Tensor Regression

TL;DR

Tensor Regression provides a comprehensive overview of tensor-based regression models, addressing challenges of high-dimensional data across various fields, and offering practical guidance on methods, datasets, and software tools.

Contribution

This work is the first thorough overview of tensor regression, covering fundamentals, algorithms, applications, datasets, and software resources in a systematic manner.

Findings

Systematic analysis of tensor regression models

Illustration of methods and applications in high-dimensional data

Guidance on datasets and software for tensor regression

Abstract

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.