Tensor decompositions in cancer study; A comprehensive review

Abstract

Tensor decomposition techniques have gained significant attention in cancer research due to their ability to unravel complex and high-dimensional data structures. In this study, we comprehensively review the research trends from 2013 to 2023. Several themes are dis- cussed, including the problems and challenges regarding cancer datasets, specifically image data and omics data. We also explore proposed tensor decomposition algorithms to tackle these challenges and their applications in different types of cancer, as well as the limita- tions and shortcomings of this field, which call for further research and development. Our objective is to investigate the application of tensor decomposition methods in cancer re- search. We first introduce the concept of tensors as multidimensional arrays and highlight their relevance in modeling cancer data. Subsequently, we discuss various tensor decom- position algorithms, such as Tucker decomposition and Canonical Polyadic decomposition, along with their advantages and limitations. This review aims to assist researchers inter- ested in tensor decomposition techniques, which offer a valuable tool for analyzing complex and heterogeneous cancer data, enabling the discovery of hidden patterns and providing biological insights.