{"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/warped-mixtures-for-nonparametric-cluster-1","title":"Warped Mixtures for Nonparametric Cluster Shapes","arxiv_id":"1206.1846","date":"2012-06-08","proceeding":null,"authors":["Tomoharu Iwata","David Duvenaud","Zoubin Ghahramani"],"abstract":"A mixture of Gaussians fit to a single curved or heavy-tailed cluster will report that the data contains many clusters. To produce more appropriate clusterings, we introduce a model which warps a latent mixture of Gaussians to produce nonparametric cluster shapes. The possibly low-dimensional latent mixture model allows us to summarize the properties of the high-dimensional clusters (or density manifolds) describing the data. The number of manifolds, as well as the shape and dimension of each manifold is automatically inferred. We derive a simple inference scheme for this model which analytically integrates out both the mixture parameters and the warping function. We show that our model is effective for density estimation, performs better than infinite Gaussian mixture models at recovering the true number of clusters, and produces interpretable summaries of high-dimensional datasets.","url_abs":"https://arxiv.org/abs/1206.1846v2","url_pdf":"https://arxiv.org/pdf/1206.1846v2.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":"warped-mixtures-for-nonparametric-cluster-1","repo_url":"https://github.com/duvenaud/warped-mixtures","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"density-estimation","task_name":"Density Estimation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}