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With generous support from
Texas A & M University | |
Sandia National Laboratories | |
University of Minnesota, Twin Cities | |
University of Minnesota, Twin Cities |
Many common data sets can be modeled by a mixture of simple geometric objects, e.g., manifolds. A well known example of such data is the NIST images of hand-written digits. The effective modeling of such data together with its careful analysis is a challenging mathematical problem. Earlier work at the beginning of the current century revealed effective methods for modeling data by a single manifold. Later work modeled data by an arrangement of affine subspaces. The generalization of these works to multi-manifold data modeling is currently being developed. It has many important applications, for example, in motion segmentation, hybrid representation of images, classification of face images and classification of hand-written digits.
Different approaches for this problem have utilized theoretical insights from various mathematical disciplines and also inspired new theoretical observations. Those mathematical disciplines include probabilistic modeling, algebraic geometry, information theory, computational topology and geometry, statistical inference, linear and multilinear algebra, numerical analysis, differential geometry, and spectral graph theory. This general problem is also closely related to other directions in current applied mathematics, in particular, sparse approximation.
Monday | Tuesday | Wednesday | Thursday | | |||
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Monday October 27, 2008 | |||
Morning Session Chair: Irina Rish (IBM) Afternoon Session Chair: Richard Souvenir (University of North Carolina - Charlotte) | |||
9:00am-9:45am | Registration and coffee | EE/CS 3-176 | |
9:45am-10:00am | Welcome to the IMA | Fadil Santosa (University of Minnesota, Twin Cities) | EE/CS 3-180 |
10:00am-10:50am | The best low-rank Tucker approximation of a tensor | Lars Eldén (Linköping University) | EE/CS 3-180 |
10:55am-11:45am | Detecting mixed dimensionality and density in noisy point clouds | Gloria Haro Ortega (Universitat Politecnica de Catalunya) | EE/CS 3-180 |
11:45am-12:15pm | Coffee | EE/CS 3-176 | |
12:15pm-1:05pm | A Geometric perspective on machine Learning | Partha Niyogi (University of Chicago) | EE/CS 3-180 |
1:05pm-3:00pm | Lunch | ||
3:00pm-3:50pm | Manifold models for signal acquisition, compression, and processing | Richard Baraniuk (Rice University) | EE/CS 3-180 |
3:55pm-4:45pm | Harmonic and multiscale analysis on low-dimensional data sets in high-dimensions | Mauro Maggioni (Duke University) | EE/CS 3-180 |
4:45pm-5:00pm | Group Photo | ||
5:00pm-5:30pm | Coffee | EE/CS 3-176 | |
5:30pm-6:30pm | Large group discussion on What have we learned about manifold learning — what are its implications for machine learning and numerical analysis? What are open questions? What are successes? Where should we be optimistic and where should we be pessimistic? | Partha Niyogi (University of Chicago) | EE/CS 3-180 |
6:30pm-8:00pm | Poster Session and Reception: 5:30-7:00 Poster submissions welcome from all participantsLind Hall 400 | ||
Tuesday October 28, 2008 | |||
Morning Session Chair: Lihi Zelnik-Manor (Technion-Israel Institute of Technology) Afternoon Session Chair: Michael E. Henderson (IBM) | |||
9:30am-10:00am | Coffee | EE/CS 3-176 | |
10:00am-10:50am | Multilinear (tensor) manifold data modeling | M. Alex O. Vasilescu (The State University of New York) | EE/CS 3-180 |
10:55am-11:45am | Recovering sparsity in high dimensions | Ronald DeVore (Texas A & M University) | EE/CS 3-180 |
11:45am-12:15pm | Coffee | EE/CS 3-176 | |
12:15pm-1:05pm | Clustering linear and nonlinear manifolds | René Vidal (Johns Hopkins University) | EE/CS 3-180 |
1:05pm-3:00pm | Lunch | ||
3:00pm-3:50pm | Instance optimal adaptive regression in high dimensions | Wolfgang Dahmen (RWTH Aachen) | EE/CS 3-180 |
3:55pm-4:45pm | Spectral and geometric methods in learning | Misha Belkin (The Ohio State University) | EE/CS 3-180 |
4:45pm-5:15pm | Coffee | EE/CS 3-176 | |
5:15pm-6:15pm | Large group discussion on:
| Tristan Nguyen (Office of Naval Research) | EE/CS 3-180 |
7:30pm-9:30pm | Workshop dinner | Kikugawa at Riverplace 43 Main Street SE Minneapolis MN 55414 612-378-3006 | |
Wednesday October 29, 2008 | |||
Morning Session Chair: Stacey E. Levine (Duquesne University) Afternoon Session Chair: Ramesh Natarajan (IBM Research Division) | |||
9:30am-10:00am | Coffee | EE/CS 3-176 | |
10:00am-10:50am | Interpolation of functions on R^{n} | Charles Fefferman (Princeton University) | EE/CS 3-180 |
10:55am-11:45am | Multi-manifold data modeling via spectral curvature clustering | Gilad Lerman (University of Minnesota, Twin Cities) | EE/CS 3-180 |
