NSF Workshop
Future Directions in Tensor-Based Computation and Modeling

Date: February 20-21, 2009
Location: National Science Foundation, Room 110, 4201 Wilson Blvd., Arlington, VA 22230
Organizer: Charles Van Loan (Cornell University)
NSF Program Managers: Lenore Mullin, Frank Olken (Award Number 0908059 )

High-dimensional matrix objects (tensors) are becoming ubiquitous throughout science and engineering.
It follows that a national effort to promote computational thinking must emphasize the transition
from matrix-based computational thinking to tensor-based computational thinking. The infrastructure
provided by the numerical linear algebra community needs to be broadened and generalized requiring
the participation of researchers from many fields.

This invitation-only workshop brings together tensor-oriented individuals who are interested in physical
science, biological science, information science, large-scale matrix computations, multilinear algebra,
high-performance computing, numerical analysis, programming languages, and statistics. The goal of the
workshop is to advise the NSF on how it can best support tensor-based computational thinking across
the sciences and engineering.

Logistics for Attendees.
Printer Friendly: Program, Abstracts, Attendees, Report
Friday, February 20  

8:15-9:00  Breakfast 
Room 120  
9:00-9:30 Opening
Room 110  
  Lenore Mullin  and Frank Olken  (slides)
  Workshop Goals
  Charles Van Loan  (slides)
  Three Right Directions and Three Wrong Directions for Tensor Research
  Michael W. Mahoney  (slides)
9:30-12:30 Tensor Methods and Modeling: Why the Proliferation?
Room 110  
  Modeling and Learning with Tensors
  Lek-Heng Lim  (abstract / slides )
  Mining Graphs and Tensors
  Christos Faloutsos  (abstract / slides )
  Mathematical Modeling of DNA Microarray Data: Discovery of Biological Mechanisms with Tensor Decompositions, and Definitions of Novel Tensor Decompositions from Biological Applications
  Orly Alter (abstract / slides )
10:45-11:15 Coffee Break
Room 120  
  Tensor Clustering and Error Bounds
  Chris Ding (abstract / slides )
  Unusual Tensor Decompositions for Informatics Applications
  Brett Bader  (abstract / slides )
  (Some) Challenges in Tensor Mining
  Evrim Acar (abstract / slides )
12:30-1:30 Lunch
Room 120  
1:30-3:30 Software and Language: How Do We Build an Infrastructure that
Room 110 Supports High-Performance, Tensor-Based Computation?
  Domain-Specific Abstractions for High-Productivity, High-Performance Scientific Computing
  J. (Ram) Ramanujam   and P. (Saday) Sadayappan  (abstract / slides )
  Communication Avoiding and Tiled Algorithm for "2D" Linear Algebra.
  Julien Langou (abstract / slides )
  Software Challenges in Computational Science
  Anthony Kennedy (abstract / slides )
  Tensors and n-d Arrays: A Mathematics of Arrays (MoA), Psi Calculus, and the Composition of Tensor and Array Operations
  Lenore Mullin and James Raynolds (abstract/slides)
  Tensor Computation on High Performance Machines
  Manal Helal  and Lenore Mullin  (abstract / slides )
3:30-4:00 Coffee Break
Room 120  
4:00-5:30 The Curse of Dimensionality: A Grand Challenge?
Room 110  
  Computing with Sums of Separable Functions, with Applications in Quantum Mechanics
  Martin Mohlenkamp  (abstract / slides )
  Nonlinear Approximations, Multi-linear tools, and Algorithms with Finite but Arbitrary Accuracy.
  Gregory Beylkin (abstract / slides )
  Multi-Length Scale Matrix Computations and Applications in Quantum Mechanical Simulations.
  Zhaojun Bai  (abstract / slides )
  From Math to Peta-app: Challenges in Practical Computation with
  Tensor-Based Algorithms
  Robert J. Harrison  (abstract / slides)

Saturday, February 21 

8:15-9:00  Breakfast
Room 120  
9:00-10:45 Multilinear Optimization: More Nonlinear than Linear?
Room 110  
  Optimization Approaches for Solving Tensor Decompositions Models and Tensor Eigenvalue Problems
  Tamara G. Kolda (abstract / slides )
  Newton-Type Methods for Non-negative Tensor Approximation
  Inderjit Dhillon (abstract / slides )
  Toward Faster Nonnegative Tensor Factorization: A New Activeset type Algorithm and Comparisons
  Haesun Park (abstract / slides )
  Some Applications of Nonnegative Tensor Factorizations to Mining Hyperspectral and Global Climate Data
  Robert Plemmons  (abstract / slides )
10:45-11:15  Coffee Break
Room 120  
11:15-12:30 Tensor-Based Signal Processing and Statistics: Where To and
Room 110 Why?
  Cumulant Signal Processing, Tensors, and Some Recurring Problems
  Phillip Regalia  (abstract / slides )
  An Introduction to Tensor-Based Independent Component Analysis
  Lieven De Lathauwer (abstract / slides )
  Algebraic Models for Multilinear Dependence
  Jason Morton (abstract / slides )
12:30-1:30  Lunch
Room 120  
1:30-2:45 Tensor Problems: What Makes Them Hard?
Room 110  
  Developing Tensor Operations with an Underlying Group Structure
  Carla Martin (abstract / slides )
  Results and Problems for 3-tensors
  Shmuel Friedland (abstract / slides )
  Tensor Decompositions from a Theoretical Computer Science Perspective
  Petros Drineas (abstract / slides )
2:45-3:15  Coffee Break
Room 120  
3:15-4:15 Numerical Linear Algebra: What Is Its Message?
Room 375  
  Krylov Methods for Tensors I
  Lars Elden and   (abstract / slides )
  Krylov Methods for Tensors II
  Berkant Savas  (abstract / slides )
  Numerical Linear Algebra Issues Underlying a Tensor Network Computation
  Charles Van Loan (abstract / slides )
4:15-4:30  Break
Room 375  
4:30-5:30 Closing Discussion
Room 375