{"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/deep-clustering-and-representation-learning","title":"Generalized Clustering and Multi-Manifold Learning with Geometric Structure Preservation","arxiv_id":"2009.09590","date":"2020-09-21","proceeding":null,"authors":["Lirong Wu","Zicheng Liu","Zelin Zang","Jun Xia","Siyuan Li","Stan Z. Li"],"abstract":"Though manifold-based clustering has become a popular research topic, we observe that one important factor has been omitted by these works, namely that the defined clustering loss may corrupt the local and global structure of the latent space. In this paper, we propose a novel Generalized Clustering and Multi-manifold Learning (GCML) framework with geometric structure preservation for generalized data, i.e., not limited to 2-D image data and has a wide range of applications in speech, text, and biology domains. In the proposed framework, manifold clustering is done in the latent space guided by a clustering loss. To overcome the problem that the clustering-oriented loss may deteriorate the geometric structure of the latent space, an isometric loss is proposed for preserving intra-manifold structure locally and a ranking loss for inter-manifold structure globally. Extensive experimental results have shown that GCML exhibits superior performance to counterparts in terms of qualitative visualizations and quantitative metrics, which demonstrates the effectiveness of preserving geometric structure.","url_abs":"https://arxiv.org/abs/2009.09590v4","url_pdf":"https://arxiv.org/pdf/2009.09590v4.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":"deep-clustering-and-representation-learning","repo_url":"https://github.com/lirongwu/gcml","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"deep-clustering","task_name":"Deep Clustering"},{"task_slug":"representation-learning","task_name":"Representation Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2009.09590","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2009.09590"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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