Organizing Committee
 Andrea Bertozzi
UCLA  Thomas Laurent
Loyola Marymount University
Abstract
This working group will develop new mathematics at the interface between graph structures and high dimensional data and geometric analysis. In the last ten years we have seen an explosion of work in both (a) compressive sensing (sparsity, L1based methods) and in (b) machine learning involve graphical structures for large scale and high dimensional data. The focus is on both analysis and algorithm development. In the case of new algorithms  codes will be tested against state of art machine learning algorithms. In the case of analytical results  we will draw on expertise in diverse areas of mathematics including differential geometry, nonlinear PDE, optimization, and spectral analysis of graphs. Application areas represented include machine learning, social network data, modularity optimization, L1compressive sensing methods, and image processing.
One area of focus is community detection in large networks. A current approach for community detection consists in minimizing the socalled modularity functional. Preliminary experiments using fast compress sensing algorithms shows very promising results for modularity optimization. A second area of focus is data retrieval, where L1 approaches could lead to significant advances. Thirdly, graph matching is another problem in which compressed sensing and total variation methods for graphs could have an impact.
Confirmed Speakers & Participants
 Speaker
 Poster Presenter
 Attendee
 Virtual Attendee

Milan Bradonjic
Bell Labs

Xavier Bresson
Universite de Lausanne

Mihai Cucuringu
University of California, Los Angeles

Arjuna Flenner
Naval Air Warfare Center

Cristina Garcia
Claremont Graduate University

Nicolas Garcia Trillos
Carnegie Mellon University

Steven Heilman
Courant Institute of Mathematical Sciences

Huiyi Hu
University of California, Los Angeles

Blake Hunter
Claremont McKenna College

Slav Kirov
Carnegie Mellon University

Gitta Kutyniok
TU Berlin

Thomas Laurent
Loyola Marymount University

Ekaterina Merkurjev
University of California, Los Angeles

Francois Meyer
University of Colorado

Braxton Osting
University of California, Los Angeles

Yuan (Alan) Qi
Purdue University

Michaela Rombach
University of California, Los Angeles

Dejan Slepcev
Carnegie Mellon University

Arthur Szlam
City College, CUNY

XueCheng Tai
University of Bergen

Yves van Gennip
University of Nottingham

James von Brecht
University of California, Los Angeles

Ulrike von Luxburg
Universität Hamburg

Christopher White
University of Texas at Austin

Joseph Woodworth
University of California, Los Angeles

Dominique Zosso
University of California, Los Angeles
Workshop Schedule
Tuesday, February 4, 2014
Time  Event  Location  Materials 

9:15  9:30am EST  Welcome  11th Floor Lecture Hall  
9:30  10:30am EST  The geometry of unweighted knearest neighbor graphs first results and many questions  Ulrike von Luxbourg, Universitat Hamburg  11th Floor Lecture Hall  
10:30  11:30am EST  From partial differential equations to graphs curvature and clusters  Yves van Gennip, University of Nottingham  11th Floor Lecture Hall  
11:30  1:00pm EST  Break for Lunch  
1:00  1:30pm EST  Distance geometry on graphs via synchronization  Mihai Cucuringu, UCLA  11th Floor Lecture Hall  
1:30  2:00pm EST  TBA  Michaela Puck Rombach, UCLA  11th Floor Lecture Hall  
2:00  2:15pm EST  Break  11th Floor Collaborative Space  
2:15  3:15pm EST  Applied Harmonic Analysis meets Compressed Sensing  Gitta Kutyniok, TU Berlin  11th Floor Lecture Hall  
4:45  5:45pm EST  Poster Session  11th Floor Collaborative Space 
Wednesday, February 5, 2014
Time  Event  Location  Materials 

10:00  11:00am EST  Scalable Gaussian process models on matrices and tensors  Yuan Qi, Purdue University  11th Floor Lecture Hall  
11:00  11:30am EST  Break  11th Floor Collaborative Space  
11:30  12:00pm EST  Spectral Methods for Analyzing Large Data  Blake Hunter, UCLA  11th Floor Lecture Hall  
12:00  12:30pm EST  Minimal Dirichlet energy partitions for graphs  Chris White, University of Texas at Austin  11th Floor Lecture Hall 
Thursday, February 6, 2014
Time  Event  Location  Materials 

10:00  11:00am EST  Proximal splitting algorithms for two class and multiclass total variation clustering  Thomas Laurent, Loyola Marymount University  11th Floor Lecture Hall  
11:00  12:00pm EST  Pooling fidelity and phase recovery  Arthur Szlam, City College, CUNY  11th Floor Lecture Hall 
Friday, February 7, 2014
Time  Event  Location  Materials 

9:00  10:00am EST  Random Graph Models for Image Patches  Francois Meyer, University of Colorado at Boulder  11th Floor Lecture Hall  
11:00  11:30am EST  Break  11th Floor Collaborative Space  
11:30  12:00pm EST  Nonlocal Beltrami and Beltrami on graph  Dominique Zosso, UCLA  11th Floor Lecture Hall  
1:30  2:30pm EST  Graph cut, convex relaxation and continuous maxflow problems  Tai XueCheng, University of Bergen  10th Floor Classroom 