Tensor Methods in High Dimensional Data Analysis: Opportunities and Challenges

TL;DR

This paper reviews recent advances in tensor methods for high-dimensional data analysis, highlighting opportunities and challenges across various fields, and emphasizing interdisciplinary approaches for efficient information extraction.

Contribution

It provides a comprehensive overview of key developments in tensor analysis techniques across multiple statistical settings, identifying common themes and future directions.

Findings

Significant progress in tensor decomposition methods over the last decade

Interdisciplinary approaches are crucial for addressing computational challenges

Tensor methods enable new insights in diverse scientific fields

Abstract

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.