Euler principal component analysis

Liwicki, Stephan; Tzimiropoulos, Georgios; Zafeiriou, Stefanos; Pantic, Maja

Abstract

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.

• Journal Article Type: Article
• Publication Date: Feb 1, 2013
• Deposit Date: Jan 29, 2016
• Publicly Available Date: Jan 29, 2016
• Journal: International Journal of Computer Vision
• Print ISSN: 0920-5691
• Electronic ISSN: 1573-1405
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 101
• Issue: 3
• DOI: https://doi.org/10.1007/s11263-012-0558-z
• Keywords: Euler PCA, Robust Subspace, Online Learning, Tracking, Background Modeling
• Public URL: https://nottingham-repository.worktribe.com/output/1002863
• Publisher URL: http://link.springer.com/article/10.1007%2Fs11263-012-0558-z
• Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s11263-012-0558-z