The N-way Toolbox for MATLAB

doi:10.1016/S0169-7439(00)00071-X

Chemometrics and Intelligent Laboratory Systems

Volume 52, Issue 1, 14 August 2000, Pages 1-4

https://doi.org/10.1016/S0169-7439(00)00071-X Get rights and content

Abstract

This communication describes a free toolbox for MATLAB^® for analysis of multiway data. The toolbox is called “The N-way Toolbox for MATLAB” and is available on the internet at http://www.models.kvl.dk/source/. This communication is by no means an attempt to summarize or review the extensive work done in multiway data analysis but is intended solely for informing the reader of the existence, functionality, and applicability of the N-way Toolbox for MATLAB.

Introduction

The N-way Toolbox for MATLAB^® is a freely available collection of functions and algorithms for modelling multiway data sets by a range of multilinear models. Several types of models are covered; canonical decomposition–parallel factor analysis (CANDECOMP–PARAFAC), multilinear partial least-squares regression (PLSR), generalised rank annihilation method (GRAM), direct trilinear decomposition (DTLD) and the class of Tucker models. When denoting missing observations by not-a-number (NaN), the algorithms apply expectation maximization to obtain the parameters that minimize the least-squares error term.

Selected types of optional constraints have been built into the least-squares error minimization algorithms for CANDECOMP–PARAFAC and Tucker models; nonnegativity, unimodality, and orthogonality. Different constraints may be set up for the different modes. In addition to these constraints, the structure of the Tucker models can be forced to allow only selected factor interactions. Furthermore, three methods for core simplification by orthogonal rotations have been implemented. Most of the algorithms in the toolbox can handle any number of modes (N≥2) in data.

The N-way Toolbox for MATLAB can be downloaded via internet from http://www.models.kvl.dk/source/. Two interactive internet courses accompany The N-way Toolbox for MATLAB, and they are freely available at http://www.models.kvl.dk/courses. Both the Tucker and the PARAFAC courses come with real and simulated multiway data sets and are intended for training in applying the models to different kinds of chemometric problems.

Section snippets

Requirements

The collection of functions, algorithms and helper-files are provided as MATLAB source files (m-files), with no requirements for any add-ins beyond the standard MATLAB installation. The toolbox has been developed under MATLAB 5.x, (MathWorks), but the functions have been designed for optimal MATLAB 4.2c compatibility. Multiway data tables require much memory by nature, typically suggesting somewhat more than 32 MB RAM under Microsoft Windows 9x/NT/2000. The computational requirements depend

Models and solution algorithms

The common types of multiway models are contained in the toolbox — in particular models that have found good applications in chemometrics. In the sequel, the implemented models are briefly presented and references to various applications are given.

References (20)

C.A. Andersson et al.
Improving the speed of multi-way algorithms: Part I. Tucker3
Chemom. Intell. Lab. Syst.
(1998)
C.A. Andersson et al.
A general algorithm for obtaining simple-structure of core arrays in N-way PCA with application to fluorometric data
Comp. Stat. Data Anal.
(1999)
J.L. Beltran et al.
Multivariate calibration of polycyclic aromatic hydrocarbon mixtures from excitation-emission fluorescence spectra
Anal. Chim. Acta
(1998)
R. Bro et al.
Enzymatic browning of vegetables
Calibration and analysis of variance by multiway methods
Chemom. Intell. Lab. Syst.
(1996)
R. Henrion et al.
A new criterion for simple-structure core transformations in N-way principal components analysis
Chemom. Intell. Lab. Syst.
(1999)
Å.K. Pettersson et al.
Simultaneous determination of orthophosphate and arsenate based on multi-way spectroscopic-kinetic data evaluation
Anal. Chim. Acta
(1997)
S. Bijlsma et al.
Estimating rate constants and pure UV–VIS spectra of a two-step reaction using trilinear models
J. Chemom.
(1999)
K.S. Booksh et al.
Extension of trilinear decomposition method with an application to the flow probe sensor
Anal. Chem.
(1994)
R. Boqué et al.
Monitoring and diagnosing batch processes with multiway regression models
AIChE J.
(1999)
R. Bro
Multiway calibration. Multi-linear PLS
J. Chemom.
(1996)

There are more references available in the full text version of this article.

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View full text

The N-way Toolbox for MATLAB

Abstract

Introduction

Section snippets

Requirements

Models and solution algorithms

Chemom. Intell. Lab. Syst.

Comp. Stat. Data Anal.

Anal. Chim. Acta

Chemom. Intell. Lab. Syst.

Chemom. Intell. Lab. Syst.

Anal. Chim. Acta

Estimating rate constants and pure UV–VIS spectra of a two-step reaction using trilinear models

J. Chemom.

Extension of trilinear decomposition method with an application to the flow probe sensor

Anal. Chem.

Monitoring and diagnosing batch processes with multiway regression models

AIChE J.

Multiway calibration. Multi-linear PLS

J. Chemom.