11:45am-12:15pm | Coffee | EE/CS 3-176 | |
12:15pm-1:05pm | Visualization & matching for graphs and data | Tony Jebara (Columbia University) | EE/CS 3-180 |
1:05pm-3:00pm | Lunch | ||
3:00pm-3:50pm | Topology and data | Gunnar Carlsson (Stanford University) | EE/CS 3-180 |
3:55pm-4:45pm | Dense error correction via L1 minimization | Yi Ma (University of Illinois at Urbana-Champaign) | EE/CS 3-180 |
4:45pm-5:15pm | Coffee | EE/CS 3-176 | |
5:15pm-6:15pm | Large group discussion on Manifold Clustering 1) What have have been recent advances on manifold clustering? a) Algebraic approaches b) Spectral approaches c) Probabilistic approaches
| René Vidal (Johns Hopkins University) | EE/CS 3-180 |
6:15pm-7:30pm | Math matters public lecture reception | Lind Hall 400 | |
8:00pm-9:15pm | Math matters public lecture: Surfing with wavelets | Ingrid Daubechies (Princeton University) | Willey 125 |
Thursday October 30, 2008 | |||
Chair: Lek-Heng Lim (University of California, Berkeley) | |||
9:30am-10:00am | Coffee | EE/CS 3-176 | |
10:00am-10:50am | CPOPT: Optimization for fitting CANDECOMP/PARAFAC models | Tamara Kolda (Sandia National Laboratories) | EE/CS 3-180 |
10:55am-11:45am | Semi-supervised learning by multi-manifold separation | Xiaojin (Jerry) Zhu (University of Wisconsin, Madison) | EE/CS 3-180 |
11:45am-12:15pm | Coffee | EE/CS 3-176 | |
12:15pm-1:05pm | Mathematical problems suggested by Analog-to-Digital conversion | Ingrid Daubechies (Princeton University) | EE/CS 3-180 |
1:05pm-1:10pm | Closing remark | EE/CS 3-180 | |
1:10pm-3:00pm | Conference lunch at Loring Pasta Bar in Dinkytown | Loring Pasta Bar in Dinkytown |
NAME | DEPARTMENT | AFFILIATION |
---|---|---|
Iman Aganj | Department of Electrical and Computer Engineering | University of Minnesota, Twin Cities |
Bradley Alpert | Mathematical and Computational Sciences Division | National Institute of Standards and Technology |
Ery Arias-Castro | Department of Mathematics | University of California, San Diego |
Leah Bar | Department of Electrical and Computer Engineering | University of Minnesota, Twin Cities |
Richard Baraniuk | Department of Electrical and Computer Engineering | Rice University |
Misha Belkin | Department of Computer Science and Engineering | The Ohio State University |
Peter Binev | Department of Mathematics | University of South Carolina |
Francisco Blanco-Silva | Department of Mathematics | University of South Carolina |
Edward Bosch | Basic and Applied Research | National Geospatial Intelligence Agency |
Gunnar Carlsson | Department of Mathematics | Stanford University |
Pete Casazza | Department of Mathematics | University of Missouri |
William Casey | Battelle Pacific Northwest National Laboratory | |
Frédéric Chazal | Geometrica | INRIA Saclay - Île-de-France |
Guangliang Chen | Department of Mathematics | University of Minnesota, Twin Cities |
Jie Chen | University of Minnesota, Twin Cities | |
Xianjin Chen | Institute for Mathematics and its Applications | University of Minnesota, Twin Cities |
Wolfgang Dahmen | Institut fur Geometrie und Praktische Mathematik | RWTH Aachen |
Steven Damelin | Department of Mathematical Sciences | Georgia Southern University |
Ingrid Daubechies | Department of Mathematics | Princeton University |
Mark Davenport | Department of Electrical and Computer Engineering | Rice University |
Ronald DeVore | Department of Mathematics | Texas A & M University |
Julio Duarte | Eastman Kodak Company | |
Marco Duarte | Department of Electrical and Computer Engineering | Rice University |
Lars Eldén | Department of Mathematics | Linköping University |
Ehsan Elhamifar | Department of Electrical and Computer Engineering | Johns Hopkins University |
Ahmel El-Mawas | University of Minnesota, Twin Cities | |
Charles Fefferman | Department of Mathematics | Princeton University |
Daniel Flath | Department of Mathematics, Statistics and Computer Science | Macalester College |
Massimo Fornasier | Department of Applied and Computational Mathematics | Johann Radon Institute for Computational and Applied Mathematics |
Stephen Fulling | Department of Mathematics | Texas A & M University |
Weiguo Gao | School of Mathematical Sciences | Fudan University |
Alvina Goh | Department of Biomedical Engineering | Johns Hopkins University |
Vikrham Gowreesunker | Department of Electrical and Computer Engineering | University of Minnesota, Twin Cities |
John Greer | National Geospatial Intelligence Agency | |
Gloria Haro Ortega | Teoria Senyal i Comunicacions | Universitat Politecnica de Catalunya |
Chinmay Hegde | Department of Electrical and Computer Engineering | Rice University |
Michael Henderson | Thomas J. Watson Research Center | IBM |
Mark Iwen | Institute for Mathematics and its Applications | University of Minnesota, Twin Cities |
