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.
Attendees Logistics for Attendees. Printer Friendly: Program, Abstracts, Attendees, Report| 8:15-9:00 | Breakfast |
| Room 120 | |
| 9:00-9:30 | Opening |
| Room 110 | |
| Welcome | |
| 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 |