| Summary: | The purpose of this paper is to describe the <b>R</b> package {<b>PTAk</b> 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 <b>R</b> 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 <b>R</b> package <b>PTAk</b> also support non-identity metrics, as well as penalizations during the optimization process. As a result of these flexibilities, together with pre-processing facilities, <b>PTAk</b> constitutes a framework for devising extensions of multidimensional methods such ascorrespondence analysis, discriminant analysis, and multidimensional scaling, also enabling spatio-temporal constraints.
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