{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T13:14:46Z","timestamp":1783689286501,"version":"3.55.0"},"reference-count":46,"publisher":"Oxford University Press (OUP)","issue":"Supplement_1","license":[{"start":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T00:00:00Z","timestamp":1783382400000},"content-version":"vor","delay-in-days":6,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000054","name":"NCI","doi-asserted-by":"publisher","award":["U24CA248453"],"award-info":[{"award-number":["U24CA248453"]}],"id":[{"id":"10.13039\/100000054","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000054","name":"NCI","doi-asserted-by":"publisher","award":["U24CA264027"],"award-info":[{"award-number":["U24CA264027"]}],"id":[{"id":"10.13039\/100000054","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Princeton Catalysis Initiative, and Ludwig Cancer Research"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Motivation<\/jats:title>\n                    <jats:p>Recent spatial technologies measure the transcriptome, epigenome, proteome, metabolome, and other modalities from thousands of cells across a tissue. Most assays typically profile only one modality from a tissue slice, raising the question of how to align spatial data from heterogeneous feature spaces. While multiple approaches have been developed for multi-modal integration of single-cell datasets, few existing techniques perform spatial alignment across arbitrary modalities incorporating both spatial and feature information.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>We introduce Manifold Gromov-Wasserstein (MGW), a metric-learning framework that exploits the product structure of spatial multiomics to infer modality-specific Riemannian pull-back metrics with neural fields. MGW aligns Riemannian distances induced by these metrics via Gromov-Wasserstein optimal transport, yielding a hyperparameter-free cost across arbitrary modalities sharing a spatial base. The formulation enjoys theoretical invariances\u2014including orthogonal transformations of the spatial and feature domains as well as global feature scalings. We demonstrate the advantages of MGW on multiple alignment tasks, including Stereo-Seq spatiotemporal transcriptomics of mouse embryo, Xenium and Visium spatial transcriptomics of colorectal cancer, and spatial metabolomics-transcriptomics from human striatum and kidney cancer. MGW recovers biologically meaningful correspondences and spatially coherent tissue structures, outperforming existing OT and non-OT based multi-modal baselines.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Availability and implementation<\/jats:title>\n                    <jats:p>Software is available at https:\/\/github.com\/raphael-group\/MGW.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1093\/bioinformatics\/btag220","type":"journal-article","created":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T16:32:51Z","timestamp":1783441971000},"source":"Crossref","is-referenced-by-count":0,"title":["Riemannian metric learning for alignment of spatial multiomics"],"prefix":"10.1093","volume":"42","author":[{"given":"Peter","family":"Halmos","sequence":"first","affiliation":[{"name":"Department of Computer Science, Princeton University , Princeton, NJ 08544,","place":["United 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