Hot Topics Workshop: Multi-Manifold Data Modeling and Applications, October 27-30, 2008

October 27-30, 2008

Sponsors

With generous support from IBM Research and the Office of Naval Research.

Organizers:
Ronald A. DeVore	Mathematics, Texas A&M University
Tamara G. Kolda	Informatics and Decision Sciences, Sandia National Laboratories
Gilad Lerman	Mathematics, University of Minnesota
Guillermo R. Sapiro	Electrical and Computer Engineering, University of Minnesota

Schedule	Participants	Program Application	Feedback
IMA Live Streaming and Webcasting		Photo Gallery	Maps
Abstracts and Talk Materials			Dining Guide

Description:

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.

Schedule

Monday | Tuesday | Wednesday | Thursday

Monday, October 27

Morning Session Chair: Irina Rish (IBM)
Afternoon Session Chair: Richard Souvenir (University of North Carolina - Charlotte)

8:00am-8:45am

Registration and coffee

EE/CS 3-176

8:45am-9:00am

Welcome to the IMA

Fadil Santosa (University of Minnesota)

EE/CS 3-180

9:00am-9:50am

The best low-rank Tucker approximation of a tensor

Lars Eldén (Linköping University)

EE/CS 3-180

9:55am-10:45am

Detecting mixed dimensionality and density in noisy point clouds

Gloria Haro Ortega (Universitat Politecnica de Catalunya)

EE/CS 3-180

10:45am-11:15am

Coffee

EE/CS 3-176

11:15am-12:05pm

A Geometric perspective on machine Learning

Partha Niyogi (University of Chicago)

EE/CS 3-180

12:05pm-2:00pm

Lunch

2:00pm-2:50pm

Manifold models for signal acquisition, compression, and processing

Richard G. Baraniuk (Rice University)

EE/CS 3-180

2:55pm-3:45pm

Harmonic and multiscale analysis on low-dimensional data sets in high-dimensions

Mauro Maggioni (Duke University)

EE/CS 3-180

3:45pm-4:00pm

Group Photo

4:00pm-4:30pm

Coffee

EE/CS 3-176

4:30pm-5:30pm

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

5:30pm-7:00pm

Poster Session and Reception: 5:30-7:00
Poster submissions welcome from all participants
Lind Hall 400

Compressive sampling reconstruction by subspace refinement (poster)	Bradley K. Alpert (National Institute of Standards and Technology)
Analysis of scalar fields over point cloud data (poster)	Frédéric Chazal (INRIA Saclay - Île-de-France )
Joint manifold models for collaborative inference (poster)	Mark Andrew Davenport (Rice University)
The smashed filter for compressive classification(poster)	Marco F. Duarte (Rice University)
3-D motion segmentation via robust subspace separation (poster)	Ehsan Elhamifar (Johns Hopkins University)
teratively re-weighted least squares and vector valued data restoration from lower dimensional samples (poster)	Massimo Fornasier (Johann Radon Institute for Computational and Applied Mathematics )
Clustering on Riemannian manifolds (poster)	Alvina Goh (Johns Hopkins University) René Vidal (Johns Hopkins University)
Random projections for manifold learning (poster)	Chinmay Hegde (Rice University)
Representing and manipulating implicitly defined manifolds (poster)	Michael E. Henderson (IBM)
Fast multiscale clustering and manifold identification (poster)	Dan Kushnir (Yale University)
Supervised dictionary learning (poster)	Julien Mairal (INRIA )
A supervised dimensionality reduction framework for exponential-family variables (poster)	Irina Rish (IBM)
Tensor approximation - structure and methods (poster)	Berkant Savas (Linköping University)
Structure determination of proteins using cryo-electron microscopy (poster)	Yoel Shkolnisky (Yale University) Amit Singer (Princeton University)
High order consistency relations for classification and de-noising of Cryo-EM images (poster)	Yoel Shkolnisky (Yale University) Amit Singer (Princeton University)
k-planes for classification (poster)	Arthur Szlam (University of California, Los Angeles)
Manifold models for single- and multi-signal recovery (poster)	Michael Wakin (Colorado School of Mines)
Using persistent homology to recover spatial information from encounter traces (poster)	Brenton Walker (Laborartory For Telecommunications Sciences)
Mixed data segmentation via lossy data compression (poster)	John Wright (University of Illinois at Urbana-Champaign)
Orthant-wise gradient projection method for sparse reconstruction (poster)	Qiu Wu (University of Texas)
High-dimensional multi-model estimation – its Algebra, statistics, and sparse representation (poster)	Allen Yang Yang (University of California, Berkeley)
Approximate nearest subspace search with applications to pattern recognition (poster)	Lihi Zelnik-Manor (Technion-Israel Institute of Technology)

