Multi-Omics Factor Analysis (MOFA)

A classical statistical method that finds linear combinations of variables from two datasets that are maximally correlated. Unlike MOFA's single latent space, CCA explicitly models the cross-covariance between two specific omics blocks. Sparse CCA extends this by applying L1 regularization to select only the most relevant features, improving interpretability in high-dimensional genomic settings where the number of features vastly exceeds the sample size.

A computational method that constructs patient similarity networks for each omics data type and iteratively fuses them into a single comprehensive network. SNF excels at identifying patient subtypes by capturing both shared and complementary information across data types. Unlike MOFA's factor-based decomposition, SNF operates on a graph-based paradigm, making it particularly effective for unsupervised patient stratification and clustering applications in cancer genomics.

A supervised extension of sparse generalized CCA designed to discriminate between phenotypic outcome classes while simultaneously selecting correlated molecular features across multiple omics blocks. DIABLO is part of the mixOmics R package and is particularly suited for biomarker panel discovery where the goal is to identify a minimal set of multi-omics features that predict a known clinical outcome, contrasting with MOFA's unsupervised variance decomposition approach.

A neural network architecture that learns a compressed, non-linear latent representation by encoding high-dimensional multi-omics inputs into a bottleneck layer and reconstructing the original modalities. Unlike MOFA's linear factor model, autoencoders capture complex non-linear interactions. Variational Autoencoders (VAEs) further impose a probabilistic structure on the latent space, enabling generative applications such as simulating realistic synthetic molecular profiles for data augmentation.

A dimensionality reduction technique that decomposes a non-negative data matrix into additive, parts-based representations. In multi-omics, NMF identifies coherent molecular signatures and mutational processes across data types. Its non-negativity constraint yields highly interpretable factors that correspond to absolute biological signal, making it a popular alternative to MOFA for identifying mutational signatures in cancer genomics and deconvolving bulk tissue mixtures.

A machine learning approach that combines multiple kernel functions, each representing a different omics data type or similarity measure, to learn an optimal composite kernel for classification or regression. MKL provides a principled framework for weighting the contribution of each data modality. Unlike MOFA's joint latent space, MKL operates in the kernel-induced feature space, enabling the integration of non-vectorial data types such as molecular graphs and sequence alignments.