Microbiome data analysis using multi-way methods

In recent years, the growing recognition of the microbiome’s role in health and disease has led to the generation of increasingly complex longitudinal and multi-omics datasets. Traditional analytical approaches often struggle to exploit the structured nature of these data. This thesis therefore investigates multi-way methods as a more natural and interpretable framework for microbiome research.
The work begins with an introduction to four key multi-way approaches. CANDECOMP/PARAFAC enables unsupervised decomposition of time-resolved variation, while N-way Partial Least Squares extends this to supervised modelling of outcome-related patterns. Advanced Coupled Matrix and Tensor Factorisation (ACMTF) further integrates multiple datasets to identify shared and distinct sources of variation, and a novel ACMTF-Regression method incorporates regression directly within this framework. All methods are implemented as R packages to support broader use in microbiome studies.
Because effective modelling depends on appropriate data preparation, the thesis next outlines the major statistical challenges of longitudinal microbiome data, such as compositionality, over-dispersion, zero-inflation, and high dimensionality, and presents corresponding processing strategies, including centred log-ratio transformation and feature filtering, as well as considerations for multi-omics integration.
These methodological foundations are then applied in four original studies spanning gingivitis development, mother-infant obesity transmission, gender-affirming hormone therapy, and apical periodontitis. Together, they illustrate how multi-way methods reveal complementary biological insights. A comparative synthesis highlights the strengths of unsupervised approaches for capturing dominant variation and the advantages of supervised methods for isolating outcome-specific components, culminating in practical guidelines for method selection.
The thesis concludes by reflecting on broader analytical challenges and emphasising how structured, integrative multi-way modelling can advance microbiome research both methodologically and biologically.