Spatio-temporal multiway decompositions using principal tensor analysis on k-modes: the R package PTAk

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.