Multiway data analysis
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Multiway data analysis is a method of analyzing large data sets by representing a collection of observations as a multiway array, \in^. 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 Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
,
econometrics Econometrics is the application of Statistics, statistical methods to economic data in order to give Empirical evidence, empirical content to economic relationships.M. Hashem Pesaran (1987). "Econometrics," ''The New Palgrave: A Dictionary of ...
and
psychometrics Psychometrics is a field of study within psychology concerned with the theory and technique of measurement. Psychometrics generally refers to specialized fields within psychology and education devoted to testing, measurement, assessment, and ...
. In recent years, applications have expanded to include
chemometrics Chemometrics is the science of extracting information from chemical systems by data-driven means. Chemometrics is inherently interdisciplinary, using methods frequently employed in core data-analytic disciplines such as multivariate statistics, a ...
,
agriculture Agriculture or farming is the practice of cultivating plants and livestock. Agriculture was the key development in the rise of sedentary human civilization, whereby farming of domesticated species created food surpluses that enabled people to ...
,
social network analysis Social network analysis (SNA) is the process of investigating social structures through the use of networks and graph theory. It characterizes networked structures in terms of ''nodes'' (individual actors, people, or things within the network) a ...
and the
food industry The food industry is a complex, global network of diverse businesses that supplies most of the food consumed by the world's population. The food industry today has become highly diversified, with manufacturing ranging from small, traditiona ...
.


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-dimensions, \in ^ is a
vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...
or data point that is stored in a ''one-way array'' data structure. * ''Two-way data:'' A collection of I_1 data points \in ^ is stored in a ''two-way array'', \in ^. A
spreadsheet A spreadsheet is a computer application for computation, organization, analysis and storage of data in tabular form. Spreadsheets were developed as computerized analogs of paper accounting worksheets. The program operates on data entered in cel ...
can be used to visualize such data in the case of discrete dimensions. * ''Three-way data'': A collection of data \in ^ that has two modes of variation is stored in a three-way array, \in ^. 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. In general, a multiway data is stored in a multiway array and 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: *
Computer vision Computer vision is an interdisciplinary scientific field that deals with how computers can gain high-level understanding from digital images or videos. From the perspective of engineering, it seeks to understand and automate tasks that the hum ...
- TensorFacesM.A.O. Vasilescu, D. Terzopoulos (2005
"Multilinear Independent Component Analysis"
"Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR’05), San Diego, CA, June 2005, vol.1, 547–553."
and Human motion signaturesM.A.O. Vasilescu (2002
"Human Motion Signatures: Analysis, Synthesis, Recognition," Proceedings of International Conference on Pattern Recognition (ICPR 2002), Vol. 3, Quebec City, Canada, Aug, 2002, 456–460.
/ref> analyzes facial images and human joint angle data organizes in a multiway array. The multiway data analysis is employed to compute a set of causal factor representations. *
Electroanalytical chemistry Electroanalytical methods are a class of techniques in analytical chemistry which study an analyte by measuring the potential (volts) and/or current ( amperes) in an electrochemical cell containing the analyte. These methods can be broken down int ...
*
Neuroscience Neuroscience is the scientific study of the nervous system (the brain, spinal cord, and peripheral nervous system), its functions and disorders. It is a multidisciplinary science that combines physiology, anatomy, molecular biology, development ...
*
Process analysis Process analysis is a form of technical writing and expository writing The rhetorical modes (also known as modes of discourse) are a long-standing attempt to broadly classify the major kinds of language-based communication, particularly writing a ...
*
Social network analysis Social network analysis (SNA) is the process of investigating social structures through the use of networks and graph theory. It characterizes networked structures in terms of ''nodes'' (individual actors, people, or things within the network) a ...
/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.


See also

*
Multilinear subspace learning Multilinear subspace learning is an approach to dimensionality reduction.M. A. O. Vasilescu, D. Terzopoulos (2003"Multilinear Subspace Analysis of Image Ensembles" "Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVP ...


References

{{reflist Data analysis