Table 2:

Inter-modality data harmonization approaches with a free modality scope

Method name	Strategy	Main advantages	Main limitations	Citation
DeepMF	Deep learning and non-negative matrix factorization	Robust to noise and missing data	Manual parameter tuning and prior information may be required	[70]
JIVE	Dimensionality reduction	Identifies the global modes of variation that drive associations across and within data types	Not robust to outliers, missing values, or class imbalance	[71]
GCCA	Generalized canonical correlation analysis	Identifies blocks of variables within datasets for correlation across datasets	Less effective if the number of observations is smaller than the number of variables or if multiple linear correlations are present between datasets. Biases towards strong variation in the data	[72]
NetICS	Graph diffusion	Robust to frequency of aberrant genes in sample	Can only examine effects of known genes present in a defined interaction network	[73]
DIABLO	Multivariate model and latent variable model	Captures quantitative information. Visual outputs aid interpretation	Assumes a linear relationship between the selected omics features. Parameter tuning is required	[20]
iCluster	Latent variable model	Captures both concordant and unique alterations across data types	Sensitive to initial subset selection. Trained only on array data	[62]
GFA	Latent variable model	Accepts data with missing values	Manual parameter tuning. Prior information may be required	[63]
MOFA	Latent variable model and probabilistic Bayesian	Leverages multiomics to impute missing values. Single-cell version available	Assumes a linear relationship between the selected omics features. Manual parameter tuning required	[74]
seurat	Mutual nearest neighbours	Effective in intra-modality as well as inter-modality integration. Robust to parameter changes	Restricted to single cell. Requires robust reference data	[69]
SNF	Network analysis	Effective in small heterogeneous samples. Captures quantitative information	Does not yield quantitative data. Trained only on array data	[75]
NMF	Non-negative matrix factorization	Accounts for complex modular structures in multimodal data	Trained only on array data	[65]
iNMF	Non-negative matrix factorization	Stable even in heterogeneous conditions	Trained only on array data	[66]
LIGER	Non-negative matrix factorization	Effective in intra-modality as well as inter-modality integration; effective in highly divergent datasets	Restricted to single cell	[67]
sMBPLS	Sparse multi-block partial least-squares regression	Derives weights for modalities indicating contributions to expression	Performance is reduced with lower data dimensions	[76]

Note that seurat and LIGER are specific to single-cell data and the others are intended for bulk data. Names, strategies, advantages, and limitations of each method are provided. Regarding advantages and limitations, a few major points are highlighted. A citation for reference to the original publication of each method is provided where full details can be obtained.