Generalized mean for robust principal component analysis

doi:10.1016/j.patcog.2016.01.002

Pattern Recognition

Volume 54, June 2016, Pages 116-127

https://doi.org/10.1016/j.patcog.2016.01.002 Get rights and content

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Highlights

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We propose a robust principal component analysis.
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The generalized mean is used in the proposed method instead of the arithmetic mean.
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A novel method is also presented to solve our optimization problem.

Abstract

In this paper, we propose a robust principal component analysis (PCA) to overcome the problem that PCA is prone to outliers included in the training set. Different from the other alternatives which commonly replace L₂-norm by other distance measures, the proposed method alleviates the negative effect of outliers using the characteristic of the generalized mean keeping the use of the Euclidean distance. The optimization problem based on the generalized mean is solved by a novel method. We also present a generalized sample mean, which is a generalization of the sample mean, to estimate a robust mean in the presence of outliers. The proposed method shows better or equivalent performance than the conventional PCAs in various problems such as face reconstruction, clustering, and object categorization.

Keywords

Generalized mean

Principal component analysis

Robust PCA

Dimensionality reduction

Cited by (0)

Jiyong Oh received the B.S. degree from the School of Electronic Engineering, Ajou University, Korea in 2004 and the M.S. and Ph.D. degrees from the School of Electrical Engineering and Computer Science, Seoul National University, Korea in 2006 and 2012, respectively. He was a postdoctoral researcher in Sungkyunkwan and Ajou University, Korea in 2012 and 2013, respectively. Since Sept. 2013, he has been a research fellow in the graduate school of convergence science and technology, Seoul National University, Korea, where he currently holds a position of BK assistant professor. His research interests include feature extraction, machine learning, pattern recognition, computer vision, and their applications.

Nojun Kwak was born in Seoul, Korea in 1974. He received the BS, MS, and PhD degrees from the School of Electrical Engineering and Computer Science, Seoul National University, Seoul, Korea, in 1997, 1999 and 2003 respectively. From 2003 to 2006, he was with Samsung Electronics. In 2006, he joined Seoul National University as a BK21 Assistant Professor. From 2007 to 2013, he was a Faculty Member of the Department of Electrical and Computer Engineering, Ajou University, Suwon, Korea. Since 2013, he has been with the Graduate School of Convergence Science and Technology, Seoul National University, Seoul, Korea, where he is currently an Associate Professor. His current research interests include pattern recognition, machine learning, computer vision, data mining, image processing, and their applications.