Tuesday, October 28

Morning Session Chair: Lihi Zelnik-Manor (Technion-Israel Institute of Technology)
Afternoon Session Chair: Michael E. Henderson (IBM)

8:30am-9:00am

Coffee

EE/CS 3-176

9:00am-9:50am

Multilinear (tensor) manifold data modeling

M. Alex O. Vasilescu (SUNY)

EE/CS 3-180

9:55am-10:45am

Recovering sparsity in high dimensions

Ronald DeVore (Texas A & M University)

EE/CS 3-180

10:45am-11:15am

Coffee

EE/CS 3-176

11:15am-12:05pm

Clustering linear and nonlinear manifolds

René Vidal (Johns Hopkins University)

EE/CS 3-180

12:05pm-2:00pm

Lunch

2:00pm-2:50pm

Instance optimal adaptive regression in high dimensions

Wolfgang Dahmen (RWTH Aachen)

EE/CS 3-180

2:55pm-3:45pm

Spectral and geometric methods in learning

Mikhail Belkin (Ohio State University)

EE/CS 3-180

3:45pm-4:15pm

Coffee

EE/CS 3-176

4:15pm-5:15pm

Large group discussion on:

1. The representation of high-level information and low-level data

2. The symbiotic linkage between information and data

3. The need to transform qualitative information into quantitative data sets and vice versa

4. The need to think beyond the learning for classification.

5. How mathematics can be useful to the aforementioned domains of interest in conjunction with information integration and data fusion.

Tristan Nguyen (Office of Naval Research)

EE/CS 3-180

6:30pm-8:30pm

Workshop dinner

Kikugawa at Riverplace
43 Main Street SE Minneapolis MN 55414
612-378-3006

Wednesday, October 29

Morning Session Chair: Stacey E. Levine (Duquesne University)
Afternoon Session Chair: Ramesh Natarajan (IBM Research Division)

8:30am-9:00am

Coffee

EE/CS 3-176

9:00am-9:50am

Interpolation of functions on Rⁿ

Charles L. Fefferman (Princeton University)

EE/CS 3-180

9:55am-10:45am

Multi-manifold data modeling via spectral curvature clustering

Gilad Lerman (University of Minnesota)

EE/CS 3-180

10:45am-11:15am

Coffee

EE/CS 3-176

11:15am-12:05pm

Visualization & matching for graphs and data

Tony Jebara (Columbia University)

EE/CS 3-180

12:05pm-2:00pm

Lunch

2:00pm-2:50pm

Topology and data

Gunnar Carlsson (Stanford University)

EE/CS 3-180

2:55pm-3:45pm

Dense error correction via L1 minimization

Yi Ma (University of Illinois at Urbana-Champaign)

EE/CS 3-180

3:45pm-4:15pm

Coffee

EE/CS 3-176

4:15pm-5:15pm

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

2) What have been successful applications of manifold clustering?

3) What is the role of topology, geometry, and statistics, in manifold learning, i.e.,
a) clustering based on the dimensions of the manifolds
b) clustering based on geometry
c) clustering based on statistics

3) What are the open problems in manifold clustering?

René Vidal (Johns Hopkins University)

EE/CS 3-180

5:15pm-6:30pm

Math matters public lecture reception

Lind Hall 400

7:00pm-8:15pm

Math matters public lecture: Surfing with wavelets

Ingrid Daubechies (Princeton University)

Willey Hall 125

Thursday, October 30

Chair: Lek-Heng Lim (University of California, Berkeley)

8:30am-9:00am

Coffee

EE/CS 3-176

9:00am-9:50am

CPOPT: Optimization for fitting CANDECOMP/PARAFAC models

Tamara G. Kolda (Sandia National Laboratories)

EE/CS 3-180

9:55am-10:45am

Semi-supervised learning by multi-manifold separation

Xiaojin Zhu (University of Wisconsin)

EE/CS 3-180

10:45am-11:15am

Coffee

EE/CS 3-176

11:15am-12:05pm

Mathematical problems suggested by Analog-to-Digital conversion

Ingrid Daubechies (Princeton University)

