Multi-omics data have revolutionized biomedical research by providing a comprehensive understanding of biological systems and the molecular mechanisms of disease development. However, analyzing multi-omics data is challenging due to high dimensionality and limited sample sizes, necessitating proper data-reduction pipelines to ensure reliable analyses. Additionally, its multimodal nature requires effective data-integration pipelines. While several dimensionality reduction and data fusion algorithms have been proposed, crucial aspects are often overlooked. Specifically, the choice of projection space dimension is typically heuristic and uniformly applied across all omics, neglecting the unique high dimension small sample size challenges faced by individual omics. This paper introduces a novel multi-modal dimensionality reduction pipeline tailored to individual views. By leveraging intrinsic dimensionality estimators, we assess the curse-of-dimensionality impact on each view and propose a two-step reduction strategy for significantly affected views, combining feature selection with feature extraction. Compared to traditional uniform reduction pipelines in a crucial and supervised multi-omics analysis setting, our approach shows significant improvement. Additionally, we explore three effective unsupervised multi-omics data fusion methods rooted in the main data fusion strategies to gain insights into their performance under crucial, yet overlooked, settings.

MOTIVATION: Precision medicine leverages patient-specific multimodal data to improve prevention, diagnosis, prognosis, and treatment of diseases. Advancing precision medicine requires the non-trivial integration of complex, heterogeneous, and potentially high-dimensional data sources, such as multi-omics and clinical data. In the literature, several approaches have been proposed to manage missing data, but are usually limited to the recovery of subsets of features for a subset of patients. A largely overlooked problem is the integration of multiple sources of data when one or more of them are completely missing for a subset of patients, a relatively common condition in clinical practice. RESULTS: We propose miss-Similarity Network Fusion (miss-SNF), a novel general-purpose data integration approach designed to manage completely missing data in the context of patient similarity networks. miss-SNF integrates incomplete unimodal patient similarity networks by leveraging a non-linear message-passing strategy borrowed from the SNF algorithm. miss-SNF is able to recover missing patient similarities and is "task agnostic", in the sense that can integrate partial data for both unsupervised and supervised prediction tasks. Experimental analyses on nine cancer datasets from The Cancer Genome Atlas (TCGA) demonstrate that miss-SNF achieves state-of-the-art results in recovering similarities and in identifying patients subgroups enriched in clinically relevant variables and having differential survival. Moreover, amputation experiments show that miss-SNF supervised prediction of cancer clinical outcomes and Alzheimer's disease diagnosis with completely missing data achieves results comparable to those obtained when all the data are available. AVAILABILITY AND IMPLEMENTATION: miss-SNF code, implemented in R, is available at https://github.com/AnacletoLAB/missSNF.