{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/angle-based-joint-and-individual-variation","title":"Angle-Based Joint and Individual Variation Explained","arxiv_id":"1704.02060","date":"2017-04-07","proceeding":null,"authors":["Qing Feng","Meilei Jiang","Jan Hannig","J. S. Marron"],"abstract":"Integrative analysis of disparate data blocks measured on a common set of\nexperimental subjects is a major challenge in modern data analysis. This data\nstructure naturally motivates the simultaneous exploration of the joint and\nindividual variation within each data block resulting in new insights. For\ninstance, there is a strong desire to integrate the multiple genomic data sets\nin The Cancer Genome Atlas to characterize the common and also the unique\naspects of cancer genetics and cell biology for each source. In this paper we\nintroduce Angle-Based Joint and Individual Variation Explained capturing both\njoint and individual variation within each data block. This is a major\nimprovement over earlier approaches to this challenge in terms of a new\nconceptual understanding, much better adaption to data heterogeneity and a fast\nlinear algebra computation. Important mathematical contributions are the use of\nscore subspaces as the principal descriptors of variation structure and the use\nof perturbation theory as the guide for variation segmentation. This leads to\nan exploratory data analysis method which is insensitive to the heterogeneity\namong data blocks and does not require separate normalization. An application\nto cancer data reveals different behaviors of each type of signal in\ncharacterizing tumor subtypes. An application to a mortality data set reveals\ninteresting historical lessons. Software and data are available at GitHub\n<https://github.com/MeileiJiang/AJIVE_Project>.","url_abs":"http://arxiv.org/abs/1704.02060v3","url_pdf":"http://arxiv.org/pdf/1704.02060v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"angle-based-joint-and-individual-variation","repo_url":"https://github.com/MeileiJiang/AJIVE_Project","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"angle-based-joint-and-individual-variation","repo_url":"https://github.com/idc9/py_jive","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"angle-based-joint-and-individual-variation","repo_url":"https://github.com/idc9/r_jive","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"angle-based-joint-and-individual-variation","repo_url":"https://github.com/justicesuker/DMMD_Code","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"angle-based-joint-and-individual-variation","repo_url":"https://github.com/thomaskeefe/jive_jackstraw","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1704.02060","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}