An in-depth comparison of linear and non-linear joint embedding methods for bulk and single-cell multi-omics

Multi-omic analyses contribute to understanding complex biological processes, but also to making reliable predictions about, for example, disease outcomes. Several linear joint dimensionality reduction methods exist, but recently neural networks are more commonly used to embed different-omics into the same non-linear manifold. We compared linear to non-linear joint embedding methods using bulk and single-cell data. For modality imputation, non-linear methods had a clear advantage. Comparisons in downstream supervised tasks lead to the following insights: First, concatenating the principal components of each modality is a competitive baseline for multi-modal prediction. If only one modality was available at test time, joint embeddings yielded significant performance improvements with respect to a unimodal predictor. Second, imputed omics profiles can be fed to classifiers trained on real data with limited performance drops. Overall, the product-of-experts architecture performed well in most tasks while a common encoder of concatenated modalities performed poorly.