{"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/spherical-principal-component-analysis","title":"Spherical Principal Component Analysis","arxiv_id":"1903.06877","date":"2019-03-16","proceeding":null,"authors":["Kai Liu","Qiuwei Li","Hua Wang","Gongguo Tang"],"abstract":"Principal Component Analysis (PCA) is one of the most important methods to\nhandle high dimensional data. However, most of the studies on PCA aim to\nminimize the loss after projection, which usually measures the Euclidean\ndistance, though in some fields, angle distance is known to be more important\nand critical for analysis. In this paper, we propose a method by adding\nconstraints on factors to unify the Euclidean distance and angle distance.\nHowever, due to the nonconvexity of the objective and constraints, the\noptimized solution is not easy to obtain. We propose an alternating linearized\nminimization method to solve it with provable convergence rate and guarantee.\nExperiments on synthetic data and real-world datasets have validated the\neffectiveness of our method and demonstrated its advantages over state-of-art\nclustering methods.","url_abs":"http://arxiv.org/abs/1903.06877v1","url_pdf":"http://arxiv.org/pdf/1903.06877v1.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":"spherical-principal-component-analysis","repo_url":"https://github.com/liukaizhijia/spherical-PCA","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"methods":[{"method_slug":"pca","method_name":"PCA"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1903.06877","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}