{"type":"ScholarlyArticle","title":"Angle Principal Component Analysis","authors":[{"name":"Qianqian Wang","slug":"qianqian-wang","given":"Qianqian","family":"Wang","affiliation":"State Key Lab. of Integrated Services Networks , Xidian University"},{"name":"Quanxue Gao","slug":"quanxue-gao","given":"Quanxue","family":"Gao","affiliation":"State Key Lab. of Integrated Services Networks , Xidian University"},{"name":"Xinbo Gao","slug":"xinbo-gao","given":"Xinbo","family":"Gao","affiliation":"State Key Lab. of Integrated Services Networks , Xidian University"},{"name":"Feiping Nie","slug":"feiping-nie","given":"Feiping","family":"Nie","affiliation":"State Key Lab. of Integrated Services Networks , Xidian University"}],"abstract":"Recently, many ℓ1-norm based PCA methods have been developed for dimensionality reduction, but they do not explicitly consider the reconstruction error. Moreover, they do not take into account the relationship between reconstruction error and variance of projected data. This reduces the robustness of algorithms. To handle this problem, a novel formulation for PCA, namely angle PCA, is proposed. Angle PCA employs ℓ2-norm to measure reconstruction error and variance of projected da-ta and maximizes the summation of ratio between variance and reconstruction error of each data. Angle PCA not only is robust to outliers but also retains PCA’s desirable property such as rotational invariance. To solve Angle PCA, we propose an iterative algorithm, which has closed-form solution in each iteration. Extensive experiments on several face image databases illustrate that our method is overall superior to the other robust PCA algorithms, such as PCA, PCA-L1 greedy, PCA-L1 nongreedy and HQ-PCA.","doi":"10.24963/ijcai.2017/409","url":"https://ijcai.org/proceedings/2017/409","pdf":"https://ijcai.org/proceedings/2017/0409.pdf","markdown":"https://ijcai.org/proceedings/2017/409.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/409","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Machine Learning S-Z","track":"Main track","number":409,"pages":{"first":2936,"last":2942},"keywords":["Machine Learning: Unsupervised Learning","Machine Learning: Machine Learning"],"videos":[],"references":[{"position":1,"raw":"[Belhumeur et al., 1997] Peter N. 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