Multiway Data Analysis
  General description
May 26-30, 2008  

General description of the course

Multiway data are data from various sets of entities (often called “modes”). For instance, scores of different anxiety measures, under different circumstances (three-way data) or excitation values in mass spectrometry measures of different chemical substances. To analyze such data, various techniques have been proposed. In the early days, these have been proposed most notably within psychology, and developments within psychometrics as the quantitative field is known have continued ever since. Later on, applications emerged especially in chemistry, and further developments in multiway analysis have since emerged in chemometrics as well.

The present course will provide a global introduction into the analysis of multiway data. The focus is on techniques for exploratory analysis of three-way data sets. Exploratory (rather than confirmatory) data analysis is chosen because the main challenge in the analysis of multiway data sets is to summarize and explore the data (in ways analogous to what is done with principal components analysis in the two-way case), and rarely specific hypotheses can be formulated and tested in practice on such multiway data sets. The focus on three-way (rather than multiway) is because the step from two-way to three-way analysis covers the main changes from the more standard exploratory analysis techniques for the analysis of two-way data to that of multiway data. Many standard procedures no longer work when going from two-way to three-way. The approaches taken in three-way analysis, do however, also work in four-way and higher way analysis.

In the course, first, special properties and definitions needed for three-way data will be discussed. Then, it will be described how principal component analysis can be generalized to analysis of three- and higher-way data. Several methods will be described briefly. The two most common methods, CANDECOMP/PARAFAC and Tucker3 analysis, will be described in most detail. These descriptions deal with all necessary steps in a three-way analysis:

  • preprocessing three-way data
  • fitting procedure
  • selecting the number(s) of components
  • simple structure rotation of core and component matrices
  • studying stability by split-half and bootstrap analysis
  • procedures for plotting solutions
  • possibility of degenerate solutions
Procedures will be illustrated by means of one example analyses.