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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >Noise Level Estimation for Model Selection in Kernel PCA Denoising
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Noise Level Estimation for Model Selection in Kernel PCA Denoising

机译：PCA去噪模型选择中的噪声水平估计

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摘要

One of the main challenges in unsupervised learning is to find suitable values for the model parameters. In kernel principal component analysis (kPCA), for example, these are the number of components, the kernel, and its parameters. This paper presents a model selection criterion based on distance distributions (MDDs). This criterion can be used to find the number of components and the parameter of radial basis function kernels by means of spectral comparison between information and noise. The noise content is estimated from the statistical moments of the distribution of distances in the original dataset. This allows for a type of randomization of the dataset, without actually having to permute the data points or generate artificial datasets. After comparing the eigenvalues computed from the estimated noise with the ones from the input dataset, information is retained and maximized by a set of model parameters. In addition to the model selection criterion, this paper proposes a modification to the fixed-size method and uses the incomplete Cholesky factorization, both of which are used to solve kPCA in large-scale applications. These two approaches, together with the model selection MDD, were tested in toy examples and real life applications, and it is shown that they outperform other known algorithms.
机译：在无监督学习中的主要挑战之一是为模型参数找到合适的值。例如，在内核主成分分析（kPCA）中，这些是组件数量，内核及其参数。本文提出了一种基于距离分布（MDD）的模型选择标准。通过信息和噪声之间的频谱比较，可以使用该标准来找到分量数和径向基函数核的参数。噪声含量是根据原始数据集中距离分布的统计矩估计的。这允许对数据集进行某种类型的随机化，而无需实际置换数据点或生成人工数据集。在将根据估计的噪声计算出的特征值与输入数据集中的特征值进行比较之后，信息会被一组模型参数保留并最大化。除了模型选择标准外，本文还对固定大小方法进行了修改，并使用了不完全的Cholesky因子分解法，这两种方法均用于解决大规模应用中的kPCA。这两种方法与模型选择MDD一起在玩具示例和实际应用中进行了测试，结果表明它们优于其他已知算法。

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