The Bayesian streaming tensor decomposition method is a novel method to discover the low-rank approximation of streaming data. However, when the streaming data comes from a high-order tensor, tensor structures of existing Bayesian streaming tensor decomposition algorithms may not be suitable in terms of representation and computation power. In this paper, we present a new Bayesian streaming tensor decomposition method based on tensor train (TT) decomposition. Especially, TT decomposition renders an efficient approach to represent high-order tensors. By exploiting the streaming variational inference (SVI) framework and TT decomposition, we can estimate the latent structure of high-order incomplete noisy streaming tensors. The experiments in synthetic and real-world data show the accuracy of our algorithm compared to the state-of-the-art Bayesian streaming tensor decomposition approaches.

翻译：贝叶斯流式张量分解方法是一种用于发现流式数据低秩近似的新方法。然而，当流式数据来自高阶张量时，现有贝叶斯流式张量分解算法的张量结构在表示能力和计算能力上可能并不适用。本文提出了一种基于张量列（TT）分解的新型贝叶斯流式张量分解方法。特别地，TT分解提供了一种表示高阶张量的高效途径。通过利用流式变分推理（SVI）框架和TT分解，我们能够估计高阶含噪不完整流式张量的潜在结构。合成数据与真实数据的实验表明，与最先进的贝叶斯流式张量分解方法相比，我们的算法具有更高的准确性。