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Spatio-Temporal Multiway Data Decomposition Using Principal Tensor Analysis on k-Modes: The R Package PTAk

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  • Leibovici, Didier G.

Abstract

The purpose of this paper is to describe the R package {PTAk and how the spatio-temporal context can be taken into account in the analyses. Essentially PTAk() is a multiway multidimensional method to decompose a multi-entries data-array, seen mathematically as a tensor of any order. This PTAk-modes method proposes a way of generalizing SVD (singular value decomposition), as well as some other well known methods included in the R package, such as PARAFAC or CANDECOMP and the PCAn-modes or Tucker-n model. The example datasets cover different domains with various spatio-temporal characteristics and issues: (i)~medical imaging in neuropsychology with a functional MRI (magnetic resonance imaging) study, (ii)~pharmaceutical research with a pharmacodynamic study with EEG (electro-encephaloegraphic) data for a central nervous system (CNS) drug, and (iii)~geographical information system (GIS) with a climatic dataset that characterizes arid and semi-arid variations. All the methods implemented in the R package PTAk also support non-identity metrics, as well as penalizations during the optimization process. As a result of these flexibilities, together with pre-processing facilities, PTAk constitutes a framework for devising extensions of multidimensional methods such ascorrespondence analysis, discriminant analysis, and multidimensional scaling, also enabling spatio-temporal constraints.

Suggested Citation

  • Leibovici, Didier G., 2010. "Spatio-Temporal Multiway Data Decomposition Using Principal Tensor Analysis on k-Modes: The R Package PTAk," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i10).
  • Handle: RePEc:jss:jstsof:v:034:i10
    DOI: http://hdl.handle.net/10.18637/jss.v034.i10
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    Cited by:

    1. Giordani, Paolo & Kiers, Henk A. L. & Del Ferraro, Maria Antonietta, 2014. "Three-Way Component Analysis Using the R Package ThreeWay," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 57(i07).
    2. Rubinstein, Alexander & Slutskin, Lev, 2018. "«Multiway data analysis» and the general problem of journals’ ranking," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 50, pages 90-113.
    3. Pebesma, Edzer & Bivand, Roger & Ribeiro, Paulo Justiniano, 2015. "Software for Spatial Statistics," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i01).

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