Lars Eldén: Tensor computations and applications in information sciences

Analyses of data organized as matrices are ubiquitous and well supported by theory and algorithms.  In information sciences data are often organized in more than two categories, and it is often unnatural to reorganize the data as a matrix. Therefore there is a need for theory and algorithms for tensor computations. We discuss generalizations of the matrix singular value
decomposition (principal component analysis) to tensors, in particular the so called Tucker decomposition. The analysis and computation of this decomposition need be done in terms of differential-algebraic concepts, and thus we present a Newton method and perturbation theory on the Grassmann manifold.  We give examples from pattern recognition, simultaneous
clustering of graphs, and information retrieval.

If time permits, we will also discuss the generalization of matrix Krylov methods for computations with large and sparse tensors.

This is joint work with Berkant Savas.