张量网络用于潜在变量分析。第一部分：张量列车分解的算法
Tensor Networks for Latent Variable Analysis. Part I: Algorithms for Tensor Train Decomposition
AI总结：
本文提出新的张量网络分解算法，重点在张量列车分解及其变体，通过交替更新核心张量提升大规模数据处理能力，在盲源分离、去噪和特征提取中表现优异。
摘要：
将张量分解为因子矩阵，通过核心张量相互作用，在信号处理和机器学习中有广泛应用。一种更通用的张量模型，将数据表示为顺序子张量网络，至今未被广泛研究，尽管在量子物理和科学计算中已有长期研究。本文提出新的张量网络分解算法，特别关注张量列车分解及其变体。所开发的算法在每次迭代中交替更新一个或多个核心张量，展现出增强的数学可处理性和对超大规模数据张量的可扩展性。所提出的算法在经典盲源分离、去噪和特征提取范式中进行了测试，并在张量列车分解的广泛使用截断算法上实现了优越性能。
英文摘要：
Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of sub-tensors of order-2 or order-3 has, so far, not been widely considered in these fields, although this so-called tensor network decomposition has been long studied in quantum physics and scientific computing. In this study, we present novel algorithms and applications of tensor network decompositions, with a particular focus on the tensor train decomposition and its variants. The novel algorithms developed for the tensor train decomposition update, in an alternating way, one or several core tensors at each iteration, and exhibit enhanced mathematical tractability and scalability to exceedingly large-scale data tensors. The proposed algorithms are tested in classic paradigms of blind source separation from a single mixture, denoising, and feature extraction, and achieve superior performance over the widely used truncated algorithms for tensor train decomposition.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
