Large amount of multidimensional data represented by multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. The structural complexity of such data provides vast new opportunities for modeling and analysis, but efficiently extracting information content from them, both statistically and computationally, presents unique and fundamental challenges. Addressing these challenges requires an interdisciplinary approach that brings together tools and insights from statistics, optimization and numerical linear algebra among other fields. Despite these hurdles, significant progress has been made in the last decade. This review seeks to examine some of the key advancements and identify common threads among them, under eight different statistical settings.

翻译：由多维数组或张量表示的大规模多维数据在现代应用中广泛存在，涵盖化学计量学、基因组学、物理学、心理学和信号处理等多个领域。此类数据的结构复杂性为建模与分析提供了广阔的新机遇，但从统计与计算角度高效提取其信息内容仍面临独特且根本性的挑战。应对这些挑战需要采用跨学科方法，融合统计学、优化理论与数值线性代数等多个领域的工具与洞见。尽管存在这些障碍，过去十年间该领域已取得显著进展。本综述旨在检视八种不同统计框架下的关键进展，并梳理其间的共性脉络。