Course Syllabus

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General Information:

Time: M W 3:30PM-5:00PM
Place: JES A303A
Instructor: Qixing Huang and  Chandrajit Bajaj
Office hour:  QH (Fridays 3pm-5pm at GDC 5422). CB (Zoom Fridays 1 - 3pm)

The course covers the mathematics of applications of spectral graph theory, broadly defined. Grading is based on homework (60%) and the final project (40%).

A partial list of applications to be covered:

  • Spectral Graph Theory.
  • Graph Neural Networks.
  • Spectral Clustering.
  • Spectral Map Synchronization.
  • Spectral Shape Matching.
  • Spectral Vector-Field Design.
  • Spectral Parameterization.

Prereqs: The course assumes a good knowledge of linear algebra and probability. Please talk to me or email me if you are unsure if the course is a good match for your background.

 

Schedule:

Date Topics Reading Notes
Jan 19th Introduction
Jan 24th Adjacency Matrix, Laplacian Matrix, and Spectral Graph Drawing  (lecture-notes) and see references cited
Jan 26th Normalized Adjacency Matrix and Laplacian Matrix (lecture-notes) and see references cited Homework 1 out.
Feb 2nd  Graph Properties, Graph, Laplacian Spectrum, Courant-Fischer Lecture notes Spielman's notes
Feb 7th Graph Condunctances, Expanders, Cheeger's Inequality I (lecture-notes and see references therein)
Feb 9th Random and Lazy Walks on Graphs See lecture-notes and see references cited there)
Feb 11th Markov Chain Monte Carlo - Metropolis, Hastings, Gibbs, ...  see lecture notes1 and notes2and read references cited
Feb 14th Last Eigenvalue Cheeger and Spectral Partitioning see lecture notes Homework 1 due. Homework 2 out.
Feb 16th Higher Order Cheeger and Spectral Partitioning /Clustering Algorithms I see lecture notes1 and notes2 references cited
Feburary 21th

Higher Order Cheeger and Spectral Partitioning /Clustering Algorithms II

 see lecture notes and references cited
Feburary 23th MCMC Mixing Time and Spectral Partitioning II see lecture notes and references cited
Feburary 28th Random Walks and Electrical Networks I see lecture notes and references cited
March 2rd Random Walks and Electrical Networks II see lecture notesand references cited Homework 2 due March 4, midnight
March 7th Harmonic Extensions and Embeddings I Chap 3 of Lovasz Homework 3 out .
March 9th Harmonic Extensions and Embeddings II Chap 3, 4 of Lovasz
March 21th Graph Convolutions and Graph Neural Networks I  Distill Paper and References
March 23th Graph Convolutions and Graph Neural Networks II Distill Paper and References Homework 3 due on March 27th 5:00pm. Homework 4 out
March 28th GeometricDL : GraphSage and Clustering/Partitioning

GraphSage-Notes

 

GraphSage Deep Learning-Notes

 Please read the references in the Notes
March 30th GeometricDL: DeepWalk and Clustering/Partitioning

Deep-Walk-SkipGram

 

 Please read the references in the Notes
April 4th GeometricDL: Embeddings for Link Prediction NeoDTI notes Final Project List to be circulated March 14th. Selection due by March 21st
April 6th GeometricDL: Part (molecular) Assembly Prediction, Electric Grid Resiliency, Spatio-Temporal Animation See [notes]

Homework 4 due April 10th midnight.

 
April 11th Geometric Deep Learning: Simplicial Complex Embeddings  [Notes] and also see cited  references 
April 13th Variational Inference, Corrections for Posterior Collapse [Notes]and also see cited  references 
April 18th Deep Learning Dynamical Systems with Stability  [Notes]and see references
April 20th

Deep Learning Dynamical Systems  with Control.  Guided Policy Search [notes]

 [Notes]and see references
April 25th Variations of Stochatistic Optimization for Deep Learning [Notes] and see references Final Project (phase 1) due April 25th midnight
April 27th Bayesian Bandits and Reinforcement Learning [notes]
May 2nd Game Theory and Actionable Machine Intelligence [notes]
May 4rd Markov Decision Processes and Markov Games [Notes]  Final project report due. May 12th midnight.

 

 

Final Project:

The final project is done in groups of 2-3 students. Each project should have an initial proposal, a final report, and a final poster presentation. The project proposal shall describe four key components of a research project (namely Motivation, Technical Merit, Broader Impact, and Project Plan). The final report should be written as an academic research article. A more detailed instruction will be given later. 

Course Summary:

Date Details Due