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{{short description|Method of analyzing large data sets}}
'''Multiway data analysis''' is a method of analyzing large data sets by representing a collection of observations as a [[multiway array]], <math> {\mathcal A}\in{\mathbb C}^{I_0\times I_1\times \dots I_c\times \dots I_C}</math>.
{{cite book
|editor1-last=Coppi|editor1-first=R.
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==History==
The study of multiway data analysis was first formalized as the result of a conference held in 1988. The result of this conference was the first text specifically addressed to this field, Coppi and Bolasco's ''Multiway Data Analysis''.<ref name=
{{cite book
|editor1-last=Coppi|editor1-first=R.
|page=xv▼
|editor2-last=Bolasco|editor2-first=S.
|title=Applied Multiway Data Analysis▼
|title=Multiway Data Analysis
|volume=702▼
|series=Wiley Series in Probability and Statistics▼
|___location=Amsterdam
|first=Pieter M.|last=Kroonenberg▼
▲ |publisher=John Wiley & Sons
|isbn=9780444874108
▲ |year=2008
|isbn=9780470237991▼
}}</ref> At that time, the application areas for multiway analysis included [[statistics]], [[econometrics]] and [[psychometrics]]. In recent years, applications have expanded to include [[chemometrics]], [[agriculture]], [[social network analysis]] and the [[food industry]].<ref name=Bro1998>
{{cite thesis
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===Multiway data ===
Multiway data analysts use the term ''way'' to refer to the number sources of data variation while reserving the word ''mode'' for the methods or models used to analyze the data.<ref name=Kroonenberg2008
{{ ▲ |page=xv
▲ |title=Applied Multiway Data Analysis
▲ |volume=702
▲ |series=Wiley Series in Probability and Statistics
▲ |first=Pieter M.|last=Kroonenberg
|publisher=John Wiley & Sons
|year=2008
▲ |isbn=9780470237991
}}</ref>{{rp|xviii}}
In this sense, we can define the various ''ways'' of data to analyze:
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