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
|