Wang Yunge, Zhang Lingling, Si Tong, Bishop Graham, Gong Haijun
Department of Mathematics and Statistics, Saint Louis University, St. Louis, MO 63103, USA.
Department of Mathematics and Statistics, University at Albany SUNY, Albany, NY 12222, USA.
Algorithms. 2025 Feb;18(2). doi: 10.3390/a18020062. Epub 2025 Jan 24.
The purpose of anomaly detection is to identify special data points or patterns that significantly deviate from the expected or typical behavior of the majority of the data, and it has a wide range of applications across various domains. Most existing statistical and machine learning-based anomaly detection algorithms face challenges when applied to high-dimensional data. For instance, the unconstrained least-squares importance fitting (uLSIF) method, a state-of-the-art anomaly detection approach, encounters the unboundedness problem under certain conditions. In this study, we propose a scaled Bregman divergence-based anomaly detection algorithm using both least absolute deviation and least-squares loss for parameter learning. This new algorithm effectively addresses the unboundedness problem, making it particularly suitable for high-dimensional data. The proposed technique was evaluated on both synthetic and real-world high-dimensional time series datasets, demonstrating its effectiveness in detecting anomalies. Its performance was also compared to other density ratio estimation-based anomaly detection methods.
异常检测的目的是识别那些显著偏离大多数数据预期或典型行为的特殊数据点或模式，并且它在各个领域都有广泛的应用。大多数现有的基于统计和机器学习的异常检测算法在应用于高维数据时面临挑战。例如，无约束最小二乘重要性拟合（uLSIF）方法，一种先进的异常检测方法，在某些条件下会遇到无界问题。在本研究中，我们提出了一种基于缩放布雷格曼散度的异常检测算法，该算法在参数学习中同时使用了最小绝对偏差和最小二乘损失。这种新算法有效地解决了无界问题，使其特别适用于高维数据。我们在所提出的技术在合成和真实世界的高维时间序列数据集上进行了评估，证明了其在检测异常方面的有效性。其性能也与其他基于密度比估计的异常检测方法进行了比较。
