Euler Principal Component Analysis

  • Authors:
  • Stephan Liwicki;Georgios Tzimiropoulos;Stefanos Zafeiriou;Maja Pantic

  • Affiliations:
  • Department of Computing, Imperial College London, London, UK SW7 2AZ;Department of Computing, Imperial College London, London, UK SW7 2AZ and School of Computer Science, University of Lincoln, Lincoln, UK LN6 7TS;Department of Computing, Imperial College London, London, UK SW7 2AZ;Department of Computing, Imperial College London, London, UK SW7 2AZ and Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, Enschede, The Netherlands

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 2013
  • Euler clustering

    IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence

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Abstract

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