An Incremental Tensor Train Decomposition Algorithm

Aksoy, Doruk; Gorsich, David J.; Veerapaneni, Shravan; Gorodetsky, Alex A.

doi:10.1137/22m1537734

An Incremental Tensor Train Decomposition Algorithm

Journal Article · Tue Mar 26 00:00:00 EDT 2024 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/22m1537734· OSTI ID:2283547

^[1]; Gorsich, David J. ^[2]; Veerapaneni, Shravan ^[3]; Gorodetsky, Alex A. ^[3]

University of Michigan, Ann Arbor, MI (United States); University of Michigan
U.S. Army, Warren, MI (United States)
University of Michigan, Ann Arbor, MI (United States)

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.

View Accepted Manuscript (DOE)

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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