In this paper, we address the problem of finding the pre-image of a feature vector in the feature space induced by a kernel. This is of central importance in some kernel applications, such as on using kernel principal component analysis (PCA) for image denois-ing. Unlike the traditional method in (Mika et al., 1998) which relies on nonlinear optimization, our proposed method directly finds the location of the pre-image based on distance constraints in the feature space. It is non-iterative, involves only linear algebra and does not suffer from numerical instability or local minimum problems. Performance of this method is evaluated on performing kernel PCA and kernel clustering on the USPS data set.
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机译：在本文中，我们解决了在由核引起的特征空间中找到特征向量的原像的问题。这在某些内核应用程序中至关重要，例如在使用内核主成分分析（PCA）进行图像去噪时。与（Mika et al。，1998）中依赖于非线性优化的传统方法不同，我们提出的方法基于特征空间中的距离约束直接找到原图像的位置。它是非迭代的，仅涉及线性代数，并且不存在数值不稳定或局部极小问题。在对USPS数据集执行内核PCA和内核群集时，会评估此方法的性能。
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