{"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/sparse-kernel-pca-for-outlier-detection","title":"Sparse Kernel PCA for Outlier Detection","arxiv_id":"1809.02497","date":"2018-09-07","proceeding":null,"authors":["Rudrajit Das","Aditya Golatkar","Suyash P. Awate"],"abstract":"In this paper, we propose a new method to perform Sparse Kernel Principal\nComponent Analysis (SKPCA) and also mathematically analyze the validity of\nSKPCA. We formulate SKPCA as a constrained optimization problem with elastic\nnet regularization (Hastie et al.) in kernel feature space and solve it. We\nconsider outlier detection (where KPCA is employed) as an application for\nSKPCA, using the RBF kernel. We test it on 5 real-world datasets and show that\nby using just 4% (or even less) of the principal components (PCs), where each\nPC has on average less than 12% non-zero elements in the worst case among all 5\ndatasets, we are able to nearly match and in 3 datasets even outperform KPCA.\nWe also compare the performance of our method with a recently proposed method\nfor SKPCA by Wang et al. and show that our method performs better in terms of\nboth accuracy and sparsity. We also provide a novel probabilistic proof to\njustify the existence of sparse solutions for KPCA using the RBF kernel. To the\nbest of our knowledge, this is the first attempt at theoretically analyzing the\nvalidity of SKPCA.","url_abs":"http://arxiv.org/abs/1809.02497v2","url_pdf":"http://arxiv.org/pdf/1809.02497v2.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":"sparse-kernel-pca-for-outlier-detection","repo_url":"https://github.com/AdityaGolatkar/Sparse-Kernel-PCA-for-outlier-detection","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"outlier-detection","task_name":"Outlier Detection"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}