Multiway data analysis

Multiway data analysis is a method of analyzing large data sets by representing a collection of observations as a multiway array,

A

∈

C

I

0

×

I

1

×

…

I

c

×

…

I

C

{\displaystyle {\mathcal {A}}\in {\mathbb {C} }^{I_{0}\times I_{1}\times \dots I_{c}\times \dots I_{C}}}

. The proper choice of data organization into (C+1)-way array, and analysis techniques can reveal patterns in the underlying data undetected by other methods.

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. 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.

Composition of multiway data analysis

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.

In this sense, we can define the various ways of data to analyze:

One way data: A data point with

I

0

{\displaystyle I_{0}}

-dimensions,

a

∈

C

I

0

{\displaystyle {\bf {a}}\in {\mathbb {C} }^{I_{0}}}

is a vector or data point that is stored in a one-way array data structure.

Two-way data: A collection of

I

1

{\displaystyle I_{1}}

data points

a

∈

C

I

0

{\displaystyle {\bf {a}}\in {\mathbb {C} }^{I_{0}}}

is stored in a two-way array,

A

∈

C

I

0

×

I

1

{\displaystyle {\bf {A}}\in {\mathbb {C} }^{I_{0}\times I_{1}}}

. A spreadsheet can be used to visualize such data in the case of discrete dimensions.