Multiway data analysis
Multiway data analysis is a method of analyzing large data sets by representing the data as a multidimensional array. The proper choice of array dimensions and analysis techniques can reveal patterns in the underlying data undetected by other methods.[1]
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.[2] 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.[3]
Composition of multiway data analysis
Multiway data array
Multiway data analysts use the term way to refer to a "dimension" of the data while reserving the word mode for the methods or models used to analyze the data.[2]: xviii .
In this sense, we can define the various ways of data to analyze:
- One-way data array with N entried (dimensions) stores an N-dimensional vector.
- Two-way data array stores a grid of data, a "data matrix"; a spreadsheet can be used to visualize such data in the case of discrete dimensions.
- Three-way data array stores a cube of data. Such data might represent the temperature at different locations (two-way data) sampled over different times (leading to three-way data)
- Four-way data array, using the same spreadsheet analogy, can be represented as a file folder full of separate workbooks.
- Five-way data array and six-way data can be represented by similarly higher levels of data aggregation.
In general, a multway data array may be measured at different times, or in different places, using different methodologies, and may contain inconsistencies such as missing data or discrepancies in data representation.
Multiway model
Multiway application
Multiway data analysis can be employed in various multiway applications so as to address the problem of finding hidden multilinear structure in multiway datasets. Following are examples of applications in different fields:[4]
- Computer vision
- Electroanalytical chemistry
- Neuroscience
- Process analysis
- Social network analysis/web-mining
Multiway processing
Multiway processing is the execution of designed and determined multiway model(s) transforming multiway data to the desirable level by addressing the specific need of particular multiway application. A typical example of data generated with a potentiometric electronic tongue illustrates relevant multiway processing.[5]
See also
References
- ^ Coppi, R.; Bolasco, S., eds. (1989). Multiway Data Analysis. Amsterdam: North-Holland. ISBN 9780444874108.
- ^ a b Kroonenberg, Pieter M. (2008). Applied Multiway Data Analysis. Wiley Series in Probability and Statistics. Vol. 702. John Wiley & Sons. p. xv. ISBN 9780470237991.
- ^ Bro, Rasmus (20 November 1998). Multi-way Analysis in the Food Industry: Models, Algorithms, and Applications (PDF) (Ph.D. thesis). University of Amsterdam.
- ^ Acar, Evrim; Yener, Bulent. Unsupervised Multiway Data Analysis: A Literature Survey (PDF) (Thesis). Rensselaer Polytechnic Institute.
- ^ Cartas, Raul; Mimendia, Aitor; Legin, Andrey; del Valle, Manel (2011). "Multiway Processing of Data Generated with a Potentiometric Electronic Tongue in a SIA System". Electroanalysis. 23 (4): 953–961. doi:10.1002/elan.201000642.