tensorOmics: Data integration for longitudinal omics data using tensor factorisation

Abstract Multi-omics studies capture comprehensive molecular profiles across biological layers to understand complex biological processes. A central challenge is integrating information across heterogeneous data types to identify coordinated molecular responses, particularly when measurements are collected longitudinally. Traditional integration methods can be broadly classified as unsupervised (exploring patterns without phenotypic information) or supervised (discriminating between groups or predicting outcomes). These approaches rely predominantly on matrix-based techniques that concatenate or project data into lower-dimensional spaces. However, matrix methods struggle with longitudinal data, as flattening multi-dimensional structures obscures temporal trajectories and violates independence assumptions. Tensor-based methods preserve the natural multi-way structure of longitudinal data but existing approaches are predominantly unsupervised, cannot incorporate phenotypic responses for discriminant analysis, and lack frameworks for integrating multiple omics layers. We present tensorOmics, a comprehensive framework for longitudinal omics analysis using tensor factorisation. The framework encompasses supervised and unsupervised methods for both single-omic (tensor PCA, tensor PLS discriminant analysis) and multi-omic settings (tensor PLS, block tensor PLS, block tensor PLS discriminant analysis). This unified approach captures coordinated responses across biological layers while preserving temporal structure. We validated tensorOmics through three case studies: antibiotic perturbation experiments, anaerobic digestion systems, and fecal microbiota transplantation. These applications demonstrate tensorOmics differentiates treatment groups, captures time-dependent molecular signatures, and reveals multi-layer coordinated responses that cross-sectional methods miss. Author summary Longitudinal multi-omics studies track molecular changes over time to understand how biological systems respond to treatments, diseases, or environmental shifts. However, analysing these complex datasets presents significant challenges: traditional methods either flatten the time dimension, losing temporal information, or handle only single omics layers without integration. We developed tensorOmics, a comprehensive computational framework that preserves the natural three-way structure of longitudinal data (samples × features × time) while integrating multiple omics layers. Our approach combines tensor decomposition with multi-block analysis, offering five complementary methods that address both exploratory and supervised analyses across single and multi-omic settings. Through three diverse case studies (antibiotic recovery in humans, anaerobic digestion systems, and fecal microbiota transplantation), we demonstrate that tensorOmics successfully identifies biologically meaningful temporal signatures that distinguish treatment groups and reveal coordinated molecular responses across omic layers. The framework handles the unique statistical properties of different omics types and efficiently manages high-dimensional data through tensor-based data compression. tensorOmics is available as an R package, providing researchers with flexible tools to extract interpretable insights from longitudinal multi-omics experiments while properly accounting for repeated measurements and temporal dynamics.