{"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/model-based-clustering-in-very-high","title":"Model-based clustering in very high dimensions via adaptive projections","arxiv_id":"1902.08472","date":"2019-02-22","proceeding":null,"authors":["Bernd Taschler","Frank Dondelinger","Sach Mukherjee"],"abstract":"Mixture models are a standard approach to dealing with heterogeneous data\nwith non-i.i.d. structure. However, when the dimension $p$ is large relative to\nsample size $n$ and where either or both of means and covariances/graphical\nmodels may differ between the latent groups, mixture models face statistical\nand computational difficulties and currently available methods cannot\nrealistically go beyond $p \\! \\sim \\! 10^4$ or so. We propose an approach\ncalled Model-based Clustering via Adaptive Projections (MCAP). Instead of\nestimating mixtures in the original space, we work with a low-dimensional\nrepresentation obtained by linear projection. The projection dimension itself\nplays an important role and governs a type of bias-variance tradeoff with\nrespect to recovery of the relevant signals. MCAP sets the projection dimension\nautomatically in a data-adaptive manner, using a proxy for the assignment risk.\nCombining a full covariance formulation with the adaptive projection allows\ndetection of both mean and covariance signals in very high dimensional\nproblems. We show real-data examples in which covariance signals are reliably\ndetected in problems with $p \\! \\sim \\! 10^4$ or more, and simulations going up\nto $p = 10^6$. In some examples, MCAP performs well even when the mean signal\nis entirely removed, leaving differential covariance structure in the\nhigh-dimensional space as the only signal. Across a number of regimes, MCAP\nperforms as well or better than a range of existing methods, including a\nrecently-proposed $\\ell_1$-penalized approach; and performance remains broadly\nstable with increasing dimension. MCAP can be run \"out of the box\" and is fast\nenough for interactive use on large-$p$ problems using standard desktop\ncomputing resources.","url_abs":"http://arxiv.org/abs/1902.08472v1","url_pdf":"http://arxiv.org/pdf/1902.08472v1.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":"model-based-clustering-in-very-high","repo_url":"https://github.com/btaschler/mcap","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}