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arXiv · 2105.11634

Robust Principal Component Analysis Using a Novel Kernel Related with the L1-Norm

Hongyi Pan·Diaa Badawi·Erdem Koyuncu·A. Enis Cetin
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Abstract

We consider a family of vector dot products that can be implemented using sign changes and addition operations only. The dot products are energy-efficient as they avoid the multiplication operation entirely. Moreover, the dot products induce the $\ell_1$-norm, thus providing robustness to impulsive noise. First, we analytically prove that the dot products yield symmetric, positive semi-definite generalized covariance matrices, thus enabling principal component analysis (PCA). Moreover, the generalized covariance matrices can be constructed in an Energy Efficient (EEF) manner due to the multiplication-free property of the underlying vector products. We present image reconstruction examples in which our EEF PCA method result in the highest peak signal-to-noise ratios compared to the ordinary $\ell_2$-PCA and the recursive $\ell_1$-PCA.

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Hongyi Pan, Diaa Badawi, Erdem Koyuncu, A. Enis Cetin. 2021-05-25. Robust Principal Component Analysis Using a Novel Kernel Related with the L1-Norm. https://arxiv.org/abs/2105.11634

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