Tensor Seminar --- Fall 2011

Day: Wednesday

Time: 4:00 - 5:00 PM

Location: 4201 SAS Hall

Organizer: Seth Sullivant

This semester we will have a reading/ learning seminar on the topic of tensors, with an algebraic and geometric perspective. This will run with the symbolic computation seminar, on weeks when there is no ordinary symbolic computation talk. The schedule of individual talks will be posted on the symbolic computation seminar website.

On this page, we maintain a list of (possible) readings that could be covered during the semester. If there are topics you would like to see added, please let me know.

Introductory Readings

  1. J.M. Landsberg, Tensors: Geometry and Applications (This has the first two chapters of the book, which is coming out this fall. Good place to get background and definitions if you are unfamiliar with tensors.)
  2. Pierre Comon, Gene Golub, Lek-Heng Lim, Bernard Mourrain, Symmetric tensors and symmetric tensor rank
  3. T. G. Kolda and B. W. Bader. Tensor Decompositions and Applications. SIAM Review 51(3):455-500, September 2009

Uniqueness of Tensor Decompositions

  1. John A. Rhodes. A concise proof of Kruskal's theorem on tensor decomposition.
  2. J. M. Landsberg. Kruskal's theorem.
  3. Luca Chiantini, Giorgio Ottaviani. On generic identifiability of 3-tensors of small rank.

Applications of Uniqueness of Tensor Decompositions to Statistical Models

  1. Elizabeth S. Allman, Catherine Matias, John A. Rhodes. Identifiability of parameters in latent structure models with many observed variables.
  2. John A. Rhodes, Seth Sullivant. Identifiability of large phylogenetic mixture models.

Computational Aspects of Symmetric Tensor Decomposition

  1. Jerome Brachat, Pierre Comon, Bernard Mourrain, Elias Tsigaridas Symmetric tensor decomposition
  2. Luke Oeding, Giorgio Ottaviani Eigenvectors of tensors and algorithms for Waring decomposition

Applications of Tensor Decomposition to Signal Processing

  1. Lek-Heng Lim, Pierre Comon. Multiarray Signal Processing: Tensor decomposition meets compressed sensing
  2. Silvia Gandy, Benjamin Rechts, and Isao Yamada Tensor completion and low-n-rank tensor recovery via convex optimization

Nuclear Norm Minimization and Application to Tensor Rank

  1. Benjamin Recht, Maryam Fazel, Pablo A. Parrilo Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
  2. Signoretto M., De Lathauwer L., Suykens J.A.K., Nuclear Norms for Tensors and Their Use for Convex Multilinear Estimation