Alexander Izzo | Department of Mathematics & Statistics | Bowling Green State University |
Tony Jebara | Department of Computer Science | Columbia University |
Ajay Joshi | University of Minnesota, Twin Cities | |
Markus Keel | School of Mathematics | University of Minnesota, Twin Cities |
Tamara Kolda | Informatics and Systems Assessments | Sandia National Laboratories |
Dan Kushnir | Department of Computer Science and Applied Mathematics | Yale University |
Arie Landau | University of Southern California | |
Triet Le | Department of Mathematics | Yale University |
Federico Lecumberry | Instituto de Ingenieria Electrica | University of the Republic |
Chiun-Chang Lee | Department of Mathematics | National Taiwan University |
Hijin Lee | Mathematics Department | Korea Advanced Institute of Science and Technology (KAIST) |
Gilad Lerman | School of Mathematics | University of Minnesota, Twin Cities |
Stacey Levine | Department of Mathematics and Computer Science | Duquesne University |
Tianjiang Li | Department of Mathematics | The Pennsylvania State University |
Yongfeng Li | Institute for Mathematics and its Applications | University of Minnesota, Twin Cities |
Hstau Liao | Department of Biochemistry and Molecular Biophysics | Columbia University |
Lek-Heng Lim | Mathematics Department | University of California, Berkeley |
Chun Liu | Department of Mathematics | University of Minnesota, Twin Cities |
Yi Ma | Department of Electrical and Computer Engineering | University of Illinois at Urbana-Champaign |
Mauro Maggioni | Department of Mathematics and Computer Science | Duke University |
Julien Mairal | LEAR Team | INRIA |
Vasileios Maroulas | Institute for Mathematics and its Applications | University of Minnesota, Twin Cities |
Willard Miller | School of Mathematics | University of Minnesota, Twin Cities |
Washington Mio | Department of Mathematics | Florida State University |
Vassilios Morellas | University of Minnesota, Twin Cities | |
Dmitriy Morozov | Department of Computer Science | Duke University |
Ramesh Natarajan | Mathematics Department | IBM Research Division |
Tristan Nguyen | Office of Naval Research | |
Yasunori Nishimori | Neuroscience Research Institute | National Institute of Advanced Industrial Science and Technology |
Partha Niyogi | Department of Computer Science | University of Chicago |
Igor Pak | University of Minnesota, Twin Cities | |
Amogh Rajanna | University of Minnesota | |
Ignacio Ramirez | University of Minnesota, Twin Cities | |
Shankar Rao | University of Illinois at Urbana-Champaign | |
Irina Rish | T. J. Watson Research Center | IBM |
Murti Sacapaka | University of Minnesota, Twin Cities | |
Fadil Santosa | School of Mathematics | University of Minnesota, Twin Cities |
Guillermo Sapiro | Department of Electrical and Computer Engineering | University of Minnesota, Twin Cities |
Berkant Savas | Department of Mathematics | Linköping University |
Yoel Shkolnisky | Department of Mathematics | Yale University |
Amit Singer | Department of Mathematics | Princeton University |
Ravishankar Sivalingam | University of Minnesota, Twin Cities | |
Richard Souvenir | Department of Computer Science | University of North Carolina - Charlotte |
Panagiotis Stinis | University of Minnesota, Twin Cities | |
Arthur Szlam | Department of Mathematics | University of California, Los Angeles |
William Toczyski | University of Minnesota, Twin Cities | |
Carl Toews | Department of Mathematics | Duquesne University |
Birkan Tunc | Istanbul Technical University | |
M. Alex O. Vasilescu | Department of Computer Science | The State University of New York |
René Vidal | Vision, Dynamics, and Learning Lab | Johns Hopkins University |
Michael Wakin | Division of Engineering | Colorado School of Mines |
Brenton Walker | Laborartory For Telecommunications Sciences | |
Yi Wang | Department of Mathematics | University of Minnesota, Twin Cities |
Tyler Whitehouse | Department of Mathematics | University of Minnesota, Twin Cities |
John Wright | Department of Electrical and Computer Engineering | University of Illinois at Urbana-Champaign |
Qiu Wu | Department of Electrical and Computer Engineering | The University of Texas at Austin |
Allen Yang | Rm 307, Cory Hall | University of California, Berkeley |
Chao Yang | Computational Research Division | Lawrence Berkeley National Laboratory |
Fei Yang | Department of Biomedical Engineering | University of Minnesota, Twin Cities |
Ahmad Yasamin | Department of Mathematics | Statistical and Applied Mathematical Sciences Institute (SAMSI) |
Lihi Zelnik-Manor | Department of Electrical Engineering | Technion-Israel Institute of Technology |
Teng Zhang | School of Mathematics | University of Minnesota, Twin Cities |
Xiaojin (Jerry) Zhu | Department of Computer Science | University of Wisconsin, Madison |
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