we discuss methods with only one X- and one Y-block we will use the indices JX and JY for the number of variables in the X- and Y-block, respectively. When there are multiple X-blocks, we will differentiate between the number of variables in the X-blocks using the indices Jm(m=1,…,M); for the Y-block we will then use simply the index J. We try to be as consistent as possible as far as terminology is concerned. Hence, we will use the terms scores, loadings, and weights throughout (see Figure 1.2 and the surrounding text). We will also use the term explained variance which is a slight abuse of the term variance, since it does not pertain to the statistical notion of variance. However, since it is used widely, we will use the term explained variance instead of explained variation as much as possible. Sometimes we need to use a predefined symbol (such as P) in an alternative meaning in order to harmonise the text. We will make this explicit at those places.
1.11 Abbreviations
In this book we will use a lot of abbreviations. Below follows a table with abbreviations used including the chapter(s) in which they appear. A small character ‘s’ in front of an abbreviation means ‘sparse’, e.g., sMB-PLS is the method sparse MB-PLS. For many methods mentioned below there are sparse versions; such as sPCA, sPLS, sSCA, sGCA, sMB-PLS and sMB-RDA. These are not mentioned explicitly in the table.
Table 1.2 Abbreviations of the different methods
Abbreviation
Full Description
Chapter
ACMTF
Advanced coupled matrix tensor factorisation
5
ASCA
ANOVA-simultaneous component analysis
6
BIBFA
Bayesian inter-battery factor analysis
9
DIABLO
Data integration analysis biomarker latent component omics
9
DI-PLS
Domain-invariant PLS
10
DISCO
Distinct and common components
5
ED-CMTF
Exponential dispersion CMTF
9
ESCA
Exponential family Simultaneous Component Analysis
5
GAS
Generalised association study
4,9
GAC
Generalised association coefficient
4
GCA
Generalised canonical analysis
2,5,7
GCD
General coefficient of determination
4
GCTF
Generalised coupled tensor factorisation
9
GFA
Group factor analysis
9
GPA
Generalised Procrustes analysis
9
GSCA
Generalised simultaneous component analysis
5
GSVD
Generalised singular value decomposition
9
IBFA
Inter-battery factor analysis
9
IDIOMIX
INDORT for mixed variables
9
INDORT
Individual differences scaling with orthogonal constraints