International Journal of Computer Vision

, Volume 101, Issue 3, pp 498–518 | Cite as

Euler Principal Component Analysis

  • Stephan Liwicki
  • Georgios Tzimiropoulos
  • Stefanos Zafeiriou
  • Maja Pantic


Principal Component Analysis (PCA) is perhaps the most prominent learning tool for dimensionality reduction in pattern recognition and computer vision. However, the 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.


Euler PCA Robust subspace Online learning Tracking Background modeling 



The research presented in this paper is supported in part by the European Research Council (ERC) under the ERC Starting Grant Agreement ERC-2007- StG-203143 (MAHNOB). The work of S. Liwicki is supported by the Engineering and Physical Science Research Council DTA Studentship. The work of G. Tzimiropoulos is currently supported in part by the European Community’s 7th Framework Programme FP7/2007-2013 under Grant Agreement 288235 (FROG).

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Stephan Liwicki
    • 1
  • Georgios Tzimiropoulos
    • 1
    • 2
  • Stefanos Zafeiriou
    • 1
  • Maja Pantic
    • 1
    • 3
  1. 1.Department of ComputingImperial College LondonLondonUK
  2. 2.School of Computer ScienceUniversity of LincolnLincolnUK
  3. 3.Faculty of Electrical Engineering, Mathematics and Computer ScienceUniversity of TwenteEnschedeThe Netherlands

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