Euler principal component analysis

Stephan Liwicki, Georgios Tzimiropoulos, Stefanos Zafeiriou, Maja Pantic

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    72 Citations (Scopus)


    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.
    Original languageUndefined
    Pages (from-to)498-518
    Number of pages21
    JournalInternational journal of computer vision
    Issue number3
    Publication statusPublished - Feb 2013


    • METIS-302618
    • Euler PCA · Robust subspace · Online learning · Tracking ·Background modeling
    • IR-89548
    • EWI-24259
    • HMI-HF: Human Factors
    • EC Grant Agreement nr.: FP7/288235
    • EC Grant Agreement nr.: FP7/2007-2013
    • EC Grant Agreement nr.: ERC-2007-STG-203143 (MAHNOB)

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