Multiway data analysis: Difference between revisions

Revision as of 18:21, 18 March 2023

Revision as of 21:18, 18 March 2023

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'''Multiway data analysis''' is a method of analyzing large data sets by representing the data as a [[multiway array]], <math> {\mathcal A}\in{\mathbb C}^{I_0\times I_1\times \dots I_mI_c\times \dots I_MI_C}</math>. The proper choice of data organization into ''M(C+1)''-way array, and analysis techniques can reveal patterns in the underlying data undetected by other methods.<ref name=Coppi1989>

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

* ''One way data'': A data point with <math>I_0</math>-dimensions, <math>{\bf a}\in {\mathbb C}^{I_0}</math> is a [[Vector (mathematics and physics)|vector]] or data point that is stored in a ''one-way array'' data structure.

* ''Two-way data:'' Is aA collection of <math>I_1</math> data points <math>{\bf witha}\in dimensions{\mathbb <math>C}^{I_0}</math> that is stored in a ''two-way array'', <math>{\bf A}\in {\mathbb C}^{I_0\times I_1}</math>. A [[spreadsheet]] can be used to visualize such data in the case of discrete dimensions.

* ''Three-way data'': withA dimensionscollection of data <math>I_0{\timesbf I_1a}\timesin I_2{\mathbb C}^{I_0}</math> isthat ahas cubetwo modes of data thatvariation is stored in a three-way array, <math>{\bf A}\in {\mathbb C}^{I_0\times I_1\times I_2}</math>. Such data might represent the temperature at different locations (two-way data) sampled over different times (leading to three-way data)

* ''Four-way data'', using the same spreadsheet analogy, can be represented as a file folder full of separate workbooks.

* ''Five-way data'' and ''six-way data'' can be represented by similarly higher levels of data aggregation.