EE/CS 3-180

12:05pm-12:10pm

Closing remark

EE/CS 3-180

12:10pm-2:00pm

Conference lunch at Loring Pasta Bar in Dinkytown

Loring Pasta Bar in Dinkytown

LIST OF CONFIRMED PARTICIPANTS

Name	Department	Affiliation
Iman Aganj	Department of Electrical and Computer Engineering	University of Minnesota
Bradley K. 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
Richard G. Baraniuk	Department of Electrical and Computer Engineering	Rice University
Mikhail Belkin	Department of Computer Science and Engineering	Ohio State University
Peter Binev	Department of Mathematics	University of South Carolina
Francisco Blanco-Silva	Department of Mathematics	University of South Carolina
Edward Howard Bosch	Basic and Applied Research	National Geospatial Intelligence Agency
Gunnar Carlsson	Department of Mathematics	Stanford University
Pete George Casazza	Department of Mathematics	University of Missouri
William Austin Casey		Pacific Northwest National Laboratory
Frédéric Chazal		INRIA Saclay - Île-de-France
Guangliang Chen	Department of Mathematics	University of Minnesota
Jie Chen	Department of Computer Science and Engineering	University of Minnesota
Xianjin Chen	Institute for Mathematics and its Applications	University of Minnesota
Wolfgang Dahmen	Institut fur Geometrie und Praktische Mathematik	RWTH Aachen
Steven Benjamin Damelin	Department of Mathematical Sciences	Georgia Southern University
Ingrid Daubechies	Department of Mathematics	Princeton University
Mark Andrew Davenport	Department of Electrical and Computer Engineering	Rice University
Ronald DeVore	Department of Mathematics	Texas A & M University
Julio Duarte		Eastman Kodak Company
Marco F. 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	Department of Electrical Engineering	University of Minnesota
Charles L. Fefferman	Department of Mathematics	Princeton University
Daniel Flath	Department of Mathematics and Computer Science	Macalester College
Massimo Fornasier	Applied and Computational Mathematics Department	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
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 E. Henderson	Thomas J. Watson Research Center	IBM
Mark Iwen	Institute for Mathematics and its Applications	University of Minnesota
Alexander Izzo	Department of Mathematics and Statistics	Bowling Green State University
Tony Jebara	Department of Computer Science	Columbia University
Ajay Joshi	Department of Computer Science	University of Minnesota
Tamara G. Kolda	Informatics and Decision Sciences	Sandia National Laboratories
Dan Kushnir	Department of Applied Mathematics	Yale University
Arie Landau		University of Southern California
Triet Minh 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
Stacey E. Levine	Department of Mathematics and Computer Science	Duquesne University
Tianjiang Li	Department of Mathematics	Pennsylvania State University
Yongfeng Li	Institute for Mathematics and its Applications	University of Minnesota
Hstau Y Liao	Department of Biochemistry and Molecular Biophysics	Columbia University
Lek-Heng Lim	Mathematics Department	University of California, Berkeley
Chun Liu	Institute for Mathematics and Its Applications	University of Minnesota
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	Département d'informatique	INRIA
Vasileios Maroulas	Institute for Mathematics and its Applications	University of Minnesota
Willard Miller	School of Mathematics	University of Minnesota
Washington Mio	Department of Mathematics	Florida State University
Vassilios Morellas	Department of Computer Science and Engineering	University of Minnesota
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
Amogh Rajanna	Department of Electrical Engineering	University of Minnesota
Ignacio Ramirez	Electrical Engineering and Computer Science	University of Minnesota
Shankar Rao	Electrical Engineering	University of Illinois at Urbana-Champaign
Irina Rish	Computational Biology Center	IBM
Murti Sacapaka	Department of Electrical Engineering	University of Minnesota
Fadil Santosa	Institute for Mathematics and its Applications	University of Minnesota
Guillermo R. Sapiro	Department of Electrical and Computer Engineering	University of Minnesota
Berkant Savas	Department of Mathematics	Linköping University
Yoel Shkolnisky	Department of Mathematics	Yale University
Amit Singer	Department of Mathematics	Princeton University
Ravishankar Sivalingam	Electrical Engineering	University of Minnesota
Richard Souvenir	Department of Computer Science	University of North Carolina - Charlotte
Panagiotis Stinis		University of Minnesota
Arthur Szlam	Department of Mathematics	University of California, Los Angeles
William Toczyski		University of Minnesota
Carl Toews	Department of Mathematics	Duquesne University
Birkan Tunc		Istanbul Technical University
M. Alex O. Vasilescu	Computer Science Department	SUNY
René Vidal	Department of Biomedical Engineering	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
Jonathan Tyler Whitehouse	Department of Mathematics	University of Minnesota
John Wright	Department of Electrical and Computer Engineering	University of Illinois at Urbana-Champaign
Qiu Wu	Department of Electrical and Computer Engineering	University of Texas
Allen Yang Yang		University of California, Berkeley
Chao Yang	Computational Research Division	Lawrence Berkeley National Laboratory
Fei Yang	Department of Biomedical Engineering	University of Minnesota
Ahmad S Yasamin		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
Xiaojin Zhu	Department of Computer Sciences	University of Wisconsin

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