Mon 31 Mar: Introduction: graphs and matrices; graph Laplacians. [Matlab diary; Matlab files]
Wed 2 Apr: Examples of graphs; Rayleigh quotient theorem; the second eigenvalue.
[Matlab diary;
Matlab files]
Reading for this class:
Spielman notes Chapter 1
and Chapter 2.
Mon 7 Apr: Partitioning and isoperimetry.
[Latest Index]
Reading for this class:
Spielman notes Chapter 4.
Wed 9 Apr: Bounds on eigenvalues and graphic inequalities.
[Matlab diary;
Matlab files;
Latest Index]
Reading for this class:
Spielman notes Chapter 4.
Mon 14 Apr: Cheeger's inequality, conductance, and the normalized Laplacian.
[Latest Index]
Reading for this class:
Spielman notes Chapter 6.
Wed 16 Apr: The planar separator theorem via spectral partitioning.
Reading for this class:
Spielman-Teng paper on
spectral partitioning and planar graphs, Sections 1-4.
Fri 18 Apr: Homework 1 due, Homework 2 assigned.
Mon 21 Apr:
Numerical methods for eigenanalysis: Dense matrices.
[Matlab diary;
Matlab files;
Latest Index]
Reading for this class:
Eigenvalue templates book online nodes:
Introduction through Hermitian eigenproblems [nodes 19-29].
Chapters 5 and 7 of Jim Demmel's "Applied Numerical Linear Algebra"
(see reference page)
are an excellent introduction to eigenvalue algorithms.
Wed 23 Apr:
More numerical eigenanalysis: Power method and Lanczos algorithm.
Reading for this class:
Eigenvalue templates book online nodes:
Algorithms for Hermitian eigenproblems
[nodes 85 (introduction) through 112 (Lanczos software availability)];
Spectral transformations [node 84].
Mon 28 Apr:
More numerical eigenanalysis: Implicitly restarted Lanczos, computational experience.
[Matlab diary;
Matlab files]
Reading for this class:
Implicitly restarted Lanczos [nodes 117 through 130];
John Conroy's paper
on computational experience with Laplacian eigenvalues of brain scans (especially Section 3).
Wed 30 Apr:
Resistive networks, effective resistance, and linear equations.
Reading for this class:
Spielman notes Chapter 8.
Mon 5 May:
Numerical methods for linear equations: Conjugate gradients.
[Latest Index]
Reading for this class:
Linear systems templates book online nodes:
Conjugate gradient method
[nodes 20 (CG) through through 24 (implementation)];
Shewchuk's
Introduction to the conjugate gradient method without the agonizing pain,
Sections 1-8.
Homework 2 due.
Wed 7 May:
CG convergence analysis; preconditioning.
[Matlab diary;
Matlab files;
Latest Index]
Reading for this class:
Shewchuk Sections 9-12;
Spielman notes Chapter 19.
Fri 9 May:
Final project proposals due.
[project guidelines and suggestions,
final project reports]
Homework 3 assigned.
[pdf,
tex]
Mon 12 May:
Preconditioning Laplacians by trees.
[Matlab diary;
Matlab figure;
Matlab files;
Latest Index]
Reading for this class:
Spielman's
Survey of Laplacian matrices and linear solvers.
Wed 14 May:
A different combinatorial approach to Laplacian solvers. (Kevin Deweese, guest speaker.)
Reading for this class:
Kelner et al.,
A simple, combinatorial algorithm for solving SDD systems in nearly-linear time.
Mon 19 May:
Application: Genomics, power iteration clustering, etc. (Veronika Strnadova, guest speaker.)
Reading for this class:
Lin and Cohen,
Power iteration clustering.
Wed 21 May:
Spectral sparsification and combinatorial preconditioning.
Reading for this class:
Koutis, Miller, and Peng,
Approaching optimality for solving SDD linear systems;
Koutis, Miller, and Tolliver,
Combinatorial preconditioners and multilevel solvers
for problems in computer vision and image processing.
Homework 3 due.
Mon 26 May: (Memorial Day holiday, no class)
Wed 28 May:
Generative graph models.
Reading for this class:
Aaron Clauset's
Introduction to stochastic blockmodels;
Frank McSherry,
Spectral partitioning of random graphs;
Sussman, Tang, Fishkind, and Priebe,
A consistent adjacency spectral embedding for stochastic blockmodel graphs;
Seshadhri, Kolda, and Pinar,
Community structure and scale-free collections of Erdős-Rényi graphs.
Mon 2 Jun: (JRG travel, no class)
Wed 4 Jun: (JRG travel, no class)
Wed 11 Jun: (Final project reports due)
