反模态与通过自适应深度分位函数的图形异常探索
Antimodes and Graphical Anomaly Exploration via Adaptive Depth Quantile Functions
AI总结：
本文提出了一种新颖的异常检测方法，基于深度分位函数的扩展，在欧几里得和非欧几里得情况下均表现出竞争力，通过可视化分析提升异常检测性能。
摘要：
本文提出并研究了一种新颖的异常检测方法，该方法基于深度分位函数（DQF）的扩展。DQF方法通过单变量函数编码点云的几何信息，每个数据点关联一个单变量函数。绘制这些函数提供有益的可视化视角。该技术可应用于任何位于希尔伯特空间中的数据。所提出的异常检测方法受到数据中异常的存在与数据生成分布中反模态存在的几何洞察的启发。结合对DQF形状的新型理论理解，提出了自适应DQF（aDQF）方法。对各种数据集的应用展示了DQF和aDQF在异常检测中的强大性能以及其可视化方面的优势。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
