Robust Principal Component Analysis Using a Novel Kernel Related with the L1-Norm
| Autor: | Hongyi Pan, Diaa Badawi, Erdem Koyuncu, A. Enis Cetin |
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| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Machine Learning Image and Video Processing (eess.IV) 0202 electrical engineering electronic engineering information engineering FOS: Electrical engineering electronic engineering information engineering 020206 networking & telecommunications 020201 artificial intelligence & image processing 02 engineering and technology Electrical Engineering and Systems Science - Image and Video Processing Machine Learning (cs.LG) |
| DOI: | 10.48550/arxiv.2105.11634 |
| Popis: | 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. Comment: 6 pages, 3 tables and one figure |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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