Tensor decompositions

July 19 to July 23, 2004

at the

American Institute of Mathematics, Palo Alto, California

organized by

Gene H. Golub, Tamara G. Kolda, James G. Nagy, and Charles F. Van Loan

This workshop, sponsored by AIM and the NSF, will consider mathematical problems of tensor decomposition. Though higher-order tensor (also known as multidimensional, multi-way, or n-way array) decompositions have been around for more than three decades, the door is now opening on greater mathematical understanding and new applications. Previously, this topic has been the domain of researchers in psychometrics and chemometrics. Now, however, computationally oriented mathematicians have begun to take an interest and envision many more potential applications ranging from image and signal processing to data mining and more. The challenge is to find ways to extend these methods to larger data sets, i.e., data sets with thousands to millions of entries. This will require advances in the theory and computation of higher-order tensor decompositions.

The workshop will bring together researchers on this topic with specialists in scientific computing, linear algebra, and applications. The goal of the workshop is to develop the theoretical and computational tools necessary to tackle larger problems and new applications. Some of the specific issues to be addressed are

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and working sessions.

Participants include O. Alter, B. Bader, R. Bro, P. Comon, E. D'Azevedo, L. De Lathauwer, L. De Pillis, P. Drineas, L. Elden, V. Fernando, G. Golub, R. Harshman, J. Haws, B. Hendrickson, V. Howle, M. Huhtanen, M. Kilmer, T. Kolda, P. Kroonenberg, T. Laudadio, S. Le Borne, L. Lim, M. Mahoney, C. Martin, N. Mastronardi, C. Moler, J. Nagy, V. Pereyra, L. Perrone, L. Reichel, J. Ryan, M. Saunders, B. Savas, D. Terzopoulos, E. Tyrtyshnikov, C. Van Loan, and M. Vasilescu.

The deadline to apply for support to participate in this workshop has passed.

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