An Incremental Tensor Train Decomposition Algorithm

TL;DR

This paper introduces TT-ICE, an incremental tensor train decomposition algorithm that adaptively updates tensor cores with slower rank growth, achieving high compression efficiency and accuracy for large-scale data streams.

Contribution

The paper proposes TT-ICE, a novel adaptive incremental tensor train algorithm with improved compression, slower rank growth, and proven correctness, outperforming existing methods.

Findings

TT-ICE achieves 57x higher compression than previous methods.

TT-ICE$^*$ reduces computational time by up to 95%.

The algorithm effectively compresses large-scale video and scientific data.

Abstract

We present a new algorithm for incrementally updating the tensor train decomposition of a stream of tensor data. This new algorithm, called the {\em 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$^*$). 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 $57\times$ higher compression and up to $95\%$ reduction in computational time.