Machine Learning Meets Geometry

Announcements

01/07/2020:
Welcome to the course!

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General Information

Times & Places
TuTh 3:30PM - 4:50PM, EBU3B 4140

Course Staff

	Name	Email	Office Hours	Location
Instructor	Hao Su	haosu@ucsd.edu	5:00PM-6:00PM, Tu	CSE Building 4109
Course Assistant	Meng Song	mes050@ucsd.edu	5:15PM-6:15PM, Th	CSE Building 4109

Objectives

This is a graduate level course to cover core concepts and algorithms of geometry that are being used in computer graphics, computer vision and machine learning. I will cover key concepts of differential geometry, the usage of geometry in computer graphics, vision, and machine learning. Students are required to do a course project in pairs.

Prerequisites

Background assumed includes basic material in linear algebra, optimization, and machine learning.

Grading (tentative)

• Quizzes 20%
• Course project presentation 40%
• Course project writeup 40%
• There will not be a final exam.

Syllabus

The planned syllabus is as below. Certain contents may be added or removed based upon the interactions in class and other situations.

• Geometry Basics (3 weeks)
  • Curves
  • Surfaces
  • First Fundamental Form
  • Second Fundamental Form
  • Geodesics
  • Gauss' Remarkable Theorem
  • Gauss-Bonnet Theorem
  • Vector Field, Flow, Parallel Transportation
  • Levi-Civita Connection
  • Surface Representation in Computer
  • Delaunay Triangulation
  • Discrete Differential Geometry
• Laplacian Operator and Spectral Graph Theory (2 weeks)
  • Laplacian-Bertrami Operator
  • Spectral Graph Theory
  • Laplacian Shape Editing
  • Functional Map
• Data Embedding and Deep Learning (2 weeks)
  • Major Embedding Theorems
  • PCA, CCA
  • Isomap, LLE, MDS
  • Variational Auto-Encoder
  • Generative Adversarial Networks
  • Optimal Transport
  • Characterization of Local Optimas of Deep Networks
• Map Networks (2 weeks)
  • The Rigid and Non-rigid Shape Registration Problem
  • Cycle Consistency by Semi-Definite Programming
  • Functional Map Network, Deep Functional Map Network
  • Unsupervised Learning by Map Networks, Cycle GAN
• Deep Learning on 3D Data (2 weeks)
  • Multi-view Representation
  • Volumetric Representation
  • Implicit Function Representation
  • Point Cloud Representation
  • Embedded-Graph Representation (Graph CNN)
  • Structural Representation
  • Scene Understanding
• Topological Data Analysis (Optional)
  • Topology Review, Complexes
  • Homology Groups, Persistent Homology

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