@article{JSSv034i10, title={Spatio-Temporal Multiway Data Decomposition Using Principal Tensor Analysis on k-Modes: The R Package PTAk}, volume={34}, url={https://www.jstatsoft.org/index.php/jss/article/view/v034i10}, doi={10.18637/jss.v034.i10}, abstract={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 <code>PTAk()</code> is a multiway multidimensional method to decompose a multi-entries data-array, seen mathematically as a tensor of any order. This PTA<i>k</i>-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 PCA<i>n</i>-modes or Tucker-<i>n</i> 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.}, number={10}, journal={Journal of Statistical Software}, author={Leibovici, Didier G.}, year={2010}, pages={1–34} }