Joint Dimensionality Reduction

Projects multiple high-dimensional omics matrices into a common low-dimensional space where samples are represented by unified coordinates. Unlike concatenation-based approaches, this preserves the joint covariance structure across modalities. The latent dimensions capture coordinated biological programs—such as a pathway active simultaneously at the transcriptomic and proteomic level—enabling direct cross-modality sample comparison and integrated clustering.

Assigns learnable importance scores to each omics data type during factorization, preventing high-dimensional or noisy modalities from dominating the shared representation. For example, in MOFA, each factor is associated with a variance explained metric per modality, allowing analysts to trace which molecular layer drives each latent dimension. This addresses the heterogeneity of signal-to-noise ratios across proteomics, metabolomics, and transcriptomics.

Incorporates L1 or elastic net penalties to produce sparse factor loadings where only a small subset of features contribute to each latent dimension. This yields interpretable factors where each axis corresponds to a specific biological process rather than an opaque linear combination of thousands of genes. Sparse CCA and sGCCA variants enforce feature selection simultaneously with subspace learning, directly identifying biomarker candidates.

Deep variants like Deep CCA and multi-omics autoencoders replace linear projections with neural network encoders, capturing complex non-linear molecular interactions. A variational autoencoder (VAE) learns a probabilistic latent distribution rather than a point estimate, enabling uncertainty quantification and synthetic sample generation. Cross-modal attention mechanisms further allow dynamic re-weighting of inter-modality relationships during representation learning.

Accommodates incomplete multi-omics profiles where not all assays are performed on every sample—a common reality in clinical cohorts. Bayesian frameworks like MOFA treat missing modalities as latent variables to be inferred from observed data, while autoencoder-based methods can reconstruct missing modalities from the shared latent code. This maximizes sample retention without imputation artifacts.

Extends unsupervised factorization to incorporate phenotypic outcome labels, learning latent dimensions that simultaneously explain multi-omics covariation and discriminate between clinical groups. DIABLO, for instance, maximizes the covariance between latent components and a design matrix encoding disease status, directly optimizing the subspace for biomarker discovery and patient stratification rather than pure reconstruction fidelity.

A classical statistical method that finds linear projections of two datasets to maximize their correlation. In multi-omics, CCA identifies coordinated patterns between modalities like gene expression and metabolite abundance.

• Linear method with closed-form solution via eigenvalue decomposition
• Maximizes Pearson correlation between projected variables
• Limitation: Cannot capture non-linear relationships without kernel or deep extensions
• Variant: Sparse CCA adds L1 penalties to select only the most relevant features from each omics layer

An unsupervised Bayesian framework that decomposes the variation across multiple omics data types into a sparse set of latent factors. MOFA disentangles the principal sources of biological and technical variability.

• Learns a low-rank representation capturing global sources of variation
• Sparsity priors automatically select which features contribute to each factor
• Handles missing data natively, accommodating incomplete multi-omics profiles
• Outputs factor scores for each sample, enabling integrated clustering and visualization

A generative deep learning model that compresses high-dimensional multi-omics data into a probabilistic latent space. VAEs learn a non-linear manifold where samples with similar molecular profiles cluster together.

• Encoder-decoder architecture with a stochastic bottleneck layer
• Learns a continuous latent distribution, not a single point estimate
• Generative capability: Can synthesize realistic multi-omics profiles
• Multi-modal VAEs extend the framework to jointly model heterogeneous data types with modality-specific encoders

A computational method that constructs patient similarity networks for each omics data type and iteratively fuses them into a single comprehensive network. SNF captures both shared and complementary information across modalities.

• Network-based approach rather than matrix factorization
• Constructs patient-patient similarity graphs from each data type
• Iterative diffusion updates each network using information from the others
• Resulting fused network enables spectral clustering for patient subtype discovery

A non-linear extension of CCA that uses deep neural networks to learn maximally correlated transformations of two datasets. DCCA discovers intricate cross-omics associations that linear methods miss.

• Two deep networks transform each modality into a shared subspace
• Maximizes total correlation of the top K canonical components
• Learns hierarchical representations capturing complex non-linear dependencies
• Requires careful regularization to prevent overfitting on small biological datasets

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.

• Enforces non-negativity constraints for interpretable, additive components
• Parts-based representation: Each sample is a positive combination of signatures
• Joint NMF extends the framework to simultaneously factorize multiple matrices
• Widely used for mutational signature extraction in cancer genomics and cross-platform integration