{"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/similarity-learning-via-kernel-preserving","title":"Similarity Learning via Kernel Preserving Embedding","arxiv_id":"1903.04235","date":"2019-03-11","proceeding":null,"authors":["Zhao Kang","Yiwei Lu","Yuanzhang Su","Changsheng Li","Zenglin Xu"],"abstract":"Data similarity is a key concept in many data-driven applications. Many\nalgorithms are sensitive to similarity measures. To tackle this fundamental\nproblem, automatically learning of similarity information from data via\nself-expression has been developed and successfully applied in various models,\nsuch as low-rank representation, sparse subspace learning, semi-supervised\nlearning. However, it just tries to reconstruct the original data and some\nvaluable information, e.g., the manifold structure, is largely ignored. In this\npaper, we argue that it is beneficial to preserve the overall relations when we\nextract similarity information. Specifically, we propose a novel similarity\nlearning framework by minimizing the reconstruction error of kernel matrices,\nrather than the reconstruction error of original data adopted by existing work.\nTaking the clustering task as an example to evaluate our method, we observe\nconsiderable improvements compared to other state-of-the-art methods. More\nimportantly, our proposed framework is very general and provides a novel and\nfundamental building block for many other similarity-based tasks. Besides, our\nproposed kernel preserving opens up a large number of possibilities to embed\nhigh-dimensional data into low-dimensional space.","url_abs":"http://arxiv.org/abs/1903.04235v1","url_pdf":"http://arxiv.org/pdf/1903.04235v1.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":"similarity-learning-via-kernel-preserving","repo_url":"https://github.com/sckangz/SLKE","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1903.04235","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}