ESEL Paper Review_20101219 by Aamir Alaud-din

1.    Title and Author

Title: The N-way Toolbox for MATLAB

Authors: Claus A. Andersson1, Rasmus Bro2

1Department of Dairy and Food Science - Food Technology, Chemometrics Group, The Royal Veterinary and Agricultural University, Rolighedsvej 30, DK-1958 Frederiksberg Denmark

2Department of Dairy and Food Science - Food Technology, Chemometrics Group, The Royal Veterinary and Agricultural University, Rolighedsvej 30, DK-1958 Frederiksberg Denmark

2.    Summary of Paper
The N-way toolbox for MATLAB contains the tools canonical decomposition?parallel factor analysis (CANDECOMP?PARAFAC), multi-linear partial least-squares regression (PLSR), generalized rank annihilation method (GRAM), direct tri-linear decomposition (DTLD), and the class of Tucker models. This toolbox contains different types of multiway models. We discuss them one by one.

2.1    The CANDECOMP-PARAFAC Model:
The CANDECOMP-PARAFAC Model used three way data array X(I×J×K) and is formulated on the following equation:
 
It can be fitted in least square sense. GRAM and DLTD models are also similar to CANDECOMP-PARAFAC model but they are not least square algorithms.

2.2    The multilinear PLS regression algorithm:
The trilinear and multilinear PLS regressions, both are the extended forms of PLS algorithms.  The only difference is that, in multilinear algorithm, multiway data is arranged into matrices to avoid the knowledge of multiway structure to be used in the decomposition.

2.3    Tucker Model:
Tucker model is the extended form of ordinary two-mode PCA to multimode equivalents. The three-way Tucker3 model with (P,Q,R) components in the 1st, 2nd and 3rd mode may be formulated according to the following equation:
 
In the case of orthonormal component, matrices A (I×P), B (J×Q) and C (K×R), the three-way array G (P×Q×R) reflects the importance of the interaction between factors.

3.    Contribution to ESEL
This paper discusses only the statistical techniques for the development of models using MATLAB. So, an understanding of statistical methods is necessary for modeling.

By: Aamir Alaud-din
aamiralauddin@gist.ac.kr