Table 1.

A non-exhaustive list of multi-block dimensionality reduction methods for multi-omics datasets. NMF: Non-negative Matrix Factorization, MOFA: Multi-Omics Factor Analysis, JIVE: Joint and Individual Variation Explained, MO: multi-omic.

Method	Principle	Purpose	Recent applications
jNMF/intNMF/nNMF [132], [133], [139]	Matrix factorization	Disease subtyping, module detection, biomarker discovery	jNMF found biomarkers in MO and pharmacological data connected to drug sensitivity in cancerous cell lines [140]. intNMF identified Glioblastoma and breast cancer subtypes from MO and clinical data [134].
MOFA/MOFA+ [141], [142]	Bayesian Factor Analysis	biomarker discovery, systemic knowledge	MOFA found new biomarkers and pathways associated with Alzeihmer’s disease based on MO data including proteomics, metabolomics, lipidomics [143].MOFA + found predictive biomarkers from DNA methylation and gene expression data in cardiovascular disease [144].
iCluster [145]	Gaussian latent variable model Generalized linear regression Bayesian integrative clustering	Disease subtyping, biomarker discovery	iCluster was used to identify subtypes of esophageal carcinoma from genomic, epigenomic and transcriptomic data [148].
iClusterPlus [146]			iClusterPlus was used to identify subtypes of non-responsive samples with ovarian cancer from different omics datasets [149].
iClusterBayes [147]			iClusterBayes was used to identify predictive biomarkers and clinically relevant subtypes on MIB cancer from 5 different omics [150].
JIVE/aJIVE [151], [152]	Matrix factorization	Disease subtyping, systemic knowledge, module detection	JIVE was used as a dimension reduction technique to improve survival prediction of patients with glioblastoma from mRNA, miRNA and methylation data [153].
Integrated PCA 64	Generalized PCA	Visualization, prediction	iPCA was used as a dimension reduction technique to improve prediction of outcome on lung cancer from CpG methylation data, mRNA and miRNA expression [154].
SLIDE [130]	Matrix factorization	Disease subtyping, module detection, biomarker discovery	SLIDE was used on DNA methylation data and gene, protein and miRNA expression for subtyping patients with breast cancer [130].