NETWORKS and MATRIX COMPUTATIONS CS 59000-NMC David F. Gleich T-Th 10:30-11:45 CIVL 2123 Course Teaser 17 August 2011.

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Presentation transcript:

NETWORKS and MATRIX COMPUTATIONS CS NMC David F. Gleich T-Th 10:30-11:45 CIVL 2123 Course Teaser 17 August 2011

Images copyright by their respective owners.

We like books …

Gene H. Golub Charles van Loan Networks cover copyright by Oxford Press

NETWORKS and MATRIX COMPUTATIONS Why looking at networks of data as a matrix is a powerful and successful paradigm.

Web graph

Citation network

TOPICS

BASICS How to state network problems as matrix problems. Matrices over a semi-ring and how this yields instant parallel algorithms! Relationships with MapReduce computations.

TROPICAL semi-rings

MARKOV CHAIN theory Random walks on networks Perron Frobenius theory State space classification How to “solve” a large linear system with a random walk. How to “solve” Markov chain problems on compressed graphs

PAGERANK Deep dive into one particular application. Is it a Markov chain or a linear system? How to compute it, FAST. How to manipulate PageRank.

Just PageRank?

SimRank BlockRank TrustRank ObjectRank HostRank Random walk with restart GeneRank DiffusionRank IsoRank ItemRank ProteinRank SocialPageRank FoodRank FutureRank TwitterRank

The Fiedler vector, the Laplacian matrix and graph cuts Semi-definite approximation problems and properties Local partitioning How to split a graph without even seeing it all! SPECTRAL GRAPH theory

QUITE A BIT MORE Higher order graph analysis with tensors. Network alignment Affine eigenvectors and centrality SVD graph analysis. Matrix based graph models.

THE WORK

A project. A proposal A paper A presentation BIG ITEM one

A lecture. Take a paper and present it to the class using the matrix paradigm. OR Present a paper that uses the matrix paradigm. BIG ITEM two

Survey Homework (2-4?) Quizzes Writing OTHER WORK

Quizzes? Taken/Missed These are for me, not you.

QUESTIONS?