Euler principal component analysis

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 0920-5691

Full content URL: http://dx.doi.org/10.1007/s11263-012-0558-z

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Item Type:Article
Item Status:Live Archive

Abstract

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 stateof-
the-art approaches.

Additional Information: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 stateof- the-art approaches.
Keywords:PCA
Subjects:G Mathematical and Computer Sciences > G760 Machine Learning
Divisions:College of Science > School of Computer Science
ID Code:7447
Deposited On:07 Feb 2013 10:11

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