Tangent Hyperplane Kernel Principal Component Analysis for Denoising

Im J.-K.; Apley D. W.; Runger G. C.

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Tangent Hyperplane Kernel Principal Component Analysis for Denoising

机译：切线超平面核主成分分析

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Kernel principal component analysis (KPCA) is a method widely used for denoising multivariate data. Using geometric arguments, we investigate why a projection operation inherent to all existing KPCA denoising algorithms can sometimes cause very poor denoising. Based on this, we propose a modification to the projection operation that remedies this problem and can be incorporated into any of the existing KPCA algorithms. Using toy examples and real datasets, we show that the proposed algorithm can substantially improve denoising performance and is more robust to misspecification of an important tuning parameter.

机译：内核主成分分析（KPCA）是一种广泛用于对多元数据进行去噪的方法。使用几何参数，我们研究了为什么所有现有KPCA去噪算法固有的投影操作有时会导致非常差的去噪。基于此，我们建议对投影操作进行修改，以解决此问题，并且可以将其合并到任何现有的KPCA算法中。通过使用玩具示例和真实数据集，我们证明了所提出的算法可以显着提高去噪性能，并且对重要调音参数的错误指定更为健壮。

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《Neural Networks and Learning Systems, IEEE Transactions on》 |2012年第4期|p.644-656|共13页
作者
Im J.-K.; Apley D. W.; Runger G. C.;
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作者单位

Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL, USA;

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正文语种 eng
中图分类
关键词
Denoising; kernel; kernel principal component analysis (KPCA); preimage problem;

机译：去噪;内核;内核主成分分析（KPCA）;原像问题;

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1. Nonlinear denoising and analysis of neuroimages with kernel principal component analysis and pre-image estimation [J] . RasmussenP.M., AbrahamsenT.J., MadsenK.H., NeuroImage . 2012,第3期

机译：神经核的非线性降噪与核主成分分析和图像前估计
2. Projection-free kernel principal component analysis for denoising [J] . Anh Tuan Bui, Im Joon-Ku, Apley Daniel W., Neurocomputing . 2019,第SEPa10期

机译：去噪的无投影核主成分分析
3. Projection-free kernel principal component analysis for denoising [J] . Anh Tuan Bui, Im Joon-Ku, Apley Daniel W., Neurocomputing . 2019,第Sepa10期

机译：脱色的非预测内核主成分分析
4. COMPREHENSIVE EVALUATION OF PARALLEL MECHANISM AND ROBOT PERFORMANCE BASED ON PRINCIPAL COMPONENT ANALYSIS AND KERNEL PRINCIPAL COMPONENT ANALYSIS [C] . Liming Li, Jing Zhao Mechanisms and robotics conference;ASME international design engineering technical conferences and computers and information in engineering conference . 2016

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5. Efficient Clustering via Kernel Principal Component Analysis and Optimal One-Dimensional Thresholding [D] . Bhide, Nachiket. 2021

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6. A diffusion-matched principal component analysis (DM-PCA) based two-channel denoising procedure for high-resolution diffusion-weighted MRI [O] . Nan-kuei Chen, Hing-Chiu Chang, Ali Bilgin, -1

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7. Fast kernel Fisher discriminant analysis via approximating the kernel principal component analysis [O] . Wang J, Li Q, You J, 2011

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Tangent Hyperplane Kernel Principal Component Analysis for Denoising

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