AbstractMotivationThe accumulation of multi-omics microbiome data provides an unprecedented opportunity to understand the diversity of bacterial, fungal, and viral components from different conditions. The changes in the composition of viruses, bacteria, and fungi communities have been associated with environments and critical illness. However, identifying and dissecting the heterogeneity of microbial samples and cross-kingdom interactions remains challenging.ResultsWe propose HONMF for the integrative analysis of multi-modal microbiome data, including bacterial, fungal, and viral composition profiles. HONMF enables identification of microbial samples and data visualization, and also facilitates downstream analysis, including feature selection and cross-kingdom association analysis between species. HONMF is an unsupervised method based on hypergraph induced orthogonal non-negative matrix factorization, where it assumes that latent variables are specific for each composition profile and integrates the distinct sets of latent variables through graph fusion strategy, which better tackles the distinct characteristics in bacterial, fungal, and viral microbiome. We implemented HONMF on several multi-omics microbiome datasets from different environments and tissues. The experimental results demonstrate the superior performance of HONMF in data visualization and clustering. HONMF also provides rich biological insights by implementing discriminative microbial feature selection and bacterium–fungus–virus association analysis, which improves our understanding of ecological interactions and microbial pathogenesis.Availability and implementationThe software and datasets are available athttps://github.com/chonghua-1983/HONMF.