An Incremental Tensor Train Decomposition Algorithm

Abstract

SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A1047-A1075, April 2024.
Abstract. We present a new algorithm for incrementally updating the tensor train decomposition of a stream of tensor data. This new algorithm, called the tensor train incremental core expansion (TT-ICE), improves upon the current state-of-the-art algorithms for compressing in tensor train format by developing a new adaptive approach that incurs significantly slower rank growth and guarantees compression accuracy. This capability is achieved by limiting the number of new vectors appended to the TT-cores of an existing accumulation tensor after each data increment. These vectors represent directions orthogonal to the span of existing cores and are limited to those needed to represent a newly arrived tensor to a target accuracy. We provide two versions of the algorithm: TT-ICE and TT-ICE accelerated with heuristics (TT-ICE[math]). We provide a proof of correctness for TT-ICE and empirically demonstrate the performance of the algorithms in compressing large-scale video and scientific simulation datasets. Compared to existing approaches that also use rank adaptation, TT-ICE[math] achieves [math] higher compression and up to [math] reduction in computational time. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available in https://github.com/dorukaks/TT-ICE as well as in the accompanying supplementary material.