{"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/a-parameter-free-graph-reduction-for-spectral","title":"A parameter-free graph reduction for spectral clustering and SpectralNet","arxiv_id":"2302.13165","date":"2023-02-25","proceeding":null,"authors":["Mashaan Alshammari","John Stavrakakis","Masahiro Takatsuka"],"abstract":"Graph-based clustering methods like spectral clustering and SpectralNet are very efficient in detecting clusters of non-convex shapes. Unlike the popular $k$-means, graph-based clustering methods do not assume that each cluster has a single mean. However, these methods need a graph where vertices in the same cluster are connected by edges of large weights. To achieve this goal, many studies have proposed graph reduction methods with parameters. Unfortunately, these parameters have to be tuned for every dataset. We introduce a graph reduction method that does not require any parameters. First, the distances from every point $p$ to its neighbors are filtered using an adaptive threshold to only keep neighbors with similar surrounding density. Second, the similarities with close neighbors are computed and only high similarities are kept. The edges that survive these two filtering steps form the constructed graph that was passed to spectral clustering and SpectralNet. The experiments showed that our method provides a stable alternative, where other methods performance fluctuated according to the setting of their parameters.","url_abs":"https://arxiv.org/abs/2302.13165v1","url_pdf":"https://arxiv.org/pdf/2302.13165v1.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":"a-parameter-free-graph-reduction-for-spectral","repo_url":"https://github.com/mashaan14/SC-parameter-free","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"tf","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"graph-clustering","task_name":"Graph Clustering"},{"task_slug":"graph-embedding","task_name":"Graph Embedding"},{"task_slug":"spectral-graph-clustering","task_name":"Spectral Graph Clustering"},{"task_slug":"graph-partitioning","task_name":"graph partitioning"}],"methods":[{"method_slug":"spectral-clustering","method_name":"Spectral Clustering"},{"method_slug":"k-means-clustering","method_name":"k-Means Clustering"},{"method_slug":"k-nn","method_name":"k-NN"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}