Joint decomposition of Hi-C maps reveals salient features of genome architecture across tissues and development

The spatial organization of chromosomes in the nucleus is fundamental to cellular processes. Contact frequency maps from Hi-C and related chromosome conformation capture assays are increasingly available for a wide variety of biosamples and conditions, creating opportunities for comprehensive studies of genome compartmentalization and long-range interactions. However, the conventional dimensionality reduction approach to study long-range contact frequency profiles projects individual datasets into different and incomparable linear subspaces, making the resulting embeddings unsuitable for large-scale integrative analysis. To address this shortcoming and overcome the computational constraints involved in doing so, we introduce an analytic framework and Python toolkit that leverages incremental principal component analysis to project interchromosomal contact frequency profiles across arbitrarily many Hi-C datasets onto a common set of components or basis vectors. Our approach produces robust and directly comparable first and higher-order principal component (PC) scores that collectively capture biologically meaningful information beyond traditional A/B compartments. By applying our framework to a collection of 89 human Hi-C samples, we uncover distinct patterns of nuclear architecture reflecting cell state categories, associated with different heterochromatin state compositions. We also demonstrate that jointly-derived higher-order PCs improve the prediction of gene expression and regulatory element activity during differentiation. Together, our joint decomposition approach provides a powerful and scalable foundation for systematically investigating genome organization, providing critical insights into its role in development and disease.