Title: An Incremental Tensor Train Decomposition Algorithm

Journal Article · · SIAM Journal on Scientific Computing
DOI: https://doi.org/10.1137/22m1537734 · OSTI ID:2283547
ORCiD logo [1];  [2];  [3];  [3]
  1. University of Michigan, Ann Arbor, MI (United States); University of Michigan
  2. U.S. Army, Warren, MI (United States)
  3. University of Michigan, Ann Arbor, MI (United States)
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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*). Here, 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* achieves 57× higher compression and up to 95% reduction in computational time.

Research Organization:
University of Michigan, Ann Arbor, MI (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
SC0020364
OSTI ID:
2283547
Journal Information:
SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 2 Vol. 46; ISSN 1064-8275
Publisher:
Society for Industrial and Applied Mathematics (SIAM)Copyright Statement
Country of Publication:
United States
Language:
English

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97 MATHEMATICS AND COMPUTING
Tensor decompositions
data compression
low-rank factorizations
streaming data