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AN INCREMENTAL TENSOR TRAIN DECOMPOSITION ALGORITHM
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DOI：10.1137/22M1537734.png)
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Abstract
En 中文
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\ast). \ast ). We provide a proof of correctness for TT-ICE and empirically demonstrate the performance of the algorithms in compressing largescale video and scientific simulation datasets. Compared to existing approaches that also use rank adaptation, TT-ICE\ast \ast achieves 57\times higher compression and up to 95\% reduction in computational time.
Keywords:
tensor decompositions
data compression
streaming data
low-rank factorizations
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