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Kernel dependence analysis and graph structure morphing for novelty detection with high-dimensional small size data set

机译：高维小尺寸数据集新奇检测核依赖性分析与图形结构变形

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摘要

In this study, we propose a new approach for novelty detection that uses kernel dependence techniques for characterizing the statistical dependencies of random variables (RV) and use this characterization as a basis for making inference. Considering the statistical dependencies of the RVs in multivariate problems is an important challenge in novelty detection. Ignoring these dependencies, when they are strong, may result in inaccurate inference, usually in the form of high false positive rates. Previously studied methods, such as graphical models or conditional classifiers, mainly use density estimation techniques as their main learning element to characterize the dependencies of the relevant RVs. Therefore, they suffer from the curse of dimensionality which makes them unable to handle high-dimensional problems. The proposed method, however, avoids using density estimation methods, and rather, employs a kernel method, which is robust with respect to dimensionality, to encode the dependencies and hence, it can handle problems with arbitrarily high-dimensional data. Furthermore, the proposed method does not need any prior information about the dependence structure of the RVs; thus, it is applicable to general novelty detection problems with no simplifying assumption. To test the performance of the proposed method, we apply it to realistic application problems for analyzing sensor networks and compare the results to those obtained by peer methods.
机译：在本研究中，我们提出了一种新的新颖性检测方法，它使用内核依赖性技术来表征随机变量（RV）的统计依赖性并使用该表征作为推理的基础。考虑到多变量问题中RV的统计依赖性是新颖性检测中的重要挑战。忽略这些依赖性，当它们强时，可能导致不准确的推断，通常以高误阳性率的形式。以前研究的方法，例如图形模型或条件分类器，主要使用密度估计技术作为其主要学习元素，以表征相关RV的依赖关系。因此，它们遭受维度的诅咒，这使得它们无法处理高维问题。然而，所提出的方法避免了使用密度估计方法，而是采用核心对维度的鲁棒方法来编码依赖性，因此可以处理任意高维数据的问题。此外，所提出的方法不需要任何关于RV的依赖结构的先前信息;因此，它适用于普通新颖性检测问题，没有简化的假设。为了测试所提出的方法的性能，我们将其应用于用于分析传感器网络的现实应用问题，并将结果与​​通过对等方法获得的结果进行比较。

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