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Applications of tensor (multiway array) factorizations and decompositions in data mining
Author(s) -
Mørup Morten
Publication year - 2011
Publication title -
wiley interdisciplinary reviews: data mining and knowledge discovery
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.506
H-Index - 47
eISSN - 1942-4795
pISSN - 1942-4787
DOI - 10.1002/widm.1
Subject(s) - matrix decomposition , computer science , exploit , scalability , decomposition , tensor (intrinsic definition) , cluster analysis , factorization , non negative matrix factorization , theoretical computer science , data mining , identification (biology) , matrix (chemical analysis) , artificial intelligence , algorithm , mathematics , database , eigenvalues and eigenvectors , ecology , physics , botany , computer security , materials science , quantum mechanics , composite material , pure mathematics , biology
Tensor (multiway array) factorization and decomposition has become an important tool for data mining. Fueled by the computational power of modern computer researchers can now analyze large‐scale tensorial structured data that only a few years ago would have been impossible. Tensor factorizations have several advantages over two‐way matrix factorizations including uniqueness of the optimal solution and component identification even when most of the data is missing. Furthermore, multiway decomposition techniques explicitly exploit the multiway structure that is lost when collapsing some of the modes of the tensor in order to analyze the data by regular matrix factorization approaches. Multiway decomposition is being applied to new fields every year and there is no doubt that the future will bring many exciting new applications. The aim of this overview is to introduce the basic concepts of tensor decompositions and demonstrate some of the many benefits and challenges of modeling data multiway for a wide variety of data and problem domains. © 2011 John Wiley & Sons, Inc. WIREs Data Mining Knowl Discov 2011 1 24‐40 DOI: 10.1002/widm.1 This article is categorized under: Algorithmic Development > Scalable Statistical Methods Technologies > Classification Technologies > Machine Learning Technologies > Structure Discovery and Clustering