{"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/minimum-spectral-connectivity-projection","title":"Minimum Spectral Connectivity Projection Pursuit","arxiv_id":"1509.01546","date":"2015-09-04","proceeding":null,"authors":["David P. Hofmeyr","Nicos G. Pavlidis","Idris A. Eckley"],"abstract":"We study the problem of determining the optimal low dimensional projection\nfor maximising the separability of a binary partition of an unlabelled dataset,\nas measured by spectral graph theory. This is achieved by finding projections\nwhich minimise the second eigenvalue of the graph Laplacian of the projected\ndata, which corresponds to a non-convex, non-smooth optimisation problem. We\nshow that the optimal univariate projection based on spectral connectivity\nconverges to the vector normal to the maximum margin hyperplane through the\ndata, as the scaling parameter is reduced to zero. This establishes a\nconnection between connectivity as measured by spectral graph theory and\nmaximal Euclidean separation. The computational cost associated with each\neigen-problem is quadratic in the number of data. To mitigate this issue, we\npropose an approximation method using microclusters with provable approximation\nerror bounds. Combining multiple binary partitions within a divisive\nhierarchical model allows us to construct clustering solutions admitting\nclusters with varying scales and lying within different subspaces. We evaluate\nthe performance of the proposed method on a large collection of benchmark\ndatasets and find that it compares favourably with existing methods for\nprojection pursuit and dimension reduction for data clustering.","url_abs":"http://arxiv.org/abs/1509.01546v3","url_pdf":"http://arxiv.org/pdf/1509.01546v3.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":"minimum-spectral-connectivity-projection","repo_url":"https://github.com/DavidHofmeyr/SCPP","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}