Novel semi-metrics for multivariate change point analysis and anomaly detection

Area of Science:

• Data Science
• Time Series Analysis
• Statistical Modeling

Background:

• Analyzing large collections of time series data presents challenges in identifying similarities and anomalies.
• Existing distance metrics like Hausdorff and Wasserstein may not be optimal for detecting subtle structural differences.

Purpose of the Study:

• To propose a new class of semi-metric distance measures, termed MJ distances, for enhanced time series similarity and anomaly detection.
• To evaluate the effectiveness of MJ distances against established metrics in identifying patterns within time series collections.

Main Methods:

• Introduction of MJ distances, a novel semi-metric for measuring distances between structural breaks in time series.
• Theoretical analysis of MJ distances' properties, including sensitivity to outliers and potential violation of the triangle inequality.
• Empirical validation using simulated data and real-world datasets (cryptocurrency, measles) with eigenvalue analysis.

Main Results:

• MJ distances demonstrate superior sensitivity to outliers and more effective similarity detection in time series collections compared to Hausdorff and Wasserstein metrics.
• Analysis confirms that MJ distances infrequently and mildly violate the transitivity property, with a computational method developed to assess this.
• Successful application of MJ distances to real-world cryptocurrency and measles time series data.

Conclusions:

• MJ distances offer a powerful and effective new tool for time series analysis, particularly for large datasets with structural breaks.
• The method provides enhanced capabilities for anomaly detection and similarity measurement, outperforming existing approaches in key aspects.
• The study validates the practical utility of MJ distances across diverse data types, paving the way for broader applications.