{"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/unsupervised-metric-learning-in-presence-of","title":"Unsupervised Metric Learning in Presence of Missing Data","arxiv_id":"1807.07610","date":"2018-07-19","proceeding":null,"authors":["Anna C. Gilbert","Rishi Sonthalia"],"abstract":"For many machine learning tasks, the input data lie on a low-dimensional\nmanifold embedded in a high dimensional space and, because of this\nhigh-dimensional structure, most algorithms are inefficient. The typical\nsolution is to reduce the dimension of the input data using standard dimension\nreduction algorithms such as ISOMAP, LAPLACIAN EIGENMAPS or LLES. This\napproach, however, does not always work in practice as these algorithms require\nthat we have somewhat ideal data. Unfortunately, most data sets either have\nmissing entries or unacceptably noisy values. That is, real data are far from\nideal and we cannot use these algorithms directly. In this paper, we focus on\nthe case when we have missing data. Some techniques, such as matrix completion,\ncan be used to fill in missing data but these methods do not capture the\nnon-linear structure of the manifold. Here, we present a new algorithm\nMR-MISSING that extends these previous algorithms and can be used to compute\nlow dimensional representation on data sets with missing entries. We\ndemonstrate the effectiveness of our algorithm by running three different\nexperiments. We visually verify the effectiveness of our algorithm on synthetic\nmanifolds, we numerically compare our projections against those computed by\nfirst filling in data using nlPCA and mDRUR on the MNIST data set, and we also\nshow that we can do classification on MNIST with missing data. We also provide\na theoretical guarantee for MR-MISSING under some simplifying assumptions.","url_abs":"http://arxiv.org/abs/1807.07610v3","url_pdf":"http://arxiv.org/pdf/1807.07610v3.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":"unsupervised-metric-learning-in-presence-of","repo_url":"https://github.com/rsonthal/MRMissing.jl","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"unsupervised-metric-learning-in-presence-of","repo_url":"https://github.com/UnofficialJuliaMirror/MRMissing.jl-d89fa356-2490-5e87-a4cc-d004309f6659","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"unsupervised-metric-learning-in-presence-of","repo_url":"https://github.com/UnofficialJuliaMirrorSnapshots/MRMissing.jl-d89fa356-2490-5e87-a4cc-d004309f6659","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"},{"task_slug":"matrix-completion","task_name":"Matrix Completion"},{"task_slug":"metric-learning","task_name":"Metric Learning"}],"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}