Organizing Committee
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

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Tuesday, February 4, 2014
TimeEventLocationMaterials
9:15 - 9:30am ESTWelcome11th Floor Lecture Hall 
9:30 - 10:30am ESTThe geometry of unweighted k-nearest neighbor graphs- first results and many questions - Ulrike von Luxbourg, Universitat Hamburg11th Floor Lecture Hall 
10:30 - 11:30am ESTFrom partial differential equations to graphs- curvature and clusters - Yves van Gennip, University of Nottingham11th Floor Lecture Hall 
11:30 - 1:00pm ESTBreak for Lunch  
1:00 - 1:30pm ESTDistance geometry on graphs via synchronization - Mihai Cucuringu, UCLA11th Floor Lecture Hall 
1:30 - 2:00pm ESTTBA - Michaela Puck Rombach, UCLA11th Floor Lecture Hall 
2:00 - 2:15pm ESTBreak11th Floor Collaborative Space 
2:15 - 3:15pm ESTApplied Harmonic Analysis meets Compressed Sensing - Gitta Kutyniok, TU Berlin11th Floor Lecture Hall 
4:45 - 5:45pm ESTPoster Session11th Floor Collaborative Space 
Wednesday, February 5, 2014
TimeEventLocationMaterials
10:00 - 11:00am ESTScalable Gaussian process models on matrices and tensors - Yuan Qi, Purdue University11th Floor Lecture Hall 
11:00 - 11:30am ESTBreak11th Floor Collaborative Space 
11:30 - 12:00pm ESTSpectral Methods for Analyzing Large Data - Blake Hunter, UCLA11th Floor Lecture Hall 
12:00 - 12:30pm ESTMinimal Dirichlet energy partitions for graphs - Chris White, University of Texas at Austin11th Floor Lecture Hall 
Thursday, February 6, 2014
TimeEventLocationMaterials
10:00 - 11:00am ESTProximal splitting algorithms for two class and multiclass total variation clustering - Thomas Laurent, Loyola Marymount University11th Floor Lecture Hall 
11:00 - 12:00pm ESTPooling fidelity and phase recovery - Arthur Szlam, City College, CUNY11th Floor Lecture Hall 
Friday, February 7, 2014
TimeEventLocationMaterials
9:00 - 10:00am ESTRandom Graph Models for Image Patches - Francois Meyer, University of Colorado at Boulder11th Floor Lecture Hall 
11:00 - 11:30am ESTBreak11th Floor Collaborative Space 
11:30 - 12:00pm ESTNon-local Beltrami and Beltrami on graph - Dominique Zosso, UCLA11th Floor Lecture Hall 
1:30 - 2:30pm ESTGraph cut, convex relaxation and continuous max-flow problems - Tai Xue-Cheng, University of Bergen10th Floor Classroom 

Associated Semester Workshops

Network Science and Graph Algorithms
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Semidefinite Programming and Graph Algorithms
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Stochastic Graph Models
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Research Clusters