Robust Principal Component Analysis Using a Novel Kernel Related with the $L_{1}$ -Norm
Robust Principal Component Analysis Using a Novel Kernel Related with the $L_{1}$ -Norm
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DOI：
10.23919/eusipco54536.2021.9615961
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发表时间：
2021-05
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通讯作者：
Hongyi Pan;Diaa Badawi;Erdem Koyuncu;A. Cetin
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作者：
Hongyi Pan;Diaa Badawi;Erdem Koyuncu;A. Cetin
我们考虑一系列只能使用符号更改和加法运算来实现的矢量点积。点积非常节能，因为它们完全避免了乘法运算。此外，点积产生 $\ell_{1}$ -范数，从而提供对脉冲噪声的鲁棒性。首先，我们分析证明点积产生对称的半正定广义协方差矩阵，从而实现主成分分析（PCA）。此外，由于基础向量乘积的免乘性质，广义协方差矩阵可以以能量有效（EEF）方式构建。我们提出了图像重建示例，其中与普通的 $\ell_{2}$ -PCA 和递归 $\ell_{1}$ - PCA 相比，我们的 EEF PCA 方法产生了最高的峰值信噪比。
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.