论文标题
通过自适应深度分位数函数的抗偶像和图形异常探索
Antimodes and Graphical Anomaly Exploration via Adaptive Depth Quantile Functions
论文作者
论文摘要
这项工作提出并研究了一种用于异常检测的新方法，并表明它在各种欧几里得和非欧国人情况下具有竞争力。它基于深度分位函数（DQF）方法的扩展。 DQF方法通过单个变量的函数编码有关点云的几何信息，而数据集中的每个观察值都与单个此类函数相关联。绘制这些功能提供了一个非常有益的可视化方面。该技术可以应用于希尔伯特空间中的任何数据。 所提出的异常检测方法是由数据在数据生成分布中存在的数据息息相关的几何见解。将这种见解与对DQF形状的新理论理解结合起来，引起了提出的自适应DQF（ADQF）方法。各种数据集的应用说明了DQF和ADQF强大的异常检测性能以及其可视化方面的好处。
This work proposes and investigates a novel method for anomaly detection and shows it to be competitive in a variety of Euclidean and non-Euclidean situations. It is based on an extension of the depth quantile functions (DQF) approach. The DQF approach encodes geometric information about a point cloud via functions of a single variable, whereas each observation in a data set is associated with a single such function. Plotting these functions provides a very beneficial visualization aspect. This technique can be applied to any data lying in a Hilbert space. The proposed anomaly detection approach is motivated by the geometric insight of the presence of anomalies in data being tied to the existence of antimodes in the data generating distribution. Coupling this insight with novel theoretical understanding into the shape of the DQFs gives rise to the proposed adaptive DQF (aDQF) methodology. Applications to various data sets illustrate the DQF and aDQF's strong anomaly detection performance, and the benefits of its visualization aspects.
