Three-Way Component Analysis Using the R Package ThreeWay

The R package ThreeWay is presented and its main features are illustrated. The aim of ThreeWay is to offer a suit of functions for handling three-way arrays. In particular, the most relevant available functions are T3 and CP, which implement, respectively, the Tucker3 and Candecomp/Parafac methods. They are the two most popular tools for summarizing three-way arrays in terms of components. After briefly recalling both techniques from a theoretical point of view, the functions T3 and CP are described by considering three real life examples.

[1]  Vin de Silva,et al.  Tensor rank and the ill-posedness of the best low-rank approximation problem , 2006, math/0607647.

[2]  H. Kiers,et al.  Selecting among three-mode principal component models of different types and complexities: a numerical convex hull based method. , 2006, The British journal of mathematical and statistical psychology.

[3]  David E. Booth,et al.  Multi-Way Analysis: Applications in the Chemical Sciences , 2005, Technometrics.

[4]  A. Agresti,et al.  Multiway Data Analysis , 1989 .

[5]  Pieter M. Kroonenberg,et al.  Three-mode principal component analysis : theory and applications , 1983 .

[6]  A. Stegeman Degeneracy in Candecomp/Parafac explained for p × p × 2 arrays of rank p + 1 or higher , 2006 .

[7]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[8]  Paolo Giordani,et al.  Constrained Candecomp/Parafac via the Lasso , 2013, Psychometrika.

[9]  P. Kroonenberg Applied Multiway Data Analysis , 2008 .

[10]  H. Kiers Towards a standardized notation and terminology in multiway analysis , 2000 .

[11]  Moonja P. Kim,et al.  The Method of Sorting as a Data-Gathering Procedure in Multivariate Research. , 1975, Multivariate behavioral research.

[12]  L. Tucker,et al.  Some mathematical notes on three-mode factor analysis , 1966, Psychometrika.

[13]  Henk A L Kiers,et al.  A fast method for choosing the numbers of components in Tucker3 analysis. , 2003, The British journal of mathematical and statistical psychology.

[14]  E. Baxter,et al.  A ‘two-stage’ farrowing and lactation system: sow behaviour and injuries , 2015 .

[15]  J. Berge,et al.  Computational solutions for the problem of negative saliences and nonsymmetry in INDSCAL , 1993 .

[16]  R. Bro,et al.  Centering and scaling in component analysis , 2003 .

[17]  A. Stegeman Degeneracy in Candecomp/Parafac and Indscal Explained For Several Three-Sliced Arrays With A Two-Valued Typical Rank , 2007, Psychometrika.

[18]  H. Kiers,et al.  Bootstrap confidence intervals for three‐way methods , 2004 .

[19]  Didier G. Leibovici,et al.  Spatio-Temporal Multiway Data Decomposition Using Principal Tensor Analysis on k-Modes: The R Package PTAk , 2010 .

[20]  Phipps Arabie,et al.  Three-way scaling and clustering. , 1987 .

[21]  J. Kruskal,et al.  A two-stage procedure incorporating good features of both trilinear and quadrilinear models , 1989 .

[22]  H. Kiers Joint Orthomax Rotation of the Core and Component Matrices Resulting from Three-mode Principal Components Analysis , 1998 .

[23]  H. Kiers,et al.  Three-mode principal components analysis: choosing the numbers of components and sensitivity to local optima. , 2000, The British journal of mathematical and statistical psychology.

[24]  Rasmus Bro,et al.  MULTI-WAY ANALYSIS IN THE FOOD INDUSTRY Models, Algorithms & Applications , 1998 .

[25]  J. Kruskal Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics , 1977 .

[26]  Richard A. Harshman,et al.  Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multi-model factor analysis , 1970 .

[27]  L. Tucker A METHOD FOR SYNTHESIS OF FACTOR ANALYSIS STUDIES , 1951 .

[28]  R. Bro,et al.  A new efficient method for determining the number of components in PARAFAC models , 2003 .

[29]  Alfred O. Hero,et al.  Multimodal factor analysis , 2015, 2015 IEEE 25th International Workshop on Machine Learning for Signal Processing (MLSP).

[30]  R. A. Harshman,et al.  Data preprocessing and the extended PARAFAC model , 1984 .

[31]  J. Chang,et al.  Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition , 1970 .

[32]  Marieke E. Timmerman,et al.  Component analysis of multisubject multivariate longitudinal data , 2001 .