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$^*$). 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.

翻译：我们提出了一种新的算法,用于逐步更新一个气压数据流的电压列分解。这个称为“气压列递增核心扩展”的新算法(TT-ICE)通过开发一种新的适应性方法改进了目前以气压列压缩的最先进算法,这种方法使排位增长大大放缓,保证压缩准确性。这种能力是通过限制在每次数据递增后现有积聚的电压阵列中附在TT-核心中的新矢量数量来实现的。这些矢量代表现有核心范围的方向或方向,并限于代表新到达的电压的精确度。我们提供了两种不同的算法:TT-ICE和TT-ICICE, 加速使用超速(TT-ICE$ $ $ $ 美元 ) 。我们证明了TT-ICE的正确性,并用经验来证明在压缩大型视频和科学模拟数据集的压缩时算法的性能。这些矢量与同时使用级调整的现有方法相比,TT-ICE$=$=新到达目标精确度。我们提供了两种算法的版本:TT-ICE_57%的压缩和更高计算。