Scalable symmetric Tucker tensor decomposition

Ruhui Jin

Abstract:

In this talk, we will study the best low-rank Tucker decomposition of symmetric tensors. The main motivation is in decomposing higher-order multivariate moments, which has crucial applications in data science.

We will show the scalable adaptations of the projected gradient descent (PGD) and the higher-order eigenvalue decomposition (HOEVD) methods to decompose sample moment tensors. With the help of implicit and streaming techniques, we can evade the overhead cost of building and storing the moment tensor. Such reductions make computing the Tucker decomposition realizable for large data instances in high dimensions.

We will also demonstrate the efficiency of the algorithms and the applicability to real-world datasets. For convergence guarantee, the update sequence derived by the PGD solver achieves first and second-order criticality.

Submission Type: Abstract