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, L1-based 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, L1-compressive 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 so-called 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
Talks will be presented virtually or in-person as indicated in the schedule below.
- 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
-
Xue-Cheng 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 k-nearest 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 | Non-local Beltrami and Beltrami on graph - Dominique Zosso, UCLA | 11th Floor Lecture Hall | |
1:30 - 2:30pm EST | Graph cut, convex relaxation and continuous max-flow problems - Tai Xue-Cheng, University of Bergen | 10th Floor Classroom |