Large amounts 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 past decade. This review seeks to examine some of the key advancements and identify common threads among them, under a number of different statistical settings.

中文翻译：

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高维数据分析中的张量：方法学机遇和理论挑战


由多路数组或张量表示的大量多维数据在化学计量学、基因组学、物理学、心理学和信号处理等各个领域的现代应用中很普遍。此类数据的结构复杂性为建模和分析提供了巨大的新机会，但从统计和计算方面有效地从中提取信息内容带来了独特而根本的挑战。应对这些挑战需要一种跨学科的方法，该方法将统计学、优化和数值线性代数等领域的工具和见解汇集在一起。尽管存在这些障碍，但在过去十年中取得了重大进展。本综述旨在研究一些关键进展，并在许多不同的统计设置下确定它们之间的共同点。