture: Leonidas Guibas |
| Week 9 / Wednesday, November 11 |
Normalizing Flows for Manifolds |
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Guest Lecture: Aaron Lou |
| Week 9 / Friday, November 13 |
Office Hour |
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Final Project Due |
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| Week 10 / Monday, November 16 |
Project Presentations |
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| Week 10 / Wednesday, November 18 |
Project Presentations |
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