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Anomaly Detection in High-Dimensional Time Series Data with Scaled Bregman Divergence.

Yunge Wang1, Lingling Zhang2, Tong Si3

  • 1Department of Mathematics and Statistics, Saint Louis University, St. Louis, MO 63103, USA.

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This study introduces a new anomaly detection algorithm that effectively handles high-dimensional data by addressing the unboundedness problem. The novel method improves anomaly identification in complex datasets.

Keywords:
anomaly detectiondensity ratio estimationleast absolute deviationscaled Bregman divergence

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Area of Science:

  • Data Science
  • Machine Learning
  • Statistics

Background:

  • Anomaly detection identifies data points deviating from normal behavior, with broad applications.
  • High-dimensional data presents challenges for existing anomaly detection algorithms.
  • The unconstrained least-squares importance fitting (uLSIF) method struggles with unboundedness in certain high-dimensional scenarios.

Purpose of the Study:

  • To propose a novel anomaly detection algorithm designed for high-dimensional data.
  • To overcome the unboundedness problem encountered by existing methods like uLSIF.
  • To enhance the accuracy and applicability of anomaly detection in complex datasets.

Main Methods:

  • Developed a scaled Bregman divergence-based anomaly detection algorithm.
  • Incorporated both least absolute deviation and least-squares loss for parameter learning.
  • Evaluated the algorithm on synthetic and real-world high-dimensional time series datasets.

Main Results:

  • The proposed algorithm effectively addresses the unboundedness problem.
  • Demonstrated superior performance in detecting anomalies within high-dimensional time series data.
  • Outperformed other density ratio estimation-based anomaly detection methods in comparative analyses.

Conclusions:

  • The scaled Bregman divergence-based algorithm is a robust solution for anomaly detection in high-dimensional data.
  • This method offers a significant improvement over existing techniques, particularly in challenging data environments.
  • The algorithm's effectiveness on real-world datasets validates its practical utility.