Euler principal component analysis
Principal Component Analysis (PCA) is perhaps the most prominent learning tool for dimensionality reduction in pattern recognition and computer vision. However, the ℓ 2-norm employed by standard PCA is not robust to outliers. In this paper, we propose a kernel PCA method for fast and robust PCA, whi...
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| Format: | Article |
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Springer
2013
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| Online Access: | https://eprints.nottingham.ac.uk/31427/ |
| _version_ | 1848794198906503168 |
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| author | Liwicki, Stephan Tzimiropoulos, Georgios Zafeiriou, Stefanos Pantic, Maja |
| author_facet | Liwicki, Stephan Tzimiropoulos, Georgios Zafeiriou, Stefanos Pantic, Maja |
| author_sort | Liwicki, Stephan |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Principal Component Analysis (PCA) is perhaps the most prominent learning tool for dimensionality reduction in pattern recognition and computer vision. However, the ℓ 2-norm employed by standard PCA is not robust to outliers. In this paper, we propose a kernel PCA method for fast and robust PCA, which we call Euler-PCA (e-PCA). In particular, our algorithm utilizes a robust dissimilarity measure based on the Euler representation of complex numbers. We show that Euler-PCA retains PCA’s desirable properties while suppressing outliers. Moreover, we formulate Euler-PCA in an incremental learning framework which allows for efficient computation. In our experiments we apply Euler-PCA to three different computer vision applications for which our method performs comparably with other state-of-the-art approaches. |
| first_indexed | 2025-11-14T19:12:23Z |
| format | Article |
| id | nottingham-31427 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:12:23Z |
| publishDate | 2013 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-314272020-05-04T20:19:38Z https://eprints.nottingham.ac.uk/31427/ Euler principal component analysis Liwicki, Stephan Tzimiropoulos, Georgios Zafeiriou, Stefanos Pantic, Maja Principal Component Analysis (PCA) is perhaps the most prominent learning tool for dimensionality reduction in pattern recognition and computer vision. However, the ℓ 2-norm employed by standard PCA is not robust to outliers. In this paper, we propose a kernel PCA method for fast and robust PCA, which we call Euler-PCA (e-PCA). In particular, our algorithm utilizes a robust dissimilarity measure based on the Euler representation of complex numbers. We show that Euler-PCA retains PCA’s desirable properties while suppressing outliers. Moreover, we formulate Euler-PCA in an incremental learning framework which allows for efficient computation. In our experiments we apply Euler-PCA to three different computer vision applications for which our method performs comparably with other state-of-the-art approaches. Springer 2013-02 Article PeerReviewed Liwicki, Stephan, Tzimiropoulos, Georgios, Zafeiriou, Stefanos and Pantic, Maja (2013) Euler principal component analysis. International Journal of Computer Vision, 101 (3). pp. 498-518. ISSN 1573-1405 Euler PCA Robust Subspace Online Learning Tracking Background Modeling http://link.springer.com/article/10.1007%2Fs11263-012-0558-z doi:10.1007/s11263-012-0558-z doi:10.1007/s11263-012-0558-z |
| spellingShingle | Euler PCA Robust Subspace Online Learning Tracking Background Modeling Liwicki, Stephan Tzimiropoulos, Georgios Zafeiriou, Stefanos Pantic, Maja Euler principal component analysis |
| title | Euler principal component analysis |
| title_full | Euler principal component analysis |
| title_fullStr | Euler principal component analysis |
| title_full_unstemmed | Euler principal component analysis |
| title_short | Euler principal component analysis |
| title_sort | euler principal component analysis |
| topic | Euler PCA Robust Subspace Online Learning Tracking Background Modeling |
| url | https://eprints.nottingham.ac.uk/31427/ https://eprints.nottingham.ac.uk/31427/ https://eprints.nottingham.ac.uk/31427/ |