Multiblock Data Fusion in Statistics and Machine Learning. Tormod Næs

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	9
JIVE	Joint and individual variation explained	5
LiMM-PCA	Linear mixed model PCA	6
L-PLS	PLS regression for L-shaped data sets	8
MB-PLS	Multiblock partial least squares	7
MB-RDA	Multiblock redundancy analysis	10
MBMWCovR	Multiblock multiway covariates regression	10
MCR	Multivariate curve resolution	5,8
MFA	Multiple factor analysis	5
MOFA	Multi-omics factor analysis	9
OS	Optimal-scaling	2,5
PCA	Principal component analysis	2,5,8
PCovR	Principal covariates regression	2
PCR	Principal component regression	2
PESCA	Penalised ESCA	9
PE-ASCA	Penalised ASCA	6
PLS	Partial least squares	2
PO-PLS	Parallel and orthogonalised PLS regression	7
RDA	Redundancy analysis	7
RGCCA	Regularized generalized canonical correlation analysis	5
RM	Representation matrix approach	9
ROSA	Response oriented sequential alternation