Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies such as neuroimaging, computer vision, climatology and social networks, has brought challenges to traditional data representation methods. Tensors, as high dimensional extensions of vectors, are considered as natural representations of high dimensional data. In this book, the authors provide a systematic study and analysis of tensor-based regression models and their applications in recent years. It groups and illustrates the existing tensor-based regression methods and covers the basics, core ideas, and theoretical characteristics of most tensor-based regression methods. In addition, readers can learn how to use existing tensor-based regression methods to solve specific regression tasks with multiway data, what datasets can be selected, and what software packages are available to start related work as soon as possible. Tensor Regression is the first thorough overview of the fundamentals, motivations, popular algorithms, strategies for efficient implementation, related applications, available datasets, and software resources for tensor-based regression analysis. It is essential reading for all students, researchers and practitioners of working on high dimensional data.

翻译：回归分析是数据分析和机器学习领域中的一个关键研究方向，致力于探索变量之间的依赖关系，通常使用向量进行分析。然而，神经影像学、计算机视觉、气候学和社会网络等技术的发展带来了高维数据，这对传统的数据表示方法提出了挑战。张量作为向量的高维扩展，被视为高维数据的自然表示方式。本书系统性地研究并分析了近年来基于张量的回归模型及其应用，对现有张量回归方法进行了分类阐述，涵盖了大多数张量回归方法的基础知识、核心思想及理论特性。此外，读者可学习如何利用现有张量回归方法解决特定多路数据回归任务，了解可选取的数据集及可用的软件包，从而尽快开展相关工作。《张量回归》首次全面概述了张量回归分析的基础、动机、流行算法、高效实现策略、相关应用、可用数据集及软件资源，是所有从事高维数据研究的学生、研究人员及从业者的必读之作。