{"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/semi-supervised-learning-via-sparse-label","title":"Semi-Supervised Learning via Sparse Label Propagation","arxiv_id":"1612.01414","date":"2016-12-05","proceeding":null,"authors":["Alexander Jung","Alfred O. Hero III","Alexandru Mara","Saeed Jahromi"],"abstract":"This work proposes a novel method for semi-supervised learning from partially\nlabeled massive network-structured datasets, i.e., big data over networks. We\nmodel the underlying hypothesis, which relates data points to labels, as a\ngraph signal, defined over some graph (network) structure intrinsic to the\ndataset. Following the key principle of supervised learning, i.e., similar\ninputs yield similar outputs, we require the graph signals induced by labels to\nhave small total variation. Accordingly, we formulate the problem of learning\nthe labels of data points as a non-smooth convex optimization problem which\namounts to balancing between the empirical loss, i.e., the discrepancy with\nsome partially available label information, and the smoothness quantified by\nthe total variation of the learned graph signal. We solve this optimization\nproblem by appealing to a recently proposed preconditioned variant of the\npopular primal-dual method by Pock and Chambolle, which results in a sparse\nlabel propagation algorithm. This learning algorithm allows for a highly\nscalable implementation as message passing over the underlying data graph. By\napplying concepts of compressed sensing to the learning problem, we are also\nable to provide a transparent sufficient condition on the underlying network\nstructure such that accurate learning of the labels is possible. We also\npresent an implementation of the message passing formulation allows for a\nhighly scalable implementation in big data frameworks.","url_abs":"http://arxiv.org/abs/1612.01414v4","url_pdf":"http://arxiv.org/pdf/1612.01414v4.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":"semi-supervised-learning-via-sparse-label","repo_url":"https://github.com/oleksii-a/sparse_label_propagation","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[{"task_slug":"compressed-sensing","task_name":"compressed sensing"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1612.01414","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}