howtoPTAk: howto for Principal Tensors Analysis of a k-modes Tensor
Description
A mini guide to handle PTAk model decomposittionDetails
The PTAk decomposition aims at building an approximation of a given multiway data, represented as a tensor, based on a variance criterion. This approximation is given by a set of rank one tensors, orthogonals to each other, in a nested algorithm process and so controlling the level of approximation by the amount of variability extracted and represented by the sum of squares of the singular values (associated to the rank one tensors). In that respect it offers a way of generalising PCA to tensors of order greater than 2.
The reference in JSS provides details about preparing a dataset and running a general PTAk and particularlities for spatio-temporal data.
The license is GPL-3, support can be provided via http://c3s2i.free.fr, donations via Paypal to c3s2i@free.fr are welcome.References
Leibovici D and Sabatier R (1998) A Singular Value Decomposition of a k-ways
array for a Principal Component Analysis of multi-way data, the PTA-k. Linear Algebra and its
Applications, 269:307-329
Leibovici D.G. (accepted in 2009) Spatio-temporal Multiway Decompositions using
Principal Tensor Analysis on k-modes: the R-package PTAk. Journal of Statistical Software, vol x issue x, http://www.jstatsoft.org