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
Original Announcement
This workshop will consider mathematical problems of tensor decomposition.
Though higherorder tensor (also known as multidimensional, multiway,
or nway 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 higherorder 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
 Mathematical Properties of Tensor Decompositions.
 Computing with Tensor Decompositions.
 Applications of Tensor Decompositions.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
Reading List and Bibliography:
A reading list and bibliography, compiled by
the organizers from participant contributions:
dvi,
postscript or
pdf.
Talks:

Carla Martin  Basics of Tensors
(PDF, 258 kb)

Pieter Kroonenberg  Applications of
threemode techniques: Overview, problems, and prospects (PDF, 427 kb)

Tammy Kolda and Brett Bader
 Tensor Notation and a MATLAB Tensor Class for Fast Algorithm Prototyping
(PDF, 1.9 MB)

Piere Comon (impromptu) (PDF, 62 kb)

Rasmus Bro  Practical Problems in Multiway Analysis (PDF, 31 MB)

Vince Fernando  3D SVD (PDF, 117 kb)

Lieven De Lathauwer  Independent Component Analysis
(PDF, 111 kb)

Alex Vasilescu  TensorFaces

Eugene Tyrtyshnikov  Tensor Approximation and
Its Use in the Computation of the Matrix Inverse (PDF, 799 kb)

Cleve Moler (impromptu)  PCA and Human Gait

Michael Mahoney (impromptu)  Extracting Structure from Matrices and Tensors
by Random Sampling (PDF, 1.3 MB; PPT, 1.2MB)

Ed D'Azevdeo (impromptu)  Questions on
Fast Solvers for Kronecker Decompositions (PDF, 82 kb)

Marko Huhtanen (impromptu)  Real Linear SVD Framework [external
link to related paper]

LekHeng Lim (impromptu)  What's Possible
and What's Impossible in Tensor Decompositions/Approximation (PDF, 103
kb)

Berkant Savas  Handwritten Digit Recognition by HOSVD

Orly Alter  Genomic Signal Processing (PDF, 29MB)

Richard Harshman  Nature of Degenerate Solutions
(PDF, 654 kb) plus
annotated bibliography (PDF, 113kb)
Links to Related Papers

B. W. Bader and T. G. Kolda,
MATLAB Tensor
Classes for Fast Algorithm Prototyping, Technical Report SAND20045187,
Sandia National Laboratories, Livermore, California, October 2004. [pdf,
code in
TGZ or
ZIP format]

P. Comon,
Canonical Tensor Decompositions,'
I3S Report, RR200417, June 17, 2004.
 P. Comon and B. Mourrain,
Decomposition of quantics in sums
of powers of linear forms,
Signal Processing, Elsevier, 53(2):93107, September 1996
 P. Comon,
Tensor Decompositions,
in J. G. McWhirter and I. K. Proudler, editors, Mathematics in Signal
Processing V, pp. 124. Clarendon Press, Oxford, UK, 2002.
 L. De Lathauwer, B. De Moor, J. Vandewalle, A multilinear singular value decomposition, SIAM J. Matrix Anal. Appl., vol. 21, no. 4, Apr. 2000, pp. 12531278.
 L. De Lathauwer, B. De Moor, J. Vandewalle, Independent component analysis and (simultaneous) thirdorder tensor diagonalization, IEEE Transactions on Signal Processing, vol. 49, no. 10, Oct. 2001, pp. 22622271.
 L. De Lathauwer, B. De Moor, J. Vandewalle, Computation of the Canonical Decomposition by Means of a Simultaneous Generalized Schur Decomposition, SIAM Journal on Matrix Analysis and Applications, vol. 26, no. 2, 2004, pp. 295327.
 L. De Lathauwer, J. Vandewalle, Dimensionality reduction in higherorder signal processing and rank(R_1, R_2,...,R_N) reduction in multilinear algebra, Linear Algebra and its Applications, Special Issue on Linear Algebra in Signal and Image Processing, vol. 391, Nov. 2004, pp. 3155.

W. S. Hodge and C.F. Westin,
Identification of translational displacements between Ndimensional data
sets using the high order SVD and phase correlation, to appear in IEEE
Trans. on Image Processing.

Misha Elena Kilmer and
Carla D. Moravitz Martin,
Decomposing a
Tensor, SIAM News, 37(9): November 2004.

V. Pereyra and G. Scherer,
Efficient Computer Manipulation of Tensor Products with Applications to
Multidimensional Approximation, Mathematics of Computation,
27(123):595605, July 1973 (PDF, 735 kb)

N.D. Sidiropoulos, LowRank Decomposition of MultiWay
Arrays: A Signal Processing Perspective, companion paper for
plenary lecture in Proceedings of
2004 IEEE Workshop on Sensor Array and Multichannel processing (SAM2004),
July 1821, Sitges, Barcelona, Spain. ("Copyright (c) 2004 Institute of
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Hongcheng Wang, Narendra Ahuja,
Facial
Expression Decomposition, International Conference on Computer Vision (ICCV),
2003

Hongcheng Wang, Narendra Ahuja ,
Compact Representation of Multidimensional Data Using Tensor RankOne
Decomposition, International Conference on Pattern Recognition (ICPR),
2004

To add a paper here, please send email to
tgkolda@sandia.gov
Papers arising from the